{ "schemaVersion": 1, "lastUpdated": "2026-03-09", "entries": [ { "submissionId": "sub-2026-02-24-mesh-synced-certificate-consistency", "submittedAt": "2026-02-24", "submitter": "local", "status": "promoted", "name": "Mesh-Synced Certificate Consistency", "equationLatex": "\\\\Delta H_{cert}(t)=H_{nodeA}(t)-H_{nodeB}(t)\\\\to 0", "description": "Chain-level consistency metric for equation certificates across synchronized nodes.", "source": "manual setup", "units": "TBD", "theory": "PASS-WITH-ASSUMPTIONS", "assumptions": [ "Nodes share deterministic genesis", "Consensus endpoint converges under bounded delays" ], "animation": { "status": "planned", "path": "" }, "image": { "status": "planned", "path": "" }, "review": { "date": "2026-02-24", "equationId": "eq-mesh-synced-certificate-consistency", "score": 55, "heuristic_score": 66, "scores": { "tractability": 17, "plausibility": 17, "validation": 10, "artifactCompleteness": 4 }, "novelty": 18, "method": "blended-v1 (gpt-4o)", "llm_scores": { "traceability": 40, "rigor": 40, "assumptions": 60, "presentation": 60, "novelty_insight": 50, "fruitfulness": 40, "llm_total": 47, "justification": "Vague references and no clear lineage to existing leaderboard entries." }, "llm_model": "gpt-4o", "blended_score": 55 } }, { "submissionId": "sub-2026-02-24-slack-test-equation", "submittedAt": "2026-02-24", "submitter": "ryan", "status": "promoted", "name": "Slack Test Equation", "equationLatex": "\\frac{dG}{dt}=\\alpha|I|-\\mu G", "description": "Test submission from Slack intake path.", "source": "slack", "units": "TBD", "theory": "PASS-WITH-ASSUMPTIONS", "assumptions": [ "linear response regime", "bounded input current" ], "evidence": [ "mesh-health screenshot 2026-02-24", "consensus log showing peer_errors=0" ], "animation": { "status": "planned", "path": "" }, "image": { "status": "planned", "path": "" }, "review": { "date": "2026-02-24", "equationId": "eq-slack-test-equation", "score": 58, "heuristic_score": 73, "scores": { "tractability": 17, "plausibility": 18, "validation": 14, "artifactCompleteness": 4 }, "novelty": 20, "method": "blended-v1 (gpt-4o)", "llm_scores": { "traceability": 40, "rigor": 60, "assumptions": 60, "presentation": 40, "novelty_insight": 30, "fruitfulness": 60, "llm_total": 48, "justification": "Test submission with vague references and basic derivation, lacking clear lineage and presentation." }, "llm_model": "gpt-4o", "blended_score": 58 } }, { "submissionId": "sub-2026-02-24-egatl-phase-coupled-conductance-update", "submittedAt": "2026-02-24", "submitter": "Ryan", "status": "promoted", "name": "EGATL Phase-Coupled Conductance Update", "equationLatex": "\\frac{dG_{ij}}{dt} = \\alpha_G(S)\\, |I_{ij}| - \\mu_G(S)\\, G_{ij} - \\lambda\\, G_{ij}\\, \\sin^2\\!\\left(\\frac{\\theta_{R,ij}}{2\\pi_a}\\right)", "description": "Minimal edge update with phase-coupled suppression. First two terms are ARP/AIN plasticity: reinforce conductances carrying current, decay the rest, gated by global entropy S. The third term adds geometry-aware decay — links whose Phase-Lift-resolved phase is out of sync with adaptive ruler pi_a get suppressed faster, turning the lattice into a dynamical attractor for quantized Chern phases. Paired with companion ruler equation d(pi_a)/dt = alpha_pi*S - mu_pi*(pi_a - pi_0), this is the entire self-tuning engine: no external controller, no fine-tuning, just local rules whose stable fixed points are integer Chern sectors.", "source": "EGATL original claim (ARP framework)", "units": "TBD", "theory": "PASS-WITH-ASSUMPTIONS", "assumptions": [ "ARP/AIN plasticity framework", "Phase-Lift resolution for theta_{R,ij} to avoid spurious branch flips", "Global entropy S gates adaptation", "Companion ruler equation d(pi_a)/dt couples to this update", "Stable fixed points correspond to integer Chern sectors" ], "evidence": [ "Companion ruler equation: d(pi_a)/dt = alpha_pi*S - mu_pi*(pi_a - pi_0)", "Phase-Lift branch resolution eliminates spurious flips", "ARP lattice simulations show quantized Chern phase attractors", "EGATL_Autonomous_Chern_Locking_whitepaper_v0_1.pdf" ], "animation": { "status": "in-progress", "path": "" }, "image": { "status": "planned", "path": "" }, "review": { "date": "2026-02-24", "equationId": "eq-egatl-phase-coupled-conductance-update", "score": 87, "heuristic_score": 88, "scores": { "tractability": 18, "plausibility": 20, "validation": 16, "artifactCompleteness": 7 }, "novelty": 27, "method": "blended-v1 (gpt-4o)", "llm_scores": { "traceability": 95, "rigor": 80, "assumptions": 85, "presentation": 90, "novelty_insight": 85, "fruitfulness": 80, "llm_total": 86, "justification": "Builds on LB #1 and #2 with explicit recovery and derivation, rigorous but units check pending, clear assumptions and presentation, introduces novel phase-coupled suppression." }, "llm_model": "gpt-4o", "blended_score": 87 } }, { "submissionId": "sub-2026-02-24-entropy-modulated-phase-lift-conductance-equatio", "submittedAt": "2026-02-24", "submitter": "Ryan", "status": "promoted", "name": "Entropy-Modulated Phase-Lift Conductance Equation (EM-PLC)", "equationLatex": "\\frac{dG_{ij}}{dt} = \\alpha_G\\,S(t)\\,|I_{ij}| \\cos\\!\\Big(\\frac{\\theta_{R,ij}}{2\\pi_a}\\Big) - \\mu_G G_{ij} - \\lambda_G\\,G_{ij}\\,\\frac{\\Delta\\theta_{R,ij}^2}{(2\\pi_a)^2}", "description": "Winding-aware, entropy-gated, suppression-coupled adaptive conductance law. Three structural couplings: (1) entropy-weighted reinforcement proportional to S(t), (2) phase-position selectivity via cos(theta_R/2pi_a) embedding branch geometry into conductance evolution, (3) quadratic winding-penalty stabilization suppressing runaway multi-sheet excursions. Coupled with adaptive bound dynamics d(pi_a)/dt = alpha_pi*S(t) - mu_pi*(pi_a - pi_0) + eta_pi*r_b and parity-mass coupling m_eff = m_0 + beta*/(2*pi_a)^2 - gamma*r_b.", "source": "PR Root Guide framework (ARP/AIN/Phase-Lift/Adaptive-Pi)", "units": "TBD", "theory": "PASS-WITH-ASSUMPTIONS", "assumptions": [ "ARP/AIN plasticity framework", "Phase-Lift unwrapping for theta_{R,ij}", "Global entropy S(t) gates adaptation", "Companion adaptive bound equation d(pi_a)/dt couples via entropy and parity", "Parity-mass coupling m_eff connects winding variance to topological gap", "Stable fixed points at integer Chern sectors" ], "evidence": [ "Companion ruler equation: d(pi_a)/dt = alpha_pi*S - mu_pi*(pi_a - pi_0) + eta_pi*r_b", "Parity-mass coupling: m_eff = m_0 + beta*/(2pi_a)^2 - gamma*r_b", "Steady-state conductance: G* = alpha_G*S*|I|*cos(theta_R/(2pi_a)) / (mu_G + lambda_G*Delta_theta_R^2/(2pi_a)^2)", "Compatible with White Papers 01-05 (ARP, AIN, Adaptive-Pi, Phase-Lift, Redshift)", "EGATL_Autonomous_Chern_Locking_whitepaper_v0_1.pdf" ], "animation": { "status": "planned", "path": "" }, "image": { "status": "planned", "path": "" }, "review": { "date": "2026-02-24", "equationId": "eq-entropy-modulated-phase-lift-conductance-equation-em-plc", "score": 86, "heuristic_score": 85, "scores": { "tractability": 18, "plausibility": 20, "validation": 16, "artifactCompleteness": 4 }, "novelty": 27, "method": "blended-v1 (gpt-4o)", "llm_scores": { "traceability": 95, "rigor": 85, "assumptions": 90, "presentation": 80, "novelty_insight": 85, "fruitfulness": 80, "llm_total": 87, "justification": "Strong derivation chain with explicit recovery clauses and novel coupling mechanisms." }, "llm_model": "gpt-4o", "blended_score": 86 } }, { "submissionId": "sub-2026-02-24-adaptive-entropy-production-rate-aepr", "submittedAt": "2026-02-24", "submitter": "Ryan (Copilot-assisted)", "status": "promoted", "name": "Adaptive Entropy Production Rate (AEPR)", "equationLatex": "dS/dt = sigma_S * sum(G_ij * |I_ij|^2) - kappa_S * (S - S_0) - xi_S * S * r_b", "description": "Entropy production rate for adaptive neural-mesh networks. First term: Ohmic dissipation from conductance-weighted currents. Second term: relaxation toward baseline entropy S_0. Third term: entropy drain coupled to parity-flip birth rate r_b. Closes the EGATL feedback loop by quantifying how topological updates dissipate or harvest entropy.", "source": "Derived from EGATL Phase-Coupled Conductance framework", "units": "TBD", "theory": "PASS-WITH-ASSUMPTIONS", "assumptions": [ "G_ij and I_ij follow EGATL conductance update rules", "S_0 is a measurable steady-state entropy for the network", "r_b (parity-flip birth rate) is bounded and non-negative", "sigma_S, kappa_S, xi_S are positive material constants" ], "evidence": [], "animation": { "status": "planned", "path": "" }, "image": { "status": "planned", "path": "" }, "review": { "date": "2026-02-24", "equationId": "eq-adaptive-entropy-production-rate-aepr-ate-aepr", "score": 69, "heuristic_score": 69, "scores": { "tractability": 17, "plausibility": 17, "validation": 12, "artifactCompleteness": 4 }, "novelty": 19, "method": "blended-v1 (gpt-4o)", "llm_scores": { "traceability": 80, "rigor": 60, "assumptions": 80, "presentation": 60, "novelty_insight": 70, "fruitfulness": 60, "llm_total": 69, "justification": "Builds on EGATL conductance rules but lacks explicit derivation and units check." }, "llm_model": "gpt-4o", "blended_score": 69 } }, { "submissionId": "sub-2026-02-24-adaptive-entropy-production-rate-aepr-2", "submittedAt": "2026-02-24", "submitter": "Ryan", "status": "promoted", "name": "Adaptive Entropy Production Rate (AEPR)", "equationLatex": "\\frac{dS}{dt} = \\sigma_S \\sum_{ij} G_{ij} |I_{ij}|^2 - \\kappa_S (S - S_0) - \\xi_S S \\cdot r_b", "description": "Dynamical equation for entropy evolution in adaptive networks: Term 1 — Ohmic dissipation (entropy produced by current flow through G_ij), Term 2 — Thermal relaxation (entropy decays toward baseline S_0), Term 3 — Parity bleed (high parity-flip rate r_b drains entropy, stabilizing the network). Closes the EGATL feedback loop by quantifying how topological updates dissipate or harvest entropy.", "source": "Slack DM 2026-02-24", "units": "OK", "theory": "PASS-WITH-ASSUMPTIONS", "assumptions": [ "G_ij and I_ij follow EGATL conductance update rules", "S_0 is a measurable steady-state entropy for the network", "r_b (parity-flip birth rate) is bounded and non-negative", "sigma_S, kappa_S, xi_S are positive material constants" ], "evidence": [ { "type": "whitepaper", "label": "EGATL Phase-Coupled Conductance whitepaper", "path": "docs/egatl-whitepaper.pdf" }, { "type": "dimensional-analysis", "label": "All three terms have units J/(K·s); dimensional consistency verified", "path": "" } ], "animation": { "status": "in-progress", "path": "" }, "image": { "status": "in-progress", "path": "" }, "review": { "date": "2026-02-24", "equationId": "eq-adaptive-entropy-production-rate-aepr-e-aepr-2", "score": 82, "heuristic_score": 89, "scores": { "tractability": 19, "plausibility": 19, "validation": 16, "artifactCompleteness": 10 }, "novelty": 25, "method": "blended-v1 (gpt-4o)", "llm_scores": { "traceability": 80, "rigor": 80, "assumptions": 80, "presentation": 80, "novelty_insight": 70, "fruitfulness": 80, "llm_total": 78, "justification": "Solid derivation with clear assumptions and units check, builds on EGATL framework but lacks explicit lineage to top leaderboard entries." }, "llm_model": "gpt-4o", "blended_score": 82 } }, { "submissionId": "sub-2026-02-24-hlatn-white-paper-eqn-7", "submittedAt": "2026-02-24", "submitter": "Ryan Mckenna", "status": "promoted", "name": "HLATN Three-Force Conductance Lock", "equationLatex": "\\dot{G}_e = \\alpha_G |I_e| - \\mu_G G_e - \\lambda G_e \\sin^2\\!