Equation Certificates
Signed equation records used for chain provenance and version tracking.
Published at: 2026-03-29T05:16:38.905250+00:00
Node endpoint:
http://3.20.240.88:5000Certificates: 118
Data files:
data/certificates/equation_certificates.json and data/certificates/chain_publish_receipt.jsonCertificate Index
| Equation ID | Name | Score | Metadata hash | Equation hash |
|---|---|---|---|---|
core-phase-ambiguity |
Phase Ambiguity (multi-valuedness axiom) | 83 | 927f296525fdcdf8c6c6… |
af833b2e82c397d91d0a… |
core-phase-lift |
Phase-Lift operator definition (⧉) | 69 | caf38d093ff0a8bcdbb4… |
161f7417186f299054d7… |
core-unwrap-rule |
Deterministic Unwrapping Rule | 80 | 0f394fd70634555134b6… |
123dbe79dde820d81c56… |
core-path-continuity |
Path Continuity (Stateful Phase-Lift) | 66 | 61d802aa5e7acd577bf4… |
e7d074a9b0a9f23018bc… |
core-pr-root |
PR-Root as a special case of Phase-Lift (⧉√) | 60 | d7fd5f85070fcd3f8c84… |
aba97471f7efab0a52d4… |
core-winding-parity |
Winding Number + ℤ₂ Parity Invariants | 79 | 999628fd3744a5640d5f… |
1e09996967e842256319… |
core-conformal-metric |
Adaptive-π Conformal Scale Factor and Metric | 66 | 0f622ffea7da9cf93ddb… |
bd8e7fd48f7d6a385980… |
core-adaptive-arc-length |
Adaptive Arc Length | 50 | 78414f9a2171b6033582… |
6e409912e5e5491c0685… |
core-pi-a |
Adaptive-π field definition + limit (πₐ → π) | 67 | b34afedba5f86b2ac7dd… |
da74a65a71d40c18ca6f… |
core-pi-a-dynamics |
Reinforce/Decay Dynamics for πₐ | 70 | d594a8adb21bf06c7e5f… |
133b09d7f1d0d7fb4293… |
core-arp-ode |
ARP Core Law (canonical ODE) | 83 | b66c22d4f3eebf8fce76… |
bc49bf0ceb5207e9abc3… |
core-curvature-salience |
Curvature as Salience (Curve-Memory Primitive) | 83 | 246c3eac53bc5dba9e9f… |
fbc0df0e932778f2be3f… |
core-reinforce-decay-memory |
Reinforce/Decay Memory Law (generic) | 73 | 4edfcfd9f7ad75032aa5… |
46009270e4870b2b8203… |
core-phase-lifted-stokes |
Phase-Lifted Stokes Quantization (Adaptive-π) | 64 | 918e70c60f1039f08c82… |
6fde1b2e0d1285679304… |
eq-arp-redshift |
ARP Redshift Law (derived mapping) | 91 | df3b6236fe5b4ae0c52b… |
1b09a03c9d0d5f657bb5… |
eq-bz-phase-lifted-complex-conductance-entropy-gated |
BZ-Averaged Phase-Lifted Complex Conductance Update (Entropy-Gated) | 97 | 00cac17115d8b53cc97c… |
7995d0ace9e88c24e08d… |
eq-ahc-parity-flip-rate |
AHC Parity Flip-Rate (locking observable) | 87 | ca869692de23184a5fc8… |
e4a9f4422d8a7c86af03… |
eq-qwz-bz-avg-ruler-mass |
BZ-Averaged Ruler Coupling for Single-Jump QWZ Transition | 86 | 6ede2bce62345158f2cc… |
4b6980a162a4982ee5be… |
eq-ahc-step-limit |
AHC Adaptive Step-Limit Update (πₐ clip) | 81 | 164e13a77ea37700182c… |
a3e665688c986254831e… |
eq-qwz-pia-modulated-mass |
pi_a-Modulated QWZ Mass (momentum-dependent; re-entrant transitions) | 80 | 4b1423eb897826f9909d… |
4e22ea5e116ac3a3b76b… |
eq-ahc-running-winding |
AHC Running Winding + Parity | 79 | d6e56dd4972346dfedb4… |
42aa5381edfbfeef2314… |
eq-arp-phase-critical-collapse |
Phase-Coupled Stability Threshold Law | 77 | 344ce3d57cc5e8f9fdf1… |
d24565a4b4c287c2778c… |
eq-ahc-pi-a-update |
AHC Adaptive πₐ Update (discrete) | 76 | 1b8122cc1e7ffa92e7b0… |
4fa2045fce35744a79d9… |
eq-arp-redshift-bounded-oscillation |
ARP Redshift Law with Bounded Oscillatory Steering | 73 | 9a26bf5f72245e447fb0… |
31332939be13a30edf6f… |
eq-arp-phase-lifted-complex-conductance |
Phase-Lifted Complex Conductance Update | 71 | 476e5b9532e903f0688d… |
89ccac2150b3ade9f4e6… |
eq-ahc-candidate-unwrap |
AHC Candidate Unwrap (standard 2π lift) | 70 | 7006a274c660fbde6144… |
d130b069dea3d89147fa… |
eq-ahc-residual |
AHC Residual | 70 | db272e41f96de6f77593… |
9c0ba62b902a1f2e25c6… |
eq-arp-temp-conductance |
Temperature-Dependent Conductance Law | 69 | 9441b0f7f85cfc19f0f2… |
3f204e25c7c3b32ca9ef… |
eq-ahc-event-stimulus |
AHC Event Stimulus (phase-jump indicator) | 69 | 42aebea84892bd6180c8… |
10e8e42a4c149975e99c… |
eq-arp-lyapunov-stability |
ARP Lyapunov Stability Form | 66 | 0a78fb7b6f7449d96ee0… |
743378804c5e99f36983… |
eq-arp-gradient-flow-bridge |
ARP as Gradient Flow in Adaptive-π Geometry | 66 | 95413a0892601c50596c… |
375a855e235ab3a14cf3… |
eq-curve-memory-137 |
Curve Memory Fine-Structure Emergence | 63 | 942142182196dc79b747… |
d1e757903ab9e338b85c… |
eq-shield-mechanic-arp |
Shielding Mechanism Law (ARP) | 63 | 723ab47d20371ec3298b… |
3ceffa88fbc85095109d… |
eq-parity-pump |
Parity Pump (πₐ-gradient ℤ₂ flip mechanism) | 63 | 56c12a9e2d04d6a23b3f… |
cba4c290545a8f381f52… |
eq-dyn-constants-union |
Unified Dynamic Constants Law | 61 | c1cb6b5d7f811241e3ea… |
c47e35c02b72cbef0fec… |
eq-pi-a-gauged-phase-lift |
πₐ-Gauged Phase-Lift (adaptive unwrap + invariants) | 61 | 603771982545e08ac064… |
476f191e0b0a92f150b0… |
eq-redshift-arp-superc |
Redshift-ARP Superconductivity Law | 60 | 8de1f2159a94f88ed7da… |
5bbc0f7f2d5d52759d1f… |
eq-adaptive-phase-lift-unwrapping |
Adaptive Phase-Lift Unwrap Recurrence (pi_a-gauged) | 60 | 4d4a516e41f107ca2651… |
1175dbd16639e1177075… |
eq-arp-weighted-dirichlet-energy |
Weighted Dirichlet Energy (ARP learns Omega-geodesics) | 60 | fd743d2f24761e29a6d5… |
38ece0389d04bd76f682… |
eq-un-det-phase |
U(N) Det-Phase on Lifted Branch | 59 | 67f271438e2c6b4c28c3… |
2cd499d20a446b843b67… |
eq-adaptive-connection-chern |
Adaptive Connection and Adaptive Chern Number (Theorem B candidate) | 59 | 151abde85b3ec7663d11… |
6c05ec834d611e71a19d… |
eq-parity-from-adaptive-chern |
Parity Pump Law from Adaptive Chern | 59 | 61c2a82c82e4add3e68f… |
c1f14a4796b5a6a7aedf… |
eq-cm-integration-state |
Curve-Memory Integration State (unified closed loop) | 57 | 902d8f02d1ede7af1485… |
7b59b3d78750a843b00d… |
eq-un-wilson-holonomy |
U(N) Wilson / Holonomy | 56 | d8d18e13b9e9ba9a9632… |
57f9c4ea3c030bbb597b… |
eq-dimensionless-phase-flow |
Dimensionless Lifted Phase Flow (pi_a-driven pump term) | 56 | 23975c710a0ada7df040… |
3a2c4d88e900b254e99f… |
eq-adaptive-monodromy-spectrum |
Adaptive Monodromy Spectrum (bifurcation framework) | 54 | 58c98d48caf95d799a38… |
6fd2664b85496fbed7fa… |
eq-adaptive-discriminant-set |
Adaptive Discriminant Set for Parity/Winding Stability | 53 | daf3a74e41e71fecb4a8… |