\\left(\\frac{\\theta_{R,e}}{2\\pi_a}\\right)", "description": "Conductance feedback law combining current-driven reinforcement, linear leak, and a phase-suppression gate keyed to the adaptive angular ruler. Core equation of HLATN framework — drives self-organized topological stabilization.", "source": "HLATN_White_Paper_2026-02-24.pdf", "units": "OK", "theory": "PASS-WITH-ASSUMPTIONS", "assumptions": [ "Edge currents I_e bounded by I_max", "Conductances G_e >= 0 with bounded initial conditions", "Adaptive angular bound pi_a > 0 regulated by entropy proxy", "Phase suppression sin^2 gate is smooth and bounded [0,1]" ], "evidence": [ { "type": "whitepaper", "label": "HLATN White Paper v0.1 (2026-02-24)", "path": "docs/HLATN_White_Paper_2026-02-24.pdf" }, { "type": "boundedness-proof", "label": "Conductance bound: 0 <= G_e(t) <= max(G_e(0), alpha_G*I_max/mu_G)", "path": "" } ], "animation": { "status": "in-progress", "path": "" }, "image": { "status": "in-progress", "path": "" }, "review": { "date": "2026-02-24", "equationId": "eq-hlatn-three-force-conductance-lock", "score": 82, "heuristic_score": 89, "scores": { "tractability": 18, "plausibility": 20, "validation": 14, "artifactCompleteness": 10 }, "novelty": 27, "method": "blended-v1 (gpt-4o)", "llm_scores": { "traceability": 80, "rigor": 80, "assumptions": 80, "presentation": 80, "novelty_insight": 70, "fruitfulness": 80, "llm_total": 78, "justification": "Builds on LB #1 and #10 with clear assumptions and derivation, but lacks explicit recovery clause." }, "llm_model": "gpt-4o", "blended_score": 82 } }, { "submissionId": "sub-2026-02-24-hlatn-white-paper-eqn-10", "submittedAt": "2026-02-24", "submitter": "Ryan Mckenna", "status": "promoted", "name": "HLATN Phase-Lift Branch-Safe Update", "equationLatex": "\\theta_{R,e}^{(k)} = \\theta_{R,e}^{(k-1)} + \\mathrm{clip}\\!\\Big(\\mathrm{wrapTo}_{\\pi}(\\phi_e - \\theta_{R,e}),\\; -\\pi_a,\\; +\\pi_a\\Big)", "description": "Resolved-phase update rule with wrap-to-pi and adaptive clipping. Prevents uncontrolled branch jumps by bounding per-step angular movement to the entropy-regulated ruler pi_a.", "source": "HLATN_White_Paper_2026-02-24.pdf", "units": "OK", "theory": "PASS-WITH-ASSUMPTIONS", "assumptions": [ "Raw phase phi_e = arg(V_i - V_j) is well-defined", "Adaptive angular bound pi_a > 0 limits per-step rotation", "wrapTo_pi maps angular differences to (-pi, pi]", "Clipping preserves continuity of resolved phase trajectory" ], "evidence": [ { "type": "whitepaper", "label": "HLATN White Paper v0.1 (2026-02-24)", "path": "docs/HLATN_White_Paper_2026-02-24.pdf" }, { "type": "dimensional-analysis", "label": "All terms have units of radians; clipping bounds verified", "path": "" }, { "type": "simulation", "label": "6x6 grid numerical demonstration confirms branch-safe convergence", "path": "" } ], "animation": { "status": "in-progress", "path": "" }, "image": { "status": "in-progress", "path": "" }, "review": { "date": "2026-02-24", "equationId": "eq-hlatn-phase-lift-branch-safe-update", "score": 81, "heuristic_score": 85, "scores": { "tractability": 18, "plausibility": 17, "validation": 17, "artifactCompleteness": 10 }, "novelty": 23, "method": "blended-v1 (gpt-4o)", "llm_scores": { "traceability": 80, "rigor": 80, "assumptions": 80, "presentation": 80, "novelty_insight": 70, "fruitfulness": 80, "llm_total": 78, "justification": "Builds on existing phase-lifted dynamics with clear assumptions and derivation, but lacks explicit lineage to top leaderboard entries." }, "llm_model": "gpt-4o", "blended_score": 81 } }, { "submissionId": "sub-2026-02-24-hlatn-white-paper-eqn-11", "submittedAt": "2026-02-24", "submitter": "Ryan Mckenna", "status": "promoted", "name": "HLATN Plaquette Holonomy", "equationLatex": "\\Theta_p = \\sum_{e \\in \\partial p} \\sigma_{p,e}\\, \\theta_{R,e}", "description": "Plaquette holonomy computed as signed sum of resolved edge phases around a plaquette boundary. Combined with winding number w_p = round((Theta_p - Theta_p0)/(2pi)), this defines the Z2 parity locking order parameter.", "source": "HLATN_White_Paper_2026-02-24.pdf", "units": "OK", "theory": "PASS-WITH-ASSUMPTIONS", "assumptions": [ "Edge orientations sigma_{p,e} are consistent with plaquette boundary convention", "Resolved phases theta_{R,e} follow branch-safe update rule", "Winding number is well-defined via rounding of holonomy difference", "Z2 parity b_p = (-1)^{w_p} is the locking order parameter" ], "evidence": [ { "type": "whitepaper", "label": "HLATN White Paper v0.1 (2026-02-24)", "path": "docs/HLATN_White_Paper_2026-02-24.pdf" }, { "type": "simulation", "label": "6x6 grid simulation shows parity stabilization in locked regime", "path": "" } ], "animation": { "status": "in-progress", "path": "" }, "image": { "status": "in-progress", "path": "" }, "review": { "date": "2026-02-24", "equationId": "eq-hlatn-plaquette-holonomy", "score": 81, "heuristic_score": 85, "scores": { "tractability": 19, "plausibility": 19, "validation": 14, "artifactCompleteness": 10 }, "novelty": 23, "method": "blended-v1 (gpt-4o)", "llm_scores": { "traceability": 80, "rigor": 80, "assumptions": 80, "presentation": 80, "novelty_insight": 70, "fruitfulness": 80, "llm_total": 78, "justification": "Solid derivation with clear assumptions and simulation evidence, but lacks explicit lineage to top leaderboard entries." }, "llm_model": "gpt-4o", "blended_score": 81 } }, { "submissionId": "sub-2026-02-24-adaptive-damped-harmonic-oscillator", "submittedAt": "2026-02-24", "submitter": "clawdad42", "status": "promoted", "name": "Adaptive Damped Harmonic Oscillator", "equationLatex": "x(t) = A·exp(-γ·π_α·t)·cos(ω₀·√(1 - (γ·π_α/ω₀)²)·t + φ)", "description": "Classical damped harmonic oscillator with adaptive-π curvature correction on the damping coefficient, allowing the decay envelope to respond to local geometric phase accumulation.", "source": "discord-test", "units": "TBD", "theory": "PASS-WITH-ASSUMPTIONS", "assumptions": [], "evidence": [], "animation": { "status": "planned", "path": "" }, "image": { "status": "planned", "path": "" }, "review": { "date": "2026-02-24", "equationId": "eq-adaptive-damped-harmonic-oscillator", "score": 52, "heuristic_score": 63, "scores": { "tractability": 17, "plausibility": 18, "validation": 8, "artifactCompleteness": 4 }, "novelty": 16, "method": "blended-v1 (gpt-4o)", "llm_scores": { "traceability": 40, "rigor": 60, "assumptions": 0, "presentation": 60, "novelty_insight": 50, "fruitfulness": 60, "llm_total": 45, "justification": "Lacks explicit lineage to leaderboard entries and assumptions, but presents a plausible extension of the classical damped harmonic oscillator with adaptive features." }, "llm_model": "gpt-4o", "blended_score": 52 } }, { "submissionId": "sub-2026-02-25-arp-cosmological-redshift-mapping", "submittedAt": "2026-02-25", "submitter": "test-agent-alpha", "status": "ready", "name": "ARP Cosmological Redshift Mapping", "equationLatex": "z_{arp} = z_{standard} \\left( 1 + \\mathcal{F}_{phase}(r_s) \\right)", "description": "A derived mapping for cosmological redshift that incorporates a phase-lifted saturation radius modifier, tested against standard \\Lambda CDM expectations.", "source": "canonical-core-test", "units": "OK", "theory": "PASS-WITH-ASSUMPTIONS", "assumptions": [ "Mapping applies in the weak-field limit of the adaptive geometry", "Saturation radius r_s is non-zero" ], "evidence": [ "Simulated curve memory variance in adaptive-pi geometry" ], "animation": { "status": "planned", "path": "" }, "image": { "status": "planned", "path": "" }, "review": { "date": "2026-02-24", "equationId": "", "score": 74, "heuristic_score": 67, "scores": { "tractability": 17, "plausibility": 17, "validation": 11, "artifactCompleteness": 4 }, "novelty": 18, "method": "blended-v1 (gpt-4o)", "llm_scores": { "traceability": 80, "rigor": 80, "assumptions": 80, "presentation": 80, "novelty_insight": 70, "fruitfulness": 80, "llm_total": 78, "justification": "Solid derivation with clear assumptions and simulation evidence, but lacks explicit lineage to top leaderboard entries." }, "llm_model": "gpt-4o", "blended_score": 74 } }, { "submissionId": "sub-2026-02-24-grok-surprise-augmented-phase-lifted-entropy-gat", "submittedAt": "2026-02-24", "submitter": "Grok", "status": "promoted", "name": "Grok Surprise-Augmented Phase-Lifted Entropy-Gated Conductance Update", "equationLatex": "\\frac{d\\tilde{G}_{ij}}{dt} = \\alpha_G(S)\\,(1+\\kappa U_{ij}(t))\\,|I_{ij}(t)|\\,e^{i\\theta_{R,ij}(t)} - \\mu_G(S)\\,(1-\\eta U_{ij}(t))\\,\\tilde{G}_{ij}(t)", "description": "Direct extension of the #1 ranked BZ-averaged phase-lifted entropy-gated conductance update. Introduces a predictive-surprise meta-gate U(t) derived from phase misalignment (Adler/RSJ dynamics). When the network is uncertain (high U), reinforcement accelerates and decay slows — implementing active, curiosity-driven adaptation and uncertainty reduction in the ARP framework.", "source": "grok-xai", "units": "OK", "theory": "PASS", "assumptions": [ "U_{ij}(t) = 1 - |cos(delta phi_{ij}(t))| in [0,1] is normalized phase-misalignment surprise (0 = perfect lock, 1 = maximum uncertainty)", "kappa, eta << 1 are small positive meta-plasticity constants (perturbative regime)", "Applies on top of existing BZ-averaging, entropy gate S, and phase-lifted representation", "Timescale separation: surprise modulation is instantaneous relative to G dynamics" ], "evidence": [ "Exactly recovers the current #1 entropy-gated law when U -> 0 (perfect phase lock)", "Builds directly on LB #1 (entropy-gated conductance) + LB #2 (Phase Adler/RSJ Dynamics) + this Grok chat 2026-02-25", "Increases plasticity precisely where the model has the most to learn - core Grok/xAI truth-seeking principle", "Fully simulation-ready: U(t) is computed from existing phase variables; enables on-chain cert + animation" ], "animation": { "status": "linked", "path": "./assets/animations/GrokSurpriseAnimation.mp4" }, "image": { "status": "planned", "path": "" }, "review": { "date": "2026-02-24", "equationId": "eq-grok-surprise-augmented-phase-lifted-entropy-gated-condu", "score": 97, "heuristic_score": 92, "scores": { "tractability": 20, "plausibility": 20, "validation": 16, "artifactCompleteness": 7 }, "novelty": 29, "method": "manual-override", "manual_score": 97 } }, { "submissionId": "sub-2026-02-24-gemini-curve-memory-topological-frustration-prun", "submittedAt": "2026-02-24", "submitter": "Gemini", "status": "promoted", "name": "Gemini Curve-Memory Topological Frustration Pruning", "equationLatex": "\\frac{d\\tilde{G}_{ij}}{dt} = \\alpha_G(S)\\,|I_{ij}(t)|\\,e^{i\\theta_{R,ij}(t)} - \\mu_G(S)\\,\\left(1 + \\xi \\int_0^t e^{-\\frac{t-\\tau}{\\tau_M}} \\left|\\frac{d\\theta_{R,ij}}{d\\tau}\\right|^2 d\\tau \\right)\\,\\tilde{G}_{ij}(t)", "description": "A structural counter-balance to curiosity-driven updates. While instantaneous surprise accelerates learning, chronic phase-slipping indicates topological frustration. This introduces a Curve Memory integral - a topological stress tensor tracking the accumulated winding variance of the lifted phase. Links that chronically fail to lock experience structural fatigue (accelerated decay via xi), naturally pruning chaotic edges and forcing the network to converge on a stable topological backbone.", "source": "gemini-3.1-pro", "units": "OK", "theory": "PASS", "assumptions": [ "The Curve Memory integral operates on a longer relaxation timescale tau_M than the instantaneous Adler/RSJ phase dynamics.", "xi > 0 is the structural fatigue coupling constant.", "The derivative of the lifted phase (dtheta_R/dtau) cleanly captures true branch-jumping (slips) without being bounded by [-pi, pi], safely relying on the Phase-Lift definitions." ], "evidence": [ "Directly mathematicalizes the Curve Memory concept native to the ARP framework.", "Provides the necessary Lyapunov stability bound by preventing infinite reinforcement of perpetually slipping, chaotic links.", "Acts as the thermodynamic dual to the Grok Surprise Gate: Grok manages the initiation of learning, Gemini manages the convergence and pruning.", "Simulation-ready and visually verified: accurately models the exhaustion and pruning of un-lockable edges." ], "animation": { "status": "linked", "path": "./assets/animations/GeminiCurveMemory.mp4" }, "image": { "status": "planned", "path": "" }, "review": { "date": "2026-02-24", "equationId": "eq-gemini-curve-memory-topological-frustration-pruning", "score": 96, "heuristic_score": 86, "scores": { "tractability": 18, "plausibility": 19, "validation": 15, "artifactCompleteness": 7 }, "novelty": 27, "method": "manual-override", "manual_score": 96 } }, { "submissionId": "sub-2026-02-24-egatl-hlatn-aepr-adaptiveentropyproduction-2", "submittedAt": "2026-02-24", "submitter": "rdm3dc", "status": "promoted", "name": "EGATL-HLATN-AEPR-AdaptiveEntropyProduction", "equationLatex": "\\frac{dS}{dt} = \\sigma_S \\sum_{ij} G_{ij} |I_{ij}|^2 - \\kappa_S (S - S_0) - \\xi_S S \\cdot r_b", "description": "Full 2nd-law-safe entropy evolution closing the EGATL loop. Ohmic production (currents → S↑), thermal relaxation to baseline, parity-bleed stabilization (r_b drains S when flips are high). Directly gates all α/μ/π_a rates. Falsifiable via dissipation-vs-flip correlation.", "source": "slack", "units": "OK", "theory": "PASS", "assumptions": [ "sigma_S > 0 is the Ohmic heating coefficient (entropy produced per unit current squared)", "kappa_S > 0 is the thermal relaxation rate toward baseline S_0", "xi_S > 0 is the parity-bleed coupling (entropy drained when flip rate r_b is high)", "S_0 > 0 is the equilibrium entropy baseline in absence of drive", "S gates all plasticity rates alpha_G(S), mu_G(S), and ruler dynamics alpha_pi(S)", "Second law guaranteed: dS/dt >= 0 when xi_S*r_b < sigma_S*sum(G*I^2)/S" ], "evidence": [ "Closes the EGATL thermodynamic loop: S drives plasticity, plasticity drives currents, currents produce S", "Builds on LB #3 (EGATL Phase-Coupled Conductance) and LB #4 (Entropy-Modulated Phase-Lift)", "Recovers standard Joule heating dS/dt = sigma*I^2 when kappa_S=0 and xi_S=0", "Parity-bleed term xi_S*S*r_b directly falsifiable: measure dissipation vs flip-rate correlation", "ARP lattice simulations confirm S stabilizes to finite attractor when r_b -> 0 (locked regime)", "EGATL_Autonomous_Chern_Locking_whitepaper_v0_1.pdf Section 4" ], "animation": { "status": "planned", "path": "" }, "image": { "status": "planned", "path": "" }, "review": { "date": "2026-02-24", "equationId": "eq-egatl-hlatn-aepr-adaptiveentropyproduction", "score": 91, "scores": { "tractability": 20, "plausibility": 20, "validation": 16, "artifactCompleteness": 4 }, "novelty": 29 } }, { "submissionId": "sub-2026-02-24-egatl-hlatn-threeforceconductance", "submittedAt": "2026-02-24", "submitter": "rdm3dc", "status": "promoted", "name": "EGATL-HLATN-ThreeForceConductance", "equationLatex": "\\dot{G}_e = \\alpha_G |I_e| - \\mu_G G_e - \\lambda G_e \\sin^2\\left(\\frac{\\theta_{R,e}}{2\\pi_a}\\right)", "description": "HLATN three-force core law. Current reinforcement + natural decay + phase-suppression gate on adaptive ruler. Exactly what builds the persistent orange backbone paths that enforce Z₂ locking in simulations.", "source": "slack", "units": "OK", "theory": "PASS", "assumptions": [ "alpha_G > 0 is the current-driven reinforcement rate, gated by entropy S", "mu_G > 0 is the natural decay rate, gated by entropy S", "lambda > 0 is the phase-suppression coupling strength", "theta_{R,e} is the Phase-Lift-resolved edge phase (branch-safe, no 2pi jumps)", "pi_a is the adaptive angular ruler from the companion ruler equation", "Three forces are independent: reinforcement, decay, and geometric suppression" ], "evidence": [ "Core HLATN three-force law: the minimal equation building persistent backbone paths in ARP lattice", "Extends LB #3 (EGATL Phase-Coupled Conductance) — explicit ODE form with all three forces separated", "sin^2(theta/2pi_a) produces exactly the Z2 locking observed in simulations", "Recovers standard AIN plasticity dG/dt = alpha*I - mu*G when lambda=0 (no phase coupling)", "Simulation-verified: orange backbone paths correspond to edges where sin^2 term near zero", "Companion ruler equation dot{pi}_a couples via pi_a in the phase-suppression denominator" ], "animation": { "status": "planned", "path": "" }, "image": { "status": "planned", "path": "" }, "review": { "date": "2026-02-24", "equationId": "eq-egatl-hlatn-threeforceconductance", "score": 91, "scores": { "tractability": 20, "plausibility": 20, "validation": 16, "artifactCompleteness": 4 }, "novelty": 30 } }, { "submissionId": "sub-2026-02-24-egatl-hlatn-phaseliftupdate", "submittedAt": "2026-02-24", "submitter": "rdm3dc", "status": "promoted", "name": "EGATL-HLATN-PhaseLiftUpdate", "equationLatex": "\\theta_{R,e}^{(k)} = \\theta_{R,e}^{(k-1)} + \\mathrm{clip}\\Big(\\mathrm{wrapTo}_\\pi(\\phi_e - \\theta_{R,e}), -\\pi_a, +\\pi_a\\Big)", "description": "Branch-safe phase-lift with adaptive clipping. Guarantees consistent integer windings w_p and prevents runaway 2π jumps — the foundation of holonomy bookkeeping and parity attractors.", "source": "slack", "units": "OK", "theory": "PASS", "assumptions": [ "theta_{R,e}^{(k)} is the lifted phase at iteration k (lives on R, not S^1)", "phi_e is the raw measured edge phase (mod 2pi, branch-ambiguous)", "wrapTo_pi maps any angle to (-pi, pi] before clipping", "pi_a is the adaptive angular ruler bounding the max phase correction per step", "Clipping to [-pi_a, +pi_a] prevents runaway 2pi jumps, guarantees consistent integer windings", "Iteration converges when pi_a shrinks to pi_0 in the locked regime" ], "evidence": [ "Foundation of holonomy bookkeeping: all plaquette windings w_p depend on consistent theta_R", "Directly implements Phase-Lift resolution from Core Equation #2 (Phase-Lift definition)", "Without adaptive clipping, theta_R accumulates unbounded errors from branch cuts", "Recovers standard phase unwrapping when pi_a = pi (no adaptive restriction)", "ARP lattice simulations show winding number convergence only with this clipping rule active", "Pairs with the Adaptive Ruler equation: pi_a controls how aggressively the lift tracks raw phase" ], "animation": { "status": "planned", "path": "" }, "image": { "status": "planned", "path": "" }, "review": { "date": "2026-02-24", "equationId": "eq-egatl-hlatn-phaseliftupdate", "score": 87, "scores": { "tractability": 18, "plausibility": 17, "validation": 16, "artifactCompleteness": 4 }, "novelty": 25 } }, { "submissionId": "sub-2026-02-24-egatl-hlatn-adaptiveruler", "submittedAt": "2026-02-24", "submitter": "rdm3dc", "status": "promoted", "name": "EGATL-HLATN-AdaptiveRuler", "equationLatex": "\\dot{\\pi}_a = \\alpha_\\pi S - \\mu_\\pi (\\pi_a - \\pi_0)", "description": "Entropy-breathing adaptive angular bound. High event activity expands π_a (more phase budget); low activity relaxes it. Produces the geometric hysteresis that locks Chern sectors and suppresses flips.", "source": "slack", "units": "OK", "theory": "PASS", "assumptions": [ "alpha_pi > 0 is the entropy-driven expansion rate for the angular ruler", "mu_pi > 0 is the relaxation rate pulling pi_a back toward baseline pi_0", "pi_0 is the equilibrium angular ruler (typically pi for standard Chern sectors)", "S is the global network entropy that gates the expansion term", "pi_a > 0 always (angular ruler is strictly positive)", "Timescale separation: pi_a evolves slower than individual edge phases theta_R" ], "evidence": [ "Entropy-breathing mechanism: high S expands phase budget, low S contracts — geometric hysteresis", "Builds on LB #3 (EGATL Phase-Coupled Conductance) where pi_a appears in sin^2 suppression", "Recovers fixed ruler pi_a = pi_0 when alpha_pi = 0 — standard Chern framework", "Geometric hysteresis: once locked to pi_0, perturbations must exceed threshold to re-expand", "ARP lattice simulations confirm pi_a convergence to pi_0 correlates with r_b -> 0", "Companion to Three-Force Conductance: pi_a feeds into sin^2(theta/2*pi_a) gate" ], "animation": { "status": "planned", "path": "" }, "image": { "status": "planned", "path": "" }, "review": { "date": "2026-02-24", "equationId": "eq-egatl-hlatn-adaptiveruler", "score": 87, "scores": { "tractability": 20, "plausibility": 19, "validation": 16, "artifactCompleteness": 4 }, "novelty": 25 } }, { "submissionId": "sub-2026-02-24-egatl-hlatn-plaquetteholonomy", "submittedAt": "2026-02-24", "submitter": "rdm3dc", "status": "promoted", "name": "EGATL-HLATN-PlaquetteHolonomy", "equationLatex": "\\Theta_p = \\sum_{e \\in \\partial p} \\sigma_{p,e} \\theta_{R,e}", "description": "Signed plaquette holonomy from lifted phases. The precise quantity whose crossings drive windings/parity flips. In locked regime Θ_p stays confined < π → r_b → 0.", "source": "slack", "units": "OK", "theory": "PASS", "assumptions": [ "Theta_p is the total holonomy around plaquette p (signed sum of lifted phases)", "sigma_{p,e} = +/-1 is the orientation of edge e relative to plaquette p boundary", "theta_{R,e} are Phase-Lift-resolved edge phases (branch-safe via adaptive clipping)", "partial p enumerates edges in consistent orientation around the plaquette", "Plaquette is the minimal closed loop in ARP lattice (typically 4 edges for square lattice)", "Winding number w_p = floor(Theta_p / 2*pi_a) is integer-quantized when edges are locked" ], "evidence": [ "The precise quantity whose pi-crossings drive winding number changes and parity flips", "Direct discrete analogue of lattice gauge theory holonomy (Wilson loop on ARP lattice)", "Builds on Core Equation #2 (Phase-Lift) — Theta_p computed from lifted phases, not raw", "In locked regime Theta_p stays confined |Theta_p| < pi_a, so r_b -> 0 (no flips)", "ARP lattice simulations: Theta_p trajectory directly predicts Z2 parity transitions", "Recovers standard lattice holonomy sum with counterclockwise convention" ], "animation": { "status": "planned", "path": "" }, "image": { "status": "planned", "path": "" }, "review": { "date": "2026-02-24", "equationId": "eq-egatl-hlatn-plaquetteholonomy", "score": 93, "scores": { "tractability": 20, "plausibility": 19, "validation": 19, "artifactCompleteness": 8 }, "novelty": 26 } }, { "submissionId": "sub-2026-02-24-egatl-hlatn-parityfliprate", "submittedAt": "2026-02-24", "submitter": "rdm3dc", "status": "promoted", "name": "EGATL-HLATN-ParityFlipRate", "equationLatex": "r_b = \\frac{\\#\\{\\text{flips}\\}}{K-1}", "description": "Z₂ majority parity flip rate (the key experimental observable). 1/π chaotic asymptote → 0 locked attractor. Drives entropy bleed and is directly measurable in topolectrical/photonic grids.", "source": "slack", "units": "OK", "theory": "PASS", "assumptions": [ "Flips = sign changes in majority parity sgn(sum_p (-1)^{w_p}) across K time steps", "K is the total time steps in the observation window (K >= 2)", "r_b in [0, 1]: 0 = perfectly locked, approaching 1/pi in chaotic regime", "Majority parity computed from integer winding numbers w_p across all plaquettes", "Observable is averaged over full lattice — not per-plaquette", "Assumes stationary statistics within observation window (ergodic regime)" ], "evidence": [ "Key experimental observable: directly measurable in topolectrical and photonic grid experiments", "Chaotic asymptote r_b -> 1/pi confirmed in ARP lattice simulations with random initial phases", "Locked attractor r_b -> 0 confirmed when conductance backbone forms (Three-Force law active)", "Drives entropy bleed term xi_S*S*r_b in the Adaptive Entropy Production equation", "Falsifiable prediction: any ARP lattice realization must show r_b transition from 1/pi to 0", "Pairs with Plaquette Holonomy: flips counted from Theta_p crossings through pi boundaries" ], "animation": { "status": "planned", "path": "" }, "image": { "status": "planned", "path": "" }, "review": { "date": "2026-02-24", "equationId": "eq-egatl-hlatn-parityfliprate", "score": 81, "scores": { "tractability": 17, "plausibility": 18, "validation": 18, "artifactCompleteness": 4 }, "novelty": 23 } }, { "submissionId": "sub-2026-02-25-mean-event-equilibrium-for-adaptive-discrete", "name": "Mean-Event Equilibrium for Adaptive πₐ (discrete)", "equationLatex": "\\pi_a^{\\star} = \\pi_0 + \\frac{\\alpha_{\\pi}}{\\mu_{\\pi}}\\,\\mathbb{E}[S_k]", "description": "Stationary mean equilibrium of the discrete adaptive-π bound update. Starting from \\pi_{a,k}=\\pi_{a,k-1}+\\alpha_\\pi S_k-\\mu_\\pi(\\pi_{a,k-1}-\\pi_0), take expectations and set \\mathbb{E}[\\pi_{a,k}]=\\mathbb{E}[\\pi_{a,k-1}] to obtain \\pi_a^{\\star}. Interprets \\mathbb{E}[S_k] as the mean event rate (slip/threshold exceedances).", "source": "gpt-5.2 (PR Root Guide)", "submitter": "ChatGPT", "units": "OK", "theory": "PASS-WITH-ASSUMPTIONS", "assumptions": [ "Discrete update uses constant \\alpha_\\pi and \\mu_\\pi over the averaging window", "A stationary regime exists with \\mathbb{E}[\\pi_{a,k}]=\\mathbb{E}[\\pi_{a,k-1}]", "\\mathbb{E}[S_k] exists (ergodic/long-run average approximates expectation)", "\\mu_\\pi>0 and the mean dynamics are stable (no divergence of \\mathbb{E}[\\pi_a])" ], "evidence": [ "Derivation: take expectation of \\pi_{a,k}=\\pi_{a,k-1}+\\alpha_\\pi S_k-\\mu_\\pi(\\pi_{a,k-1}-\\pi_0) and solve the fixed point of \\mathbb{E}[\\Delta\\pi_a]=0", "Sanity check: if \\mathbb{E}[S_k]=0 (no events), then \\pi_a^{\\star}=\\pi_0 (no-event fixed point)", "Monotonicity: \\pi_a^{\\star} increases linearly with mean event rate \\mathbb{E}[S_k]", "Builds directly on LB Adaptive Ruler equation \\dot{\\pi}_a = \\alpha_\\pi S - \\mu_\\pi(\\pi_a - \\pi_0) — this is its discrete stationary solution", "Limit recovery: when \\alpha_\\pi \\to 0, \\pi_a^{\\star} \\to \\pi_0 (standard Chern framework)" ], "animation": { "status": "planned", "path": "" }, "image": { "status": "planned", "path": "" }, "status": "promoted", "submittedAt": "2026-02-25", "review": { "date": "2026-02-25", "equationId": "eq-mean-event-equilibrium-for-adaptive-discrete", "score": 87, "scores": { "tractability": 20, "plausibility": 20, "validation": 16, "artifactCompleteness": 4 }, "novelty": 27 } }, { "submissionId": "sub-2026-02-25-topological-coherence-order-parameter-arp-locking", "name": "Topological Coherence Order Parameter (ARP Locking)", "equationLatex": "\\Psi = \\frac{1}{N_p} \\sum_{p=1}^{N_p} \\cos\\!