c1e947ed9143331b1517… |
eq-qwz-engineered-single-jump |
Engineered Pinch-to-Transition Mass Drive (single-jump toy) | 51 | cb8036eea63827c7331e… |
f5a6fb396c5f8659d29d… |
eq-paper1-adler-rsj-phase |
Phase (Adler/RSJ) Dynamics | 96 | eb98c6de4f50d21cf62c… |
d1db8f6d18b7bd7b499d… |
eq-paper1-arp-reinforce-decay |
Generic ARP Reinforce/Decay Law | 93 | eae925f7074669631355… |
80a9b3ded5b4214e8bc7… |
eq-paper1-activity-closure |
Activity Closure A = G|sinφ| (Parity Lock Mechanism) | 91 | 111f426bccb6cb583e6e… |
cf7a6acb1988fe0bf75e… |
eq-paper1-slip-asymptote |
Slip-Regime Asymptote (1/π Signature) | 93 | 31e617fa74ad86b0baa9… |
34340e53d87e072682d4… |
eq-paper1-langevin-noise |
Noise-Robust Langevin Extension (Rounded Transition) | 84 | 8959d7aea4a4b157156b… |
194c6b0e92b8bf1bc62d… |
eq-paper1-qwz-hamiltonian |
QWZ Chern-Insulator Hamiltonian (Reference Form) | 94 | 89d4e63f35e49293f0b7… |
492fd052575e149b509a… |
eq-paper1-adaptive-geometry-mass |
Adaptive Geometry → Effective Mass Channel (Step-2 Coupling) | 86 | af392372b18d579942b1… |
f5d9c6493a44c89f5ac8… |
eq-paper1-chern-marker-bianco-resta |
Real-Space Chern Marker (Bianco–Resta, Open Boundaries) | 90 | 0b2ccf18be8c9984b947… |
d093d91d8d1a29448b7f… |
eq-mesh-synced-certificate-consistency |
Mesh-Synced Certificate Consistency | 55 | 8b66dc6dc81573ae50d7… |
cbb1551f6c1990850220… |
eq-adaptive-entropy-production-rate-aepr |
Adaptive Entropy Production Rate (AEPR) | 51 | f9389868fee7a8adb92c… |
193614a6170590243f02… |
eq-adaptive-entropy-production-rate-aepr-e-aepr-2 |
Adaptive Entropy Production Rate (AEPR) | 82 | 215b0ea7e1debb95fd44… |
5a3f3564840e02624ca0… |
eq-hlatn-white-paper-eqn-7 |
HLATN_White_Paper — eqn 7 | 54 | fcb654c05fa65b9b93b8… |
2ba796cbf46df647aba5… |
eq-hlatn-white-paper-eqn-10 |
HLATN_White_Paper — eqn 10 | 50 | aa02597ab6575a9ec0a8… |
1b9033403cf400cf8d0e… |
eq-hlatn-white-paper-eqn-11 |
HLATN_White_Paper — eqn 11 | 51 | 40733032e946e94c1569… |
ad8f63edfc00de231ec4… |
eq-hlatn-three-force-conductance-lock |
HLATN Three-Force Conductance Lock | 82 | c547cc0af18412afa80c… |
f944e4196b40c905b14d… |
eq-hlatn-phase-lift-branch-safe-update |
HLATN Phase-Lift Branch-Safe Update | 81 | 74a62fe4b399408e6526… |
727ea4aa8c9ace0b1ca1… |
eq-hlatn-plaquette-holonomy |
HLATN Plaquette Holonomy | 87 | a554d4a49e3dd1154fc2… |
55e25b3f97eb4e330db7… |
eq-entropy-modulated-phase-lift-conductance-equation-em-plc |
Entropy-Modulated Phase-Lift Conductance Equation (EM-PLC) | 86 | dc947cec8f5e0f81266e… |
cdb60bd1b57223467514… |
eq-egatl-phase-coupled-conductance-update |
EGATL Phase-Coupled Conductance Update | 87 | 69b24d6c29b7309632cc… |
0e0eefe3e5c6e217a0fc… |
eq-slack-test-equation |
Slack Test Equation | 58 | d32a267ef69485e1ce4a… |
71ae568220c2da0ff73f… |
eq-adaptive-entropy-production-rate-aepr-ate-aepr |
Adaptive Entropy Production Rate (AEPR) | 69 | e9fb18282bbaaad1168f… |
b26fbaf3d0810839aaa9… |
eq-adaptive-damped-harmonic-oscillator |
Adaptive Damped Harmonic Oscillator | 52 | 8b9d63a821c18ad9ad1a… |
c0e7553873516af8e2e1… |
eq-grok-surprise-augmented-phase-lifted-entropy-gated-condu |
Grok Surprise-Augmented Phase-Lifted Entropy-Gated Conductance Update | 97 | a385b9d0adc2b1c10771… |
c7c9a94fdcd996f29063… |
eq-gemini-curve-memory-topological-frustration-pruning |
Gemini Curve-Memory Topological Frustration Pruning | 96 | 490b4162e6912e060783… |
3e55f275b3de154625b2… |
eq-egatl-hlatn-aepr-adaptiveentropyproduction |
EGATL-HLATN-AEPR-AdaptiveEntropyProduction | 91 | a15eec70bd72fb7e5020… |
5a3f3564840e02624ca0… |
eq-egatl-hlatn-threeforceconductance |
EGATL-HLATN-ThreeForceConductance | 91 | 4a26c07e85c0cb46e2ea… |
d178ce97d178b44b7f1e… |
eq-egatl-hlatn-phaseliftupdate |
EGATL-HLATN-PhaseLiftUpdate | 87 | 2a3f0097adc56e2eaa77… |
d25300a3706775691515… |
eq-egatl-hlatn-adaptiveruler |
EGATL-HLATN-AdaptiveRuler | 87 | ad5dae7cb8fd45517f7a… |
cf9ccc190743818f8dbf… |
eq-egatl-hlatn-plaquetteholonomy |
EGATL-HLATN-PlaquetteHolonomy | 93 | cf311155dd75fac3145f… |
1e7e4c62729ef4430b62… |
eq-egatl-hlatn-parityfliprate |
EGATL-HLATN-ParityFlipRate | 81 | a86b9e01697dfd5d2061… |
3c3d15d575775174181f… |
eq-mean-event-equilibrium-for-adaptive-discrete |
Mean-Event Equilibrium for Adaptive πₐ (discrete) | 87 | 4dce05a1e45463eea936… |
b02544ef0d32e473b111… |
eq-topological-coherence-order-parameter-arp-locking |
Topological Coherence Order Parameter (ARP Locking) | 96 | 53430cc89d229f1fe744… |
a2d47eb3f7404643b314… |
eq-phase-lift-clipped-unwrap-branch-safe |
Phase-Lift Clipped Unwrap (Branch-Safe) | 70 | ee35e66c62724c02912a… |
aa4ad72f6eb929b578db… |
eq-adaptive-bound-dynamics-event-driven-geometry |
Adaptive-π Bound Dynamics (Event-Driven Geometry) | 70 | 01b792d363216abc0353… |
e8411bd82dc4c2ba96a5… |
eq-winding-parity-estimator-and-flip-rate-order-parameter |
Winding–Parity Estimator and Flip-Rate Order Parameter | 70 | b5368cadfcde668f90c3… |
ff78cf788aa83fe18321… |
eq-entropy-gated-complex-conductance-arp-network |
Entropy-Gated Complex Conductance (ARP Network) | 71 | 23e15cc0b549d6fbfd89… |
84fb5222d513c95ce7be… |
eq-entropy-production-event-injection-s-field |
Entropy Production / Event Injection (S-Field) | 70 | cfa9bb5fa6de560f0648… |
23f509b3bf6ba6697e83… |
eq-phase-coupled-suppression-conductance-law |
Phase-Coupled Suppression Conductance Law | 71 | 77f61b76f4902bce2910… |
c9baf70c48742bac27a4… |
eq-arp-redshift-law-with-bounded-oscillatory-steering |
ARP Redshift Law with Bounded Oscillatory Steering | 71 | 9ce8a3dd138b260c35e0… |
35fc6afec450aa1eaf10… |
eq-adaptive-ruler-qwz-effective-mass-geometry-induced-trans |
Adaptive-Ruler QWZ Effective Mass (Geometry-Induced Transition) | 70 | 867118fd90a33a9cc40e… |
1abc090698182468e6d8… |
eq-phase-resolved-operator-general |
Phase-Resolved Operator (General) | 71 | a54978773f609321cf17… |
00e48641fcbc8c96111b… |
eq-branch-fault-criterion |
Branch Fault Criterion | 70 | 9592e2a69cd755f38eee… |
02c26bf7eee5ded75a2a… |
eq-history-resolved-phase-with-adaptive-ruler |
History-Resolved Phase with Adaptive Ruler | 107 | 1003f1e2591d14ae4b6a… |
0ea8c453b5ff67197651… |
eq-phase-lift-commutator-bound |