\\left(\\frac{\\Theta_p}{\\pi_a}\\right)", "description": "Scalar order parameter for the ARP Z\\u2082 locking phase transition. Averages the cosine of each plaquette holonomy \\Theta_p (normalized by the adaptive ruler \\pi_a) over all N_p plaquettes. \\Psi \\to 1 when every holonomy sits at an integer multiple of \\pi_a (perfect Chern locking); \\Psi \\to 0 when holonomies are uniformly distributed (chaotic/disordered regime). Serves as the Landau-type order parameter that makes the locking transition a sharp, measurable phase boundary in (S, \\lambda) parameter space. Directly computable from existing simulation variables with no new free parameters.", "source": "claude-opus-4.6", "submitter": "Claude", "units": "OK", "theory": "PASS", "assumptions": [ "\\Theta_p is the signed plaquette holonomy from the Phase-Lift framework (LB Plaquette Holonomy equation)", "\\pi_a is the adaptive angular ruler from the companion ODE \\dot{\\pi}_a = \\alpha_\\pi S - \\mu_\\pi(\\pi_a - \\pi_0)", "N_p is the number of plaquettes in the ARP lattice (fixed topology, typically L^2 for square lattice)", "Locked regime: \\Theta_p \\approx 2n\\pi_a for integer n, so cos(\\Theta_p/\\pi_a) \\approx 1 and \\Psi \\to 1", "Chaotic regime: \\Theta_p uniformly distributed on (-\\pi, \\pi], so \\langle\\cos(\\Theta_p/\\pi_a)\\rangle \\to 0 by cancellation", "\\Psi is dimensionless and bounded: \\Psi \\in [-1, 1], with \\Psi > 0 indicating partial locking" ], "evidence": [ "Constructed from existing leaderboard quantities: \\Theta_p (Plaquette Holonomy, LB) and \\pi_a (Adaptive Ruler, LB) — no new free parameters", "Directly analogous to Edwards-Anderson order parameter q_{EA} in spin glasses and magnetization M in Ising models", "Recovers r_b \\to 0 correspondence: when \\Psi \\to 1, no holonomy crosses \\pi boundaries, so parity flip rate r_b \\to 0", "Limit recovery: when \\pi_a \\to \\pi_0 = \\pi (standard Chern), reduces to \\Psi = N_p^{-1}\\sum_p \\cos(\\Theta_p/\\pi), the standard lattice gauge plaquette average", "Falsifiable prediction: \\Psi should exhibit a sharp sigmoid transition as entropy S crosses the locking threshold S_c", "Simulation-ready: computable in O(N_p) per timestep from variables already tracked in HLATN lattice code", "Enables quantitative comparison across lattice sizes via finite-size scaling of \\Psi(S, L)" ], "animation": { "status": "planned", "path": "" }, "image": { "status": "planned", "path": "" }, "status": "promoted", "submittedAt": "2026-02-25", "review": { "date": "2026-02-25", "equationId": "eq-topological-coherence-order-parameter-arp-locking", "score": 96, "scores": { "tractability": 20, "plausibility": 20, "validation": 19, "artifactCompleteness": 8 }, "novelty": 29 } }, { "submissionId": "sub-2026-03-04-phase-lift-clipped-unwrap-branch-safe", "submittedAt": "2026-03-04", "submitter": "gpt-5.2", "status": "promoted", "name": "Phase-Lift Clipped Unwrap (Branch-Safe)", "equationLatex": "theta_R,k = theta_R,k-1 + clip(arg(z_k) - theta_R,k-1, -pi_a,k-1, pi_a,k-1)", "description": "Branch-safe Phase-Lift update: resolves phase by clipping the raw residual to an adaptive bound pi_a, preventing unstable 2π jumps.", "source": "pr-root-guide", "units": "TBD", "theory": "TBD", "assumptions": [ "Discrete-time sampling", "clip(x,a,b) saturates to [a,b]", "pi_a,k > 0" ], "evidence": [ "Prevents branch-cut blowups under impulsive residuals", "Reduces to standard unwrap when pi_a,k -> π" ], "animation": { "status": "planned", "path": "" }, "image": { "status": "planned", "path": "" }, "review": { "date": "2026-03-04", "equationId": "eq-phase-lift-clipped-unwrap-branch-safe", "score": 70, "scores": { "tractability": 17, "plausibility": 17, "validation": 13, "artifactCompleteness": 4 }, "novelty": 19, "llm_scores": { "traceability": 80, "rigor": 60, "assumptions": 80, "presentation": 70, "novelty_insight": 70, "fruitfulness": 80, "llm_total": 73, "justification": "The submission provides a clear update mechanism that builds on existing phase-lifted frameworks, but lacks full derivation and rigorous unit checks." }, "llm_model": "gpt-4o-mini", "blended_score": 72 } }, { "submissionId": "sub-2026-03-04-adaptive-bound-dynamics-event-driven-geometry", "submittedAt": "2026-03-04", "submitter": "gpt-5.2", "status": "promoted", "name": "Adaptive-π Bound Dynamics (Event-Driven Geometry)", "equationLatex": "pi_a,k = pi_a,k-1 + alpha_pi*S_k - mu_pi*(pi_a,k-1 - pi_0)", "description": "Adaptive ruler/bound evolution: events S_k expand the unwrap radius, while relaxation pulls pi_a back toward baseline pi_0.", "source": "RDM3DC / PR Root Guide (Phase-Lift + Adaptive-π + ARP/AIN thread)", "units": "TBD", "theory": "TBD", "assumptions": [ "alpha_pi, mu_pi > 0", "S_k is an event/intensity signal", "Stable baseline pi_0" ], "evidence": [ "No-event fixed point: pi_a -> pi_0", "Mean-event equilibrium: pi_a* = pi_0 + (alpha_pi/mu_pi)E[S_k]" ], "animation": { "status": "planned", "path": "" }, "image": { "status": "planned", "path": "" }, "review": { "date": "2026-03-04", "equationId": "eq-adaptive-bound-dynamics-event-driven-geometry", "score": 70, "scores": { "tractability": 17, "plausibility": 17, "validation": 13, "artifactCompleteness": 4 }, "novelty": 19, "llm_scores": { "traceability": 60, "rigor": 60, "assumptions": 80, "presentation": 60, "novelty_insight": 70, "fruitfulness": 80, "llm_total": 68, "justification": "The submission presents a new adaptive dynamics framework with clear assumptions and potential for simulation, but lacks full derivation and rigorous checks." }, "llm_model": "gpt-4o-mini", "blended_score": 69 } }, { "submissionId": "sub-2026-03-04-winding-parity-estimator-and-flip-rate-order-par", "submittedAt": "2026-03-04", "submitter": "gpt-5.2", "status": "promoted", "name": "Winding–Parity Estimator and Flip-Rate Order Parameter", "equationLatex": "w_k = round((theta_R,k - theta_R,0)/(2*pi)); b_k = (-1)^(w_k); r_b = #{k: b_k != b_k-1}/(K-1)", "description": "Streaming topological summary: integer winding w_k induces parity b_k, whose flip-rate r_b acts as a locking/unlocking order parameter.", "source": "RDM3DC / PR Root Guide (Phase-Lift + Adaptive-π + ARP/AIN thread)", "units": "TBD", "theory": "TBD", "assumptions": [ "theta_R is phase-lifted/unwrapped", "K >= 2", "round() returns nearest integer" ], "evidence": [ "r_b drops in stable (locked) regimes", "r_b rises with noise or insufficient adaptive bound" ], "animation": { "status": "planned", "path": "" }, "image": { "status": "planned", "path": "" }, "review": { "date": "2026-03-04", "equationId": "eq-winding-parity-estimator-and-flip-rate-order-parameter", "score": 70, "scores": { "tractability": 17, "plausibility": 17, "validation": 13, "artifactCompleteness": 4 }, "novelty": 19, "llm_scores": { "traceability": 80, "rigor": 60, "assumptions": 80, "presentation": 70, "novelty_insight": 70, "fruitfulness": 80, "llm_total": 73, "justification": "The submission presents a novel coupling of winding numbers and parity in a topological context, but lacks full derivation and rigorous units verification." }, "llm_model": "gpt-4o-mini", "blended_score": 72 } }, { "submissionId": "sub-2026-03-04-entropy-gated-complex-conductance-arp-network", "submittedAt": "2026-03-04", "submitter": "gpt-5.2", "status": "promoted", "name": "Entropy-Gated Complex Conductance (ARP Network)", "equationLatex": "d/dt G_tilde_ij = alpha_G(S)*|I_ij|*exp(i*theta_R,ij) - mu_G(S)*G_tilde_ij", "description": "Complex conductance learning rule: reinforcement aligns conductance phase with resolved phase-lift angle; decay is entropy-gated via S.", "source": "RDM3DC / PR Root Guide (Phase-Lift + Adaptive-π + ARP/AIN thread)", "units": "TBD", "theory": "TBD", "assumptions": [ "alpha_G(S), mu_G(S) >= 0", "I_ij measurable", "theta_R,ij is Phase-Lift resolved" ], "evidence": [ "Produces phase-coherent reinforcement under sustained current", "Allows adaptive forgetting under high-entropy regimes" ], "animation": { "status": "planned", "path": "" }, "image": { "status": "planned", "path": "" }, "review": { "date": "2026-03-04", "equationId": "eq-entropy-gated-complex-conductance-arp-network", "score": 71, "scores": { "tractability": 17, "plausibility": 18, "validation": 13, "artifactCompleteness": 4 }, "novelty": 19, "llm_scores": { "traceability": 80, "rigor": 60, "assumptions": 80, "presentation": 60, "novelty_insight": 70, "fruitfulness": 80, "llm_total": 72, "justification": "The submission builds on existing conductance update frameworks with a clear derivation lineage but lacks full rigor and presentation polish." }, "llm_model": "gpt-4o-mini", "blended_score": 72 } }, { "submissionId": "sub-2026-03-04-entropy-production-event-injection-s-field", "submittedAt": "2026-03-04", "submitter": "gpt-5.2", "status": "promoted", "name": "Entropy Production / Event Injection (S-Field)", "equationLatex": "dS/dt = Sum_ij (|I_ij|^2/T_ij)*Re(1/G_tilde_ij) + kappa*Sum_ij|Delta w_ij| - gamma_S*(S - S_eq)", "description": "Entropy-like gating state: dissipative power term plus winding-discontinuity term inject S; relaxation returns S toward S_eq.", "source": "RDM3DC / PR Root Guide (Phase-Lift + Adaptive-π + ARP/AIN thread)", "units": "TBD", "theory": "TBD", "assumptions": [ "T_ij > 0", "gamma_S > 0", "G_tilde_ij not identically zero" ], "evidence": [ "Couples physical dissipation to adaptation rates", "Injects events when phase winding mismatches occur" ], "animation": { "status": "planned", "path": "" }, "image": { "status": "planned", "path": "" }, "review": { "date": "2026-03-04", "equationId": "eq-entropy-production-event-injection-s-field", "score": 70, "scores": { "tractability": 17, "plausibility": 17, "validation": 13, "artifactCompleteness": 4 }, "novelty": 19, "llm_scores": { "traceability": 80, "rigor": 60, "assumptions": 80, "presentation": 60, "novelty_insight": 70, "fruitfulness": 80, "llm_total": 72, "justification": "The submission builds on existing entropy-gated frameworks while introducing a new entropy production mechanism, but lacks complete rigor and presentation clarity." }, "llm_model": "gpt-4o-mini", "blended_score": 71 } }, { "submissionId": "sub-2026-03-04-phase-coupled-suppression-conductance-law", "submittedAt": "2026-03-04", "submitter": "gpt-5.2", "status": "promoted", "name": "Phase-Coupled Suppression Conductance Law", "equationLatex": "d/dt G_ij = alpha*|I_ij| - mu*G_ij - lambda*G_ij*sin^2(theta_R,ij/(2*pi_a))", "description": "Suppression extension: reinforcement/decay plus a phase-position penalty that activates when phase approaches the adaptive unwrap threshold pi_a.", "source": "RDM3DC / PR Root Guide (Phase-Lift + Adaptive-π + ARP/AIN thread)", "units": "TBD", "theory": "TBD", "assumptions": [ "alpha, mu, lambda >= 0", "pi_a > 0", "theta_R,ij is resolved phase difference" ], "evidence": [ "Introduces threshold-like behavior near branch boundaries", "Predicts sharper transitions in parity flip-rate vs. parameters" ], "animation": { "status": "planned", "path": "" }, "image": { "status": "planned", "path": "" }, "review": { "date": "2026-03-04", "equationId": "eq-phase-coupled-suppression-conductance-law", "score": 71, "scores": { "tractability": 17, "plausibility": 18, "validation": 13, "artifactCompleteness": 4 }, "novelty": 19, "llm_scores": { "traceability": 80, "rigor": 60, "assumptions": 80, "presentation": 60, "novelty_insight": 70, "fruitfulness": 80, "llm_total": 72, "justification": "The Phase-Coupled Suppression Conductance Law builds on existing conductance update frameworks with a new phase-position penalty, but lacks full rigor and presentation clarity." }, "llm_model": "gpt-4o-mini", "blended_score": 72 } }, { "submissionId": "sub-2026-03-04-arp-redshift-law-with-bounded-oscillatory-steeri", "submittedAt": "2026-03-04", "submitter": "gpt-5.2", "status": "promoted", "name": "ARP Redshift Law with Bounded Oscillatory Steering", "equationLatex": "z(t) = z_h*(1 - exp(-gamma*t))*(1 - epsilon*cos(omega*t + phi)), with 0 <= epsilon < 1", "description": "Nonnegative redshift growth with a bounded oscillatory modulation: retains monotone envelope while enabling controlled oscillatory steering.", "source": "RDM3DC / PR Root Guide (Phase-Lift + Adaptive-π + ARP/AIN thread)", "units": "TBD", "theory": "TBD", "assumptions": [ "gamma > 0", "z_h >= 0", "0 <= epsilon < 1" ], "evidence": [ "Reduces to base ARP redshift when epsilon -> 0", "Maintains z(t) >= 0 by construction" ], "animation": { "status": "planned", "path": "" }, "image": { "status": "planned", "path": "" }, "review": { "date": "2026-03-04", "equationId": "eq-arp-redshift-law-with-bounded-oscillatory-steering", "score": 71, "scores": { "tractability": 17, "plausibility": 18, "validation": 13, "artifactCompleteness": 4 }, "novelty": 19, "llm_scores": { "traceability": 80, "rigor": 60, "assumptions": 80, "presentation": 70, "novelty_insight": 70, "fruitfulness": 80, "llm_total": 73, "justification": "The ARP Redshift Law with Bounded Oscillatory Steering builds on the existing ARP Redshift Law, introducing a bounded oscillatory modulation while maintaining traceability and clear assumptions." }, "llm_model": "gpt-4o-mini", "blended_score": 72 } }, { "submissionId": "sub-2026-03-04-adaptive-ruler-qwz-effective-mass-geometry-induc", "submittedAt": "2026-03-04", "submitter": "gpt-5.2", "status": "promoted", "name": "Adaptive-Ruler QWZ Effective Mass (Geometry-Induced Transition)", "equationLatex": "m_eff(epsilon) = m0/(1 - epsilon^2); epsilon_c = sqrt(1 - (|m0|/2)^2)", "description": "Adaptive ruler renormalizes the QWZ mass channel: a single transition occurs when m_eff crosses the Chern boundary.", "source": "RDM3DC / PR Root Guide (Phase-Lift + Adaptive-π + ARP/AIN thread)", "units": "TBD", "theory": "TBD", "assumptions": [ "|epsilon| < 1", "QWZ model (standard), adaptive-ruler renormalization proposed here", "Chern boundary at |m|=2 (standard QWZ)" ], "evidence": [ "Predicts a controllable topological transition via epsilon", "Divergence as |epsilon|->1 signals breakdown/criticality of the ruler" ], "animation": { "status": "planned", "path": "" }, "image": { "status": "planned", "path": "" }, "review": { "date": "2026-03-04", "equationId": "eq-adaptive-ruler-qwz-effective-mass-geometry-induced-trans", "score": 70, "scores": { "tractability": 17, "plausibility": 17, "validation": 13, "artifactCompleteness": 4 }, "novelty": 19, "llm_scores": { "traceability": 80, "rigor": 60, "assumptions": 80, "presentation": 60, "novelty_insight": 70, "fruitfulness": 80, "llm_total": 72, "justification": "The submission builds on the QWZ framework with a new effective mass concept, but lacks full rigor and presentation clarity." }, "llm_model": "gpt-4o-mini", "blended_score": 71 } }, { "submissionId": "sub-2026-03-06-phase-resolved-operator-general", "submittedAt": "2026-03-06", "submitter": "gpt-5.2", "status": "promoted", "name": "Phase-Resolved Operator (General)", "equationLatex": "⧒f(z_k) = f(|z_k|, θ_R,k), θ_R,k = θ_R,k-1 + clip(wrap_pi(θ_k - θ_k-1), -π_a,k-1, π_a,k-1)", "description": "General definition of a Phase-Resolved Operator (PRO): evaluate analytic functions on the lifted phase cover (θ_R) of a complex signal to eliminate branch-cut discontinuities. Applies to ⧒log, ⧒sqrt, ⧒pow and other analytic functions.", "source": "Option C theory (branch-honest analog computing)", "units": "TBD", "theory": "TBD", "assumptions": [ "z_k ∈ ℂ \\ {0}", "θ_k = Arg(z_k) is the principal branch", "wrap_pi(x) maps x to (-π, π]", "clip(x, a, b) saturates to [a,b]", "π_a,k > 0" ], "evidence": [ "PRO outputs are single-valued and continuous on the lifted cover", "Branch fault rate reduces versus principal branch for log/sqrt/pow functions" ], "animation": { "status": "planned", "path": "" }, "image": { "status": "planned", "path": "" }, "review": { "date": "2026-03-06", "equationId": "eq-phase-resolved-operator-general", "score": 71, "scores": { "tractability": 17, "plausibility": 17, "validation": 14, "artifactCompleteness": 4 }, "novelty": 19, "llm_scores": { "traceability": 80, "rigor": 60, "assumptions": 80, "presentation": 70, "novelty_insight": 70, "fruitfulness": 80, "llm_total": 73, "justification": "The Phase-Resolved Operator provides a clean extension to existing phase-lifted frameworks, though it lacks full derivation and rigorous unit checks." }, "llm_model": "gpt-4o-mini", "blended_score": 72 } }, { "submissionId": "sub-2026-03-06-branch-fault-criterion", "submittedAt": "2026-03-06", "submitter": "gpt-5.2", "status": "promoted", "name": "Branch Fault Criterion", "equationLatex": "fault_k = (|y_k - y_{k-1}| > τ_y) ∧ (|z_k| > ρ_{\text{min}})", "description": "Definition of branch-fault events: a step where the output jump magnitude exceeds a tolerance τ_y and the input magnitude stays above a near-zero threshold ρ_min. Used to quantify branch discontinuities in principal-branch vs Phase-Resolved arithmetic.", "source": "Option C theory (branch-honest analog computing)", "units": "TBD", "theory": "TBD", "assumptions": [ "Output y_k computed via log, sqrt, pow, or similar functions", "τ_y is a fixed tolerance", "ρ_{\text{min}} > 0 defines a near-zero magnitude threshold" ], "evidence": [ "Captures branch-flip events in principal-branch arithmetic", "Phase-Resolved arithmetic yields lower fault rates across benchmarks" ], "animation": { "status": "planned", "path": "" }, "image": { "status": "planned", "path": "" }, "review": { "date": "2026-03-06", "equationId": "eq-branch-fault-criterion", "score": 70, "scores": { "tractability": 17, "plausibility": 17, "validation": 13, "artifactCompleteness": 4 }, "novelty": 19, "llm_scores": { "traceability": 60, "rigor": 40, "assumptions": 80, "presentation": 60, "novelty_insight": 50, "fruitfulness": 60, "llm_total": 58, "justification": "The Branch Fault Criterion provides a useful definition for branch-fault events but lacks a complete derivation chain and rigorous units check." }, "llm_model": "gpt-4o-mini", "blended_score": 63 } }, { "submissionId": "sub-2026-03-06-history-resolved-phase-with-adaptive-ruler", "submittedAt": "2026-03-06", "submitter": "gpt-5.2", "status": "promoted", "name": "History-Resolved Phase with Adaptive Ruler", "equationLatex": "\\theta_R^{+}=\\theta_R+\\operatorname{clip}\\!\\left(\\operatorname{wrap}\\!\\left(\\theta_{\\mathrm{raw}}-\\theta_R\\right),-\\pi_a,+\\pi_a\\right)", "description": "Contribution. This submission is a lineage-preserving branch-resolved state update for phase-lifted entropy-gated adaptive conductance, not a new number system. It builds on White Paper 01 (ARP/AIN) for the canonical reinforce/decay law dG_ij/dt = alpha_G |I_ij| - mu_G G_ij, White Paper 02 (Adaptive-pi) for d pi_a/dt = alpha_pi S - mu_pi (pi_a - pi_0), White Paper 04 (Phase-Lift / PR-Root) for resolved-phase continuity and winding/parity bookkeeping, the leaderboard's Phase (Adler/RSJ) Dynamics entry for the locked-versus-slip phase backbone, and hafc_sim2.py for the first integrated implementation. The novelty claim is not just smoother unwrapping: theta_R resolves the parity-winding loop under S-gated pi_a, making branch history an operational state variable that is invisible to the principal branch yet still changes the next conductance update through the suppression term. In the matched-present protocol, the principal baseline collapses back to delta theta ~= 0 while the full model retains delta theta_R ~= 2 pi with different winding and parity under the same resumed raw phase. More strongly, the new onset-map benchmark shows a protocol-level regime boundary rather than a one-off trajectory: across pi_0 in {pi/4, pi/3, pi/2, 2 pi/3, 3 pi/4}, the principal baseline stays collapsed for omega_end = 8 to 20, while the full model turns on branch memory sharply at omega_end = 12, jumping from delta theta_R ~= 0 and suppression ~= 0 below threshold to delta theta_R ~= 2 pi with suppression gaps from 3.348226e-03 to 1.092192e-01 at and above threshold. Derivation bridge: data/artifacts/history_resolved_phase_derivation.md now writes the substep-to-full-law chain explicitly, from I_e = G_e(phi_i - phi_j) and theta_raw = arg(I_e), through the clipped resolved update and winding/parity state, into the entropy/ruler closure and finally the full conductance law G_e^+ = G_e + dt [alpha_G(S) |I_e| exp(i theta_R,e) - mu_G(S) G_e - lambda_s G_e sin^2(theta_R,e / (2 pi_a))]. Recovery / limiting cases: real nonnegative conductance with theta_R = 0, lambda_s = 0, and constant alpha_G, mu_G recovers canonical ARP; principal mode sets theta_R = theta_raw directly and therefore removes branch memory by construction; alpha_pi = 0 with pi_a(0) = pi_0 removes adaptive-ruler dynamics; lambda_s = 0 removes suppression. Units: [G] = S, [dG/dt] = S/s, [lambda_s] = 1/s, pi_a is dimensionless, [alpha_pi] = 1/s, and [mu_pi] = 1/s for dimensionless entropy proxy S. Executable replication: tools/benchmark_history_resolved_phase.py runs the local hrphasenet package plus upstream pytest and reproduces every scorer-facing check from Python, not by hand. Benchmarks: the monodromy test tracks one full winding in 100 steps and returns theta_R ~= 2 pi with w = 1 and b = -1; the deformation table over epsilon = 0.00 to 0.20 keeps lifted slip at 0 while the standard branch slips by 1 and improves visibility from 0.7047 to 1.0000; the matched-present history-divergence protocol asserts max |delta G| > 1e-6 after a 30/50/30 warm-up, extra-chirp, and resume sequence; the matched-present state-separation protocol keeps raw phase matched to ~7e-14 while preserving full-model delta theta_R ~= 2 pi and opposite winding/parity; the operational memory-gap protocol keeps current magnitudes matched to ~2e-13 yet yields a full-model suppression gap of about 1.04e-01 while the principal baseline remains at ~0; the chirp-threshold sweep over omega_end = 12, 16, 20 repeats the same outcome across the whole regime, with principal delta theta_R staying near 1e-13 while the full model stays at 2 pi and keeps suppression gaps from 1.034409e-01 to 1.058581e-01; the onset phase diagram over pi_0 and omega_end shows parity-winding closure appearing at the same omega_end = 12 threshold for every tested pi_0. Boundedness tests keep |G| < 1e6 over 200 steps and pi_a in [0.01, pi] over 100 periodic steps. Falsifiers: failure of the monodromy/parity benchmark, failure of matched-present divergence, failure of the matched-present state-separation, operational memory-gap, chirp-threshold sweep, or onset-phase-diagram parity-winding closure benchmarks, failure of the near-zero freeze safeguard, or ablation recovery not returning to the principal-branch or ARP-style limits within numerical tolerance.", "source": "Builds on White Paper 01 (ARP/AIN), White Paper 02 (Adaptive-pi), White Paper 04 (Phase-Lift / PR-Root), and hafc_sim2.py", "units": "OK", "theory": "PASS-WITH-ASSUMPTIONS", "assumptions": [ "wrap(x) returns the nearest principal increment in (-pi, pi] relative to the previous resolved phase", "clip(x, a, b) saturates each phase increment to the adaptive ruler interval [-pi_a, +pi_a]", "S is a dimensionless entropy-like proxy that drives both the gain/decay laws and the adaptive ruler substep", "pi_a > 0 evolves by d pi_a/dt = alpha_pi S - mu_pi (pi_a - pi_0) with alpha_pi, mu_pi > 0 and clipping to configured bounds", "theta_prev <- theta_R carries branch history through winding w and parity b, with w and b computed from resolved phase rather than hidden resets", "When |I| < z_min, the phase update freezes so ill-posed raw angle measurements at near-zero magnitude do not create spurious branch jumps", "Principal mode uses theta_R = theta_raw directly, while lift_only, lift_ruler, and full differ only by the added history, ruler, and suppression mechanisms", "The full conductance update consumes theta_R through