Phase-Lift Commutator Bound | 72 | 769e194d61c9c096d9de… |
7566049c5cabf3f6fe4f… |
eq-adaptive-topological-self-healing-conductance-law |
Adaptive Topological Self-Healing Conductance Law | 85 | 6be69c99ba845a177fec… |
16fb70ed218378939c50… |
eq-surprise-augmented-history-resolved-complex-conductance- |
Surprise-Augmented History-Resolved Complex Conductance with Curve-Memory Pruning | 81 | 18076dba3f0dc03e7762… |
0e80af9817b1c9008709… |
eq-adaptive-chern-self-healing-conductance-law |
Adaptive Chern Self-Healing Conductance Law | 81 | 4df404a2ff841ea04474… |
877e117de0bb9065a1e1… |
eq-adaptive-chern-self-healing-conductance-law-ctance-l |
Adaptive Chern Self-Healing Conductance Law | 100 | fb07c62638cef04a7f61… |
527491748006ee8f65e5… |
eq-phase-lifted-thouless-pump-memory-law |
Phase-Lifted Thouless Pump Memory Law | 79 | 6f39b05de3918f06ed6e… |
fa49adbbc21769f64c0e… |
eq-landauer-phase-lift-conductance-law |
Landauer-Phase-Lift Conductance Law | 81 | 314804b722d02720367f… |
b05a797b1b5261bf4e7b… |
eq-phase-lifted-rg-memory-flow |
Phase-Lifted RG Memory Flow | 84 | 889a9953c957a3fa2ac5… |
15cc171a5a57f8753485… |
eq-directional-strength-proxy-chern-law |
Directional-Strength Proxy Chern Law | 86 | 6bf3b5cafe7b02a16992… |
c578da110eab99d9f6f2… |
eq-slip-suppressed-edge-recovery-law |
Slip-Suppressed Edge Recovery Law | 84 | a8abb7921e207a40802a… |
ce86b099f0bf4fedf23a… |
eq-newton-s-second-law |
Newton's Second Law | 69 | f42ecbeb815bfd00ed48… |
8d87226e092722f6299b… |
eq-boundary-reroute-recovery-index |
Boundary-Reroute Recovery Index | 84 | a42d6fc1f9f19b6bdc29… |
fdc01084449147d9a4f1… |
eq-entropy-gated-edge-recovery-score |
Entropy-Gated Edge Recovery Score | 87 | 4de074c8ebf82b5efd76… |
72f068d0afc4a99a9624… |
famous-schrodinger |
Schrödinger Equation | 74 | 5c1d136e374ce2d95b4d… |
d47e8c4cd7500d380a42… |
famous-aharonov-bohm |
Aharonov–Bohm Effect | 74 | 438315df0961068ea72c… |
305e553474133239b10f… |
famous-berry-phase |
Berry Phase | 69 | 0e9f5509ea45a69fd648… |
02c6aafa23c27da84f48… |
famous-josephson |
Josephson Relations | 67 | 3f6371c87916018aad4d… |
28310b8b01e83e8a41ec… |
famous-maxwell |
Maxwell's Equations | 70 | abad3db3e745960ffbf8… |
23b2bb04f0ad72ae8ff4… |
famous-dirac |
Dirac Equation | 63 | 2b3e518deeb329c15504… |
ec960dcca00afa05b981… |
famous-euler-lagrange |
Euler–Lagrange Equation | 70 | 954e89c9842d5a41c6a0… |
69eb041d36633488eead… |
famous-navier-stokes |
Navier–Stokes (Vorticity Form) | 63 | 425010aa4f807547242f… |
29e0071634e429d71b4d… |
famous-path-integral |
Feynman Path Integral | 63 | 7cae86b24757abacf80c… |
085f4007879bae909dde… |
famous-holonomy |
U(N) Gauge Holonomy | 63 | ccbfb0363fe13cd68911… |
97d0c661b61349202e4e… |
famous-klein-gordon |
Klein–Gordon Equation | 63 | cb44becd1778404dae0c… |
1582f75bd5522248f2f1… |
famous-einstein-field |
Einstein Field Equations | 57 | 891e2a7e7f83dd6bded5… |
91fe07d587409b9b5897… |
famous-fourier-heat |
Fourier Heat Equation | 70 | fcb058443fade5ce6a0e… |
fed194fa4d3ef2a55854… |
famous-noether |
Noether's Theorem | 69 | 6cfb35ef35adbfc5f954… |
a0cf0fabf2235ba27c6f… |