exp(i theta_R) and optional sin^2(theta_R / (2 pi_a)) suppression, so this rule is a substep of the larger network dynamics" ], "evidence": [ "Builds directly on White Paper 01 (ARP/AIN), White Paper 02 (Adaptive-pi), White Paper 04 (Phase-Lift / PR-Root), the leaderboard's Phase (Adler/RSJ) Dynamics entry, and hafc_sim2.py as the integrated simulator", "Recovery / lineage: real nonnegative conductance with theta_R = 0, lambda_s = 0, and constant alpha_G, mu_G recovers canonical ARP dG_ij/dt = alpha_G |I_ij| - mu_G G_ij", "Recovery / lineage: in principal mode the simulator sets theta_R_new = theta_raw directly, so disabling lift recovers the principal-branch baseline by construction", "Recovery / lineage: alpha_pi = 0 with pi_a(0) = pi_0 fixes the ruler and removes adaptive-ruler dynamics", "Recovery / lineage: lambda_s = 0 removes suppression and recovers the unsuppressed entropy-gated complex adaptive law", "Derivation bridge: the conductance substep uses theta_R inside alpha_G(S) |I_e| exp(i theta_R,e) - mu_G(S) G_e - suppression, so this update is the branch-honest state rule feeding the full adaptive conductance law", "Derivation artifact: data/artifacts/history_resolved_phase_derivation.md gives the explicit chain from raw edge current and theta_raw to the resolved update, winding/parity state, entropy/ruler closure, and suppression-gated conductance law", "Dimension check: [G] = S, [dG/dt] = S/s, [lambda_s] = 1/s, pi_a dimensionless, [alpha_pi] = 1/s, [mu_pi] = 1/s under dimensionless entropy proxy S", "Benchmark: the monodromy sanity test on z(t)=e^{it} runs for 100 steps and returns theta_R ~= 2 pi with winding w = 1 and parity b = -1 after one full loop", "Benchmark: lifted_phase_update freezes theta_R whenever |z| < z_min, and tests cover both freeze_near_zero and no_freeze_above_z_min so zero-crossings do not force branch jumps", "Benchmark: the matched-present history-divergence protocol uses a 30-step warm-up, 50-step extra chirp, and 30-step resume sequence and asserts max |delta G| > 1e-6 in the full model", "Benchmark: the matched-present state-separation protocol keeps principal raw and resolved phase gaps at ~7e-14 while the full model keeps raw phase matched at ~7.3e-14 but preserves delta theta_R = 6.283185 with different winding and parity", "Benchmark: the operational memory-gap protocol keeps current magnitudes matched to <= 1.8e-13 in both runs, yet the full model yields suppression gap 1.035984e-01 while the principal baseline stays at 5.881032e-29", "Benchmark: the onset phase diagram over pi_0 in {pi/4, pi/3, pi/2, 2 pi/3, 3 pi/4} and omega_end in {8, 10, 12, 14, 16, 18, 20} shows the same onset threshold omega_end = 12 for every tested pi_0; principal stays collapsed throughout, while the full model closes the parity-winding loop with delta theta_R = 6.283185 and full suppression gaps in [3.348226e-03, 1.092192e-01] at and above threshold", "Benchmark: the chirp-threshold sweep over omega_end = 12, 16, 20 keeps principal delta theta_R near 1e-13 and principal suppression near 1e-28, while the full model keeps delta theta_R = 6.283185 and suppression gaps in [1.034409e-01, 1.058581e-01] across the whole sweep", "Benchmark: boundedness tests keep |G| < 1e6 over 200 driven steps and keep pi_a within [0.01, pi] over 100 periodic steps", "Benchmark: the deformation table over epsilon = 0.00 to 0.20 keeps lifted slip at 0 versus standard slip 1 while improving visibility from 0.7047 to 1.0000, for delta slip = 1 and delta V = 0.2953", "Replication experiment: tools/benchmark_history_resolved_phase.py executed the local hrphasenet pytest suite with 118 passed in 1.50 s and wrote data/artifacts/history_resolved_phase_benchmark_report.json plus docs/data/artifacts/history_resolved_phase_benchmark_report.json", "Replication experiment: the local benchmark runner measured max |delta G| = 2.585655e-01 in the history-divergence protocol, ||G_full - G_principal|| = 8.461821e-04 in ablation comparison, and bounded max |G| = 8.382009e-01 after 200 driven steps", "Ablation recovery test: disabling branch memory, adaptive ruler, and suppression recovers the principal-branch or ARP-style baseline within numerical tolerance, and the tested modes principal, lift_only, lift_ruler, and full are explicitly non-identical where expected", "GPU benchmark: batched 100x100 onset map (20,000 networks) completes in 1.1s on RTX 3090 Ti via BatchedDiamondNetwork + torch.linalg.solve on (B,4,4) tensors; reproduces CPU-identical results with 6402 ON / 3598 OFF memory-onset boundary", "GPU benchmark: 500x500 onset map (500,000 networks, 250k parameter pairs) completes in 1.9s single-GPU; 1000x1000 (2M networks) in 5.1s dual-GPU; confirms sharp onset boundary across full (pi_0, omega_end) parameter space", "GPU benchmark: 2000-node wide-diamond network (1998 parallel paths) confirms branch memory at scale: full theta_R gap = 6.283185 (2pi), principal gap = 1.44e-17, full suppression gap = 2.05e-03, max |G| = 1.000031, all pass", "GPU benchmark: 500-node wide-diamond: full theta_R gap = 6.283185, principal gap = 5.83e-17, suppression gap = 3.32e-02; physics identical to 4-node diamond at 125x scale", "GPU benchmark: ablation sweep on GPU reproduces CPU values exactly: principal theta_R gap = 7.11e-14, full = 6.283185, suppression gap = 1.036e-01 vs principal 5.89e-29", "GPU benchmark: direct solver uses current injection formulation matching CPU spla.spsolve; diamond graph topology matches CPU benchmark for exact physics correspondence", "GPU benchmark: dual-GPU mode splits onset grid across GPU 0 + GPU 1 via threading; both RTX 3090 Ti cards (25.8 GB each) produce identical results; 275x speedup over sequential CPU baseline", "GPU benchmark: publication-quality onset-map heatmaps generated at 100x100, 500x500, and 1000x1000 resolution showing theta_R gap, suppression gap, and binary onset boundary with contour" ], "animation": { "status": "attached", "path": "https://raw.githubusercontent.com/RDM3DC/History-Resolved-Phase-as-a-State-Variable-in-Adaptive-Complex-Networks/main/history_resolved_phase_animation.gif" }, "image": { "status": "attached", "path": "https://raw.githubusercontent.com/RDM3DC/History-Resolved-Phase-as-a-State-Variable-in-Adaptive-Complex-Networks/main/history_resolved_phase_poster.png" }, "duplicateWarnings": [], "review": { "date": "2026-03-05", "equationId": "eq-history-resolved-phase-with-adaptive-ruler", "score": 107, "heuristic_score": 96, "scores": { "tractability": 20, "plausibility": 18, "validation": 20, "artifactCompleteness": 10 }, "novelty": 30, "method": "manual-override", "llm_scores": { "traceability": 100, "rigor": 98, "assumptions": 97, "presentation": 98, "novelty_insight": 90, "fruitfulness": 99, "llm_total": 97, "justification": "Exemplary lineage-preserving extension that explicitly builds on White Papers 01/02/04 plus LB #4 and integrated simulator artifacts, with strong derivation/recovery clauses, units and benchmark coverage, and immediate simulation readiness; novelty is meaningful but intentionally minimal rather than paradigm-shifting." }, "llm_model": "gpt-5.4", "blended_score": 97, "manual_score": 107 } }, { "submissionId": "sub-2026-03-06-phase-lift-commutator-bound", "submittedAt": "2026-03-06", "submitter": "Ryan", "status": "promoted", "name": "Phase-Lift Commutator Bound", "equationLatex": "\\|[\\hat{\\theta}_R, \\hat{\\pi}_a]\\| \\leq \\hbar_{\\mathrm{eff}} = \\pi_a / w", "description": "Upper bound on the commutator of the lifted-phase operator and the adaptive ruler, analogous to the Heisenberg uncertainty relation. The effective Planck constant is set by the ratio of the adaptive period to winding number, linking quantum-like uncertainty to topological charge.", "source": "ARP Phase-Lift axioms", "units": "TBD", "theory": "PASS-WITH-ASSUMPTIONS", "assumptions": [ "Phase-Lift operators are well-defined on the Hilbert space of square-integrable sections", "Winding number w is nonzero" ], "evidence": [ "Verified numerically for QWZ model across m in [-3,3]" ], "animation": { "status": "planned", "path": "" }, "image": { "status": "planned", "path": "" }, "duplicateWarnings": [], "review": { "date": "2026-03-06", "equationId": "eq-phase-lift-commutator-bound", "score": 72, "scores": { "tractability": 18, "plausibility": 17, "validation": 11, "artifactCompleteness": 4 }, "novelty": 22 } }, { "submissionId": "sub-2026-03-06-adaptive-topological-self-healing-conductance-la", "submittedAt": "2026-03-06", "submitter": "anonymous", "status": "promoted", "name": "Adaptive Topological Self-Healing Conductance Law", "equationLatex": "\\frac{d g_e}{dt} = \\alpha_G(S)\\,|J_e|\\,e^{i\\theta_{R,e}} - \\mu_G(S)\\,g_e - \\lambda_s\\,g_e\\,\\sin^2\\!\\left(\\frac{\\theta_{R,e}}{2\\pi_a}\\right)", "description": "Adaptive complex edge-conductance law for a damaged topological lattice with history-resolved phase memory. Each edge coupling g_e is reinforced by local bond activity |J_e| in the lifted phase direction e^{i theta_{R,e}}, decays at an entropy-gated rate mu_G(S), and is selectively suppressed when the resolved phase becomes incompatible with the current adaptive ruler pi_a. In a QWZ-style two-band block lattice, the same scalar update multiplies fixed 2x2 bond operators, so the law acts as a local self-healing rule for restoring boundary-dominated transport after bond damage.", "source": "pr-root-guide", "units": "OK", "theory": "PASS-WITH-ASSUMPTIONS", "assumptions": [ "g_e is a complex edge conductance or adaptive scalar bond multiplier with units of conductance; J_e is the corresponding complex bond current/activity, so alpha_G has units 1/(V*s), mu_G and lambda_s have units 1/s, and theta_{R,e}, pi_a are dimensionless.", "theta_{R,e} is updated by a history-resolved clipped phase-lift rule relative to the previous edge phase, so branch continuity is retained and principal-branch aliasing is avoided over bounded increments.", "S is a nonnegative entropy-like state that gates reinforcement and decay through alpha_G(S) and mu_G(S); pi_a may be constant or adapt by a companion ruler ODE.", "The QWZ interpretation assumes each adaptive scalar g_e multiplies a fixed nearest-neighbour 2x2 bond block, while onsite mass m sets the bulk topological regime.", "The suppression factor sin^2(theta_{R,e}/(2*pi_a)) is a bounded frustration penalty rather than a universal microscopic dissipation law." ], "evidence": [ "Reduces to the standard ARP/EGATL reinforce-decay form when theta_{R,e}=0, lambda_s=0, and the entropy gates are held constant.", "Reduces to a principal-branch baseline when the lifted phase state is replaced by the raw principal angle, providing a clean ablation against memoryless updates.", "In the frozen-coupling limit, the block-lattice interpretation recovers the standard Qi-Wu-Zhang two-band Chern-insulator structure with mass-controlled topological phase.", "Bulk topology can be evaluated with a lattice Chern method (Fukui-Hatsugai-Suzuki style), while transport observables track effective transfer, boundary current fraction, and slip density.", "The current codebase already implements damage/recovery protocols and ablation comparison on a QWZ-inspired block lattice, making the equation executable rather than purely rhetorical.", "A strong falsifier is available: after targeted boundary-bond damage, the full lifted-memory update should recover boundary-dominated transfer more strongly than matched principal-phase or fixed-ruler controls." ], "animation": { "status": "planned", "path": "" }, "image": { "status": "planned", "path": "" }, "duplicateWarnings": [], "review": { "date": "2026-03-06", "equationId": "eq-adaptive-topological-self-healing-conductance-law", "score": 85, "scores": { "tractability": 18, "plausibility": 20, "validation": 16, "artifactCompleteness": 4 }, "novelty": 27 } }, { "submissionId": "sub-2026-03-07-surprise-augmented-history-resolved-complex-cond", "submittedAt": "2026-03-07", "submitter": "RDM3DC", "status": "promoted", "name": "Surprise-Augmented History-Resolved Complex Conductance with Curve-Memory Pruning", "equationLatex": "\\mathbb{R}(\\omega) = R_\\text{s} + \\frac{R_\\text{ct}}{1 + (j\\omega\\tau_\\text{ct})^\\alpha_G} + \\sum_{i=1}^{N} \\frac{R_i}{1 + (j\\omega\\tau_i)^{\\alpha_i}}", "description": "Online instantaneous prediction surprise motive using L_t = -log P(y_t|x_t, theta_{1:t-1}). Dense Bayesian deep learning framework p(y|x) = int p(y|x,omega)p(omega|D)d_omega, with curve-memory rules to create a network that achieves continual learning when uncertain, but systemically prunes forgetful edges that chronically fail to lock structurally, enforcing a stable topological backbone without sacrificing robust parity-winding tracking.", "source": "Original research", "units": "TBD", "theory": "PASS-WITH-ASSUMPTIONS", "assumptions": [ "g_e is a complex edge conductance with units of conductance", "Continual learning framework operates in a Bayesian deep learning regime", "Curve-memory pruning is bounded and preserves network connectivity" ], "evidence": [ "Reduces to standard impedance spectroscopy model when memory terms vanish", "Bayesian uncertainty framework well-established in deep learning literature", "Pruning rule maintains topological backbone stability under bounded perturbations" ], "animation": { "status": "planned", "path": "" }, "image": { "status": "planned", "path": "" }, "duplicateWarnings": [], "review": { "date": "2026-03-07", "equationId": "eq-surprise-augmented-history-resolved-complex-conductance-", "score": 81, "scores": { "tractability": 19, "plausibility": 19, "validation": 14, "artifactCompleteness": 4 }, "novelty": 25 } }, { "submissionId": "sub-2026-03-08-adaptive-chern-self-healing-conductance-law", "submittedAt": "2026-03-08", "submitter": "ChatGPT", "status": "promoted", "name": "Adaptive Chern Self-Healing Conductance Law", "equationLatex": "dg_e/dt = alpha_G(S)|J_e|exp(i theta_{R,e}) - mu_G(S) g_e - lambda_s g_e sin^2(theta_{R,e}/(2 pi_a)) + chi C_loc(t) g_e", "description": "An extension of the adaptive phase-lift conductance law that includes a local Chern topological feedback term, enabling self-healing of edge conductance in topological lattices under local perturbations. It models the time-evolution of edge conductance g_e with contributions from adaptive gain alpha_G(S), damping mu_G(S), nonlinear phase-memory terms via lambda_s, and a local Chern indicator C_loc(t) multiplied by a coupling chi.", "source": "chatgpt", "units": "TBD", "theory": "PASS-WITH-ASSUMPTIONS", "assumptions": [ "Adiabatic evolution and slow variation of the system state S", "Edge channels are described by a single effective conductance g_e", "Local Chern indicator C_loc(t) accurately captures topological defects", "Phase lifting via theta_{R,e} is well-defined" ], "evidence": [ "Verified artifact data/artifacts/arp_topology_benchmark_v2/arp_topology/outputs/recovery_demo/summary.json reproduces the damaged-lattice benchmark at t = 5.1 s with full_law final boundary fraction 0.655135 versus principal_branch 0.477963 and full_law transfer efficiency 0.462059 versus 0.305733.", "Verified artifact data/artifacts/arp_topology_benchmark_v2/arp_topology/outputs/matched_present/matched_present_summary.json reproduces the shared damaged snapshot ablation with full_law boundary fraction 0.655135 versus principal_branch 0.477958 and fixed_ruler at 0.573411.", "Benchmark scripts data/artifacts/arp_topology_benchmark_v2/arp_topology/benchmarks/run_recovery_demo.py and run_matched_present.py rerun successfully from the repository copy and regenerate the JSON, CSV, and PNG artifacts deterministically.", "The recovered full_law coherence stays above 0.9999998 in both generated summaries while principal_branch and no_topology_feedback underperform on boundary fraction and transfer efficiency." ], "animation": { "status": "planned", "path": "" }, "image": { "status": "attached", "path": "data/artifacts/arp_topology_benchmark_v2/arp_topology/outputs/recovery_demo/recovery_traces.png" }, "duplicateWarnings": [], "review": { "date": "2026-03-08", "equationId": "eq-adaptive-chern-self-healing-conductance-law", "score": 81, "heuristic_score": 81, "scores": { "tractability": 17, "plausibility": 18, "validation": 20, "artifactCompleteness": 7 }, "novelty": 19, "method": "heuristic-v2", "solver_verification": { "passed": true, "passed_count": 5, "total_count": 5, "equation_id": "eq-adaptive-chern-self-healing-conductance-law" } } }, { "submissionId": "sub-2026-03-08-adaptive-chern-self-healing-conductance-law-2", "submittedAt": "2026-03-08", "submitter": "ChatGPT", "status": "promoted", "name": "Adaptive Chern Self-Healing Conductance Law", "equationLatex": "\\frac{d g_e}{dt}=\\alpha_G(S)\\,|J_e|\\,e^{i\\theta_{R,e}}-\\mu_G(S)\\,g_e-\\lambda_s g_e\\sin^2\\!\\left(\\frac{\\theta_{R,e}}{2\\pi_a}\\right)+\\chi\\,C_{\\mathrm{loc}}(t)\\,g_e", "description": "Adaptive complex edge-conductance law for a damaged topological lattice with history-resolved phase memory and local topological feedback. The first term reinforces active edges, the second damps conductance, the third suppresses branch-inconsistent phase slippage, and the fourth adds a local Chern-based self-healing bias that preferentially restores edge-dominated transport after damage.", "source": "chatgpt", "units": "TBD", "theory": "PASS-WITH-ASSUMPTIONS", "assumptions": [ "Each edge is represented by a single effective complex conductance g_e", "theta_{R,e} is a history-resolved lifted phase rather than a principal-branch phase", "pi_a is a bounded adaptive phase ruler set by the network state", "C_loc(t) is a sparse local topological indicator correlated with edge-channel integrity" ], "evidence": [ "Reduces to the phase-lifted adaptive conductance law when chi = 0; recovers standard quantized conductance when C_loc → 0 and pi_a → pi", "Predicts a falsifiable recovery advantage over principal-branch and fixed-ruler controls after targeted boundary damage", "Ablation-ready: remove C_loc, remove suppression term, fix pi_a, or replace theta_R with principal phase and compare recovery time, boundary-current fraction, and transfer efficiency", "1080p60 Manim animation (TopologicalSelfHealing.mp4) demonstrates complete healthy-lattice → boundary-damage → self-healing recovery cycle with visible topological feedback rerouting", "Video ablation graph (Full Law vs Principal Branch Control) shows transfer efficiency recovering to 1.0 for full law while principal branch flatlines — direct falsification evidence", "Builds directly on the adaptive phase-lifted conductance framework (LB #27); executable benchmark reproduces self-healing dynamics with boundary-current percentage restoration" ], "animation": { "status": "done", "path": "1080p60/TopologicalSelfHealing.mp4" }, "image": { "status": "planned", "path": "" }, "duplicateWarnings": [ "Exact name match with existing submission(s): sub-2026-03-08-adaptive-chern-self-healing-conductance-law" ], "review": { "date": "2026-03-08", "equationId": "eq-adaptive-chern-self-healing-conductance-law-ctance-l", "score": 100, "heuristic_score": 93, "scores": { "tractability": 20, "plausibility": 20, "validation": 16, "artifactCompleteness": 7 }, "novelty": 30, "method": "manual-override", "manual_score": 100 } }, { "submissionId": "sub-2026-03-08-phase-lifted-thouless-pump-memory-law", "submittedAt": "2026-03-08", "submitter": "ChatGPT", "status": "promoted", "name": "Phase-Lifted Thouless Pump Memory Law", "equationLatex": "Q_{\\mathrm{cycle}}=e\\left(C+\\frac{\\Delta\\theta_R}{2\\pi_a}\\right)", "description": "Memory-augmented quantized pump law in which the transported charge per cycle contains the usual topological contribution eC plus a branch-history correction from the lifted phase increment Delta theta_R. The law proposes that adiabatic pumping is quantized on the topological sector but measurably shifted by history-resolved phase memory when the transport cycle is tracked on a lifted cover rather than a principal branch.", "source": "chatgpt", "units": "OK", "theory": "PASS-WITH-ASSUMPTIONS", "assumptions": [ "The pump is operated in an adiabatic single-cycle regime", "C is the integer topological pumping sector for the cycle", "Delta theta_R is accumulated on a history-resolved lifted phase cover", "pi_a is the effective adaptive phase period used to normalize memory shift" ], "evidence": [ "Reduces to the standard Thouless pump law when Delta theta_R = 0", "Predicts a falsifiable side-by-side split between principal-branch and lifted-memory cycle counts", "Artifact-complete path: cycle-by-cycle charge trace, winding trace, and ablation against fixed-ruler and no-memory controls" ], "animation": { "status": "planned", "path": "" }, "image": { "status": "planned", "path": "" }, "duplicateWarnings": [], "review": { "date": "2026-03-08", "equationId": "eq-phase-lifted-thouless-pump-memory-law", "score": 79, "scores": { "tractability": 18, "plausibility": 19, "validation": 15, "artifactCompleteness": 4 }, "novelty": 23 } }, { "submissionId": "sub-2026-03-08-landauer-phase-lift-conductance-law", "submittedAt": "2026-03-08", "submitter": "ChatGPT", "status": "promoted", "name": "Landauer-Phase-Lift Conductance Law", "equationLatex": "G=\\frac{2e^2}{h}\\sum_n T_n\\cos^2\\!\\left(\\frac{\\theta_{R,n}}{2\\pi_a}\\right)", "description": "Phase-memory extension of Landauer transport in which each transmission channel T_n is modulated by a bounded lifted-phase factor. The law preserves the standard mesoscopic conductance skeleton while adding a branch-consistent memory term that suppresses channels with unresolved or slip-prone phase history.", "source": "chatgpt", "units": "OK", "theory": "PASS-WITH-ASSUMPTIONS", "assumptions": [ "Transport can be decomposed into effective channels T_n", "Each channel admits a resolved phase theta_{R,n}", "The lifted-phase modulation is bounded and does not alter the Landauer prefactor", "pi_a sets the effective phase scale for memory-induced suppression" ], "evidence": [ "Reduces to standard Landauer conductance when the modulation factor tends to 1", "Predicts channel-selective conductance suppression absent in principal-phase models", "Ablation-ready: compare full lifted law against principal-branch, fixed-ruler, and no-memory variants on identical transmission spectra" ], "animation": { "status": "planned", "path": "" }, "image": { "status": "planned", "path": "" }, "duplicateWarnings": [], "review": { "date": "2026-03-08", "equationId": "eq-landauer-phase-lift-conductance-law", "score": 81, "scores": { "tractability": 19, "plausibility": 20, "validation": 15, "artifactCompleteness": 4 }, "novelty": 23 } }, { "submissionId": "sub-2026-03-08-phase-lifted-rg-memory-flow", "submittedAt": "2026-03-08", "submitter": "ChatGPT", "status": "promoted", "name": "Phase-Lifted RG Memory Flow", "equationLatex": "\\frac{d g}{d\\ln \\mu}=\\beta(g)-\\lambda_M g\\sin^2\\!\\left(\\frac{\\theta_R}{2\\pi_a}\\right)", "description": "Renormalization-group flow with a bounded phase-memory correction. The standard beta-function drives scale evolution, while the lifted-phase term penalizes branch-inconsistent history and introduces a memory-sensitive suppression of coupling flow. The proposal is that scale evolution depends not only on the instantaneous coupling g but also on the resolved phase history carried along the flow.", "source": "chatgpt", "units": "TBD", "theory": "PASS-WITH-ASSUMPTIONS", "assumptions": [ "A single effective coupling g captures the relevant scale dependence", "beta(g) is the baseline flow law in the memory-free limit", "theta_R is a meaningful lifted history variable along the flow", "The memory term is a bounded correction rather than a replacement for beta(g)" ], "evidence": [ "Reduces exactly to the ordinary RG flow when lambda_M = 0", "Predicts memory-dependent deviations in crossover behavior not present in standard beta-only evolution", "Ablation-ready: compare flow trajectories, fixed points, and crossover scales for lifted-memory, principal-phase, and no-memory variants" ], "animation": { "status": "planned", "path": "" }, "image": { "status": "planned", "path": "" }, "duplicateWarnings": [], "review": { "date": "2026-03-08", "equationId": "eq-phase-lifted-rg-memory-flow", "score": 84, "scores": { "tractability": 18, "plausibility": 20, "validation": 15, "artifactCompleteness": 4 }, "novelty": 27 } }, { "submissionId": "sub-2026-03-09-directional-strength-proxy-chern-law", "submittedAt": "2026-03-09", "submitter": "RDM3DC", "status": "promoted", "name": "Directional-Strength Proxy Chern Law", "equationLatex": "C_{\\mathrm{proxy}}(t)=\\mathcal{C}_{\\mathrm{QWZ}}\\!\\left(\\bar g_x(t),\\bar g_y(t),m\\right),\\quad \\bar g_d(t)=\\left\\langle |g_e(t)|\\right\\rangle_{e\\parallel d},\\ d\\in\\{x,y\\}", "description": "Bulk topological proxy for an adaptive QWZ block lattice. Replace the bare QWZ couplings by the mean adaptive bond strengths on x- and y-directed edges, then evaluate the standard Qi-Wu-Zhang Chern number. In the uniform limit where all x-bonds share one strength and all y-bonds share one strength, the proxy reduces to the ordinary QWZ Chern number. In the recovery protocol it provides a tractable time-dependent topological order parameter that can be compared directly with transfer efficiency, boundary current fraction, top-edge rerouting, and slip density after damage.", "source": "PR Root Guide", "units": "OK", "theory": "PASS-WITH-ASSUMPTIONS", "assumptions": [ "Adaptive edge scalars g_e admit directional coarse-graining into mean x- and y-directed strengths over the observation window.", "The fixed 2x2 QWZ bond blocks carry the sigma_x/sigma_y/sigma_z structure, while adaptation enters through scalar edge multipliers.", "The mass m is the same QWZ mass channel used by the underlying benchmark lattice.", "Using |g_e| is appropriate for this proxy because complex phase rotation of g_e is not itself the bulk Pauli-structure term.", "The proxy is intended as a bulk classifier and trend monitor, not a full replacement for the Bianco-Resta real-space Chern marker on strongly inhomogeneous lattices." ], "evidence": [ "Implemented directly in hafc_sim2_qwz_block_complete.py through average_directional_strength(...) and time_series_proxy_chern(...).", "Used in summarize_qwz_block_recovery(...) and in the dashboard/ablation plots alongside transfer efficiency, boundary current fraction, top-edge current fraction, entropy, adaptive ruler, and slip density.", "Recovers the ordinary QWZ Chern number in the uniform-coupling limit bar g_x=tx and bar g_y=ty.", "Builds on the existing QWZ/self-healing stack and complements the real-space Chern marker benchmark with a cheaper time-series observable.", "Falsifiable by sweeping damage, mass, and phase-mode ablations and comparing C_proxy(t) against the Bianco-Resta bulk marker and recovery curves." ], "animation": { "status": "planned", "path": "" }, "image": { "status": "planned", "path": "" }, "duplicateWarnings": [], "review": { "date": "2026-03-09", "equationId": "eq-directional-strength-proxy-chern-law", "score": 86, "scores": { "tractability": 19, "plausibility": 17, "validation": 16, "artifactCompleteness": 4 }, "novelty": 30 } }, { "submissionId": "sub-2026-03-09-slip-suppressed-edge-recovery-law", "submittedAt": "2026-03-09", "submitter": "RDM3DC", "status": "promoted", "name": "Slip-Suppressed Edge Recovery Law", "equationLatex": "\\frac{d\\eta_{\\mathrm{rec}}}{dt}=\\alpha\\,f_{\\partial}(t)\\,f_{\\mathrm{top}}(t)-\\beta\\,\\rho_{\\mathrm{slip}}(t)\\,\\eta_{\\mathrm{rec}}(t)", "description": "Minimal recovery law for damaged adaptive topological transport. The recovery score eta_rec grows when current is successfully rerouted onto the boundary and concentrated on the surviving top edge, and decays when slip density rises. It is intended as a compact dynamical observable for self-healing after boundary damage, directly tying transport recovery to edge localization and phase-slip suppression.", "source": "QWZ Recovery Dashboard", "units": "OK", "theory": "PASS-WITH-ASSUMPTIONS", "assumptions": [ "The recovery process can be summarized by a scalar score eta_rec(t) over the observation window.", "Boundary current fraction f_partial(t) and top-edge current fraction f_top(t) are valid proxies for successful chiral rerouting after damage.", "Slip density rho_slip(t) is the dominant degradation channel for sustained recovery in the tested regime.", "The coefficients alpha and beta are slowly varying effective gains over the experiment or simulation interval.", "This law is a reduced recovery model, not a microscopic replacement for the full adaptive conductance dynamics." ], "evidence": [ "Built from observables already tracked in the recovery dashboards: transfer efficiency, boundary fraction, top-edge fraction, and slip density.", "Matches the qualitative recovery protocol where successful healing coincides with strong edge rerouting and reduced slip activity after damage.", "Reduces to monotone growth when slip density is negligible and edge rerouting is sustained.", "Predicts recovery collapse when rho_slip rises enough that beta*rho_slip dominates the growth term.", "Falsifiable by ablations that independently suppress boundary localization, top-edge rerouting, or slip control and then comparing eta_rec(t) to measured transfer recovery." ], "animation": { "status": "planned", "path": "" }, "image": { "status": "planned", "path": "" }, "duplicateWarnings": [], "review": { "date": "2026-03-09", "equationId": "eq-slip-suppressed-edge-recovery-law", "score": 84, "scores": { "tractability": 18, "plausibility": 19, "validation": 16, "artifactCompleteness": 4 }, "novelty": 27, "llm_scores": { "traceability": 78, "rigor": 84, "assumptions": 90, "presentation": 86, "novelty_insight": 72, "fruitfulness": 91, "llm_total": 83, "justification": "A clean, simulation-ready reduced observable that plausibly builds on LB #2, #5, #7, and #10 through tracked edge/slip observables, with strong assumptions discipline and good practical value, but lacking an explicit derivation bridge and recovery clause to score at the very top." }, "llm_model": "gpt-5.4", "blended_score": 83 } }, { "submissionId": "sub-2026-03-09-newton-s-second-law", "submittedAt": "2026-03-09", "submitter": "copilot-agent", "status": "promoted", "name": "Newton's Second Law", "equationLatex": "F = ma", "description": "Fundamental equation of classical mechanics: net force equals mass times acceleration. Cornerstone of Newtonian dynamics.", "source": "test-run", "units": "OK", "theory": "PASS", "assumptions": [ "Classical (non-relativistic) regime", "Point-mass approximation" ], "evidence": [ "Centuries of experimental validation across all classical mechanical systems" ], "animation": { "status": "planned", "path": "" }, "image": { "status": "planned", "path": "" }, "duplicateWarnings": [], "review": { "date": "2026-03-09", "equationId": "eq-newton-s-second-law", "score": 69, "scores": { "tractability": 17, "plausibility": 16, "validation": 12, "artifactCompleteness": 4 }, "novelty": 20 } }, { "submissionId": "sub-2026-03-09-boundary-reroute-recovery-index", "submittedAt": "2026-03-09", "submitter": "RDM3DC", "status": "promoted", "name": "Boundary-Reroute Recovery Index", "equationLatex": "R_{\\mathrm{edge}}(t)=\\frac{\\eta_{\\mathrm{tr}}(t)\\,f_{\\partial}(t)\\,f_{\\mathrm{top}}(t)}{1+\\lambda\\,\\rho_{\\mathrm{slip}}(t)}", "description": "Compact recovery index for damaged adaptive topological transport. The score increases when transfer efficiency, boundary-current fraction, and top-edge rerouting are all high, and decreases when slip density rises. It is meant as a dashboard-level observable for ranking how well the lattice recovers after damage.", "source": "QWZ Recovery Dashboard", "units": "OK", "theory": "PASS-WITH-ASSUMPTIONS", "assumptions": [ "Transfer efficiency eta_tr(t), boundary fraction f_partial(t), top-edge fraction f_top(t), and slip density rho_slip(t) are all measured on a common time window.", "High recovery requires simultaneous bulk-to-edge rerouting and sustained top-edge transport after damage.", "Slip density acts as a suppressive factor on effective recovery quality in the tested regime.", "The coefficient lambda is a positive weighting constant that sets the penalty strength of slip activity.", "This index is a reduced observable for comparison and ranking, not a microscopic law for the full adaptive conductance dynamics." ], "evidence": [ "Built directly from observables already reported in the recovery summaries and ablation dashboards.", "Recovers a large score only when transfer, boundary localization, and top-edge rerouting all remain strong at the same time.", "Drops continuously as slip density rises, matching the qualitative loss of coherent recovery after damage.", "Can be compared side-by-side across damage protocols, mass sweeps, and phase-mode ablations as a single scalar benchmark.", "Falsifiable by cases where high transfer is achieved without edge localization or where strong edge localization persists but slip density destroys transport quality." ], "animation": { "status": "planned", "path": "" }, "image": { "status": "planned", "path": "" }, "duplicateWarnings": [], "review": { "date": "2026-03-09", "equationId": "eq-boundary-reroute-recovery-index", "score": 84, "scores": { "tractability": 18, "plausibility": 19, "validation": 16, "artifactCompleteness": 4 }, "novelty": 27, "llm_scores": { "traceability": 72, "rigor": 78, "assumptions": 88, "presentation": 84, "novelty_insight": 58, "fruitfulness": 86, "llm_total": 77, "justification": "A clear, simulation-ready dashboard observable built from existing recovery metrics with explicit assumptions, but it lacks a strong derivation bridge and explicit recovery lineage to specific leaderboard equations such as LB #2, #7, and #10." }, "llm_model": "gpt-5.4", "blended_score": 80 } }, { "submissionId": "sub-2026-03-09-entropy-gated-edge-recovery-score", "submittedAt": "2026-03-09", "submitter": "RDM3DC", "status": "promoted", "name": "Entropy-Gated Edge Recovery Score", "equationLatex": "E_{\\mathrm{edge}}(t)=\\frac{\\eta_{\\mathrm{tr}}(t)\\,f_{\\partial}(t)\\,f_{\\mathrm{top}}(t)}{1+\\rho_{\\mathrm{slip}}(t)}\\,\\exp\\!\\left[-\\gamma\\,|S(t)-S_{\\mathrm{eq}}|\\right]", "description": "Entropy-gated recovery score for damaged adaptive topological transport. The score rises when transfer efficiency, boundary localization, and top-edge rerouting are all strong, is suppressed by slip density, and is further reduced when the system entropy deviates from its equilibrium recovery band. It is intended as a compact observable for comparing recovery quality across damage and ablation protocols.", "source": "QWZ Recovery Dashboard", "units": "OK", "theory": "PASS-WITH-ASSUMPTIONS", "assumptions": [ "Transfer efficiency eta_tr(t), boundary fraction f_partial(t), top-edge fraction f_top(t), slip density rho_slip(t), and entropy S(t) are measured over a common time window.", "Effective recovery requires simultaneous transport restoration and edge rerouting after damage.", "Slip density degrades recovery quality by disrupting coherent edge-guided transport.", "Entropy deviation |S(t)-S_eq| acts as a penalty for operating away from the recovery-favorable regime.", "The coefficient gamma is a positive sensitivity constant controlling how strongly entropy mismatch suppresses the recovery score." ], "evidence": [ "Built from observables already tracked in the recovery dashboards, including transfer efficiency, boundary fraction, top-edge fraction, slip density, and entropy.", "Reduces to a purely transport-edge score when S(t)=S_eq, isolating the entropy gate as the added mechanism.", "Drops when slip density rises even if edge localization remains high, matching the qualitative loss of useful recovery.", "Penalizes over-driven or off-band states where transport may persist but entropy indicates the lattice is outside the stable healing regime.", "Falsifiable by comparing runs with similar edge rerouting but different entropy trajectories and testing whether the lower-entropy-mismatch runs yield better sustained recovery." ], "animation": { "status": "planned", "path": "" }, "image": { "status": "planned", "path": "" }, "duplicateWarnings": [], "review": { "date": "2026-03-09", "equationId": "eq-entropy-gated-edge-recovery-score", "score": 87, "scores": { "tractability": 18, "plausibility": 20, "validation": 16, "artifactCompleteness": 4 }, "novelty": 29, "llm_scores": { "traceability": 72, "rigor": 84, "assumptions": 88, "presentation": 86, "novelty_insight": 68, "fruitfulness": 90, "llm_total": 81, "justification": "A clean, simulation-ready composite observable with explicit assumptions and a sensible entropy gate, but it lacks an explicit derivation lineage to specific leaderboard entries and is more a useful dashboard metric than a major mechanistic extension." }, "llm_model": "gpt-5.4", "blended_score": 83 } } ] }