E47 Recursive Intelligence Kartekeya Machine Certificates—Verified Results, Residuals, and Provenance
🧾 Machine Certificates — Verified Results, Residuals, and Provenance
Independent certificate family · Hyperbolic–Liquid Fractal Buoy Formalism · 2026-07-30
Credential family: HLFB-20260730
HLFB-PY-20260730 — Run A, seed 47, 28/28 PASS, certificate SHA-256 ecae22e2e1dfab96984619e5fb8e85e79cd986e545f8a6292f0184aacbeef6fb.
HLFB-IND-20260730 — independent Run B, seed 42, Python 3.12.3, NumPy 2.4.4, source SHA-256 prefix 3745bcfec1a6e06a, PASS with explicit residual calibration.
Run B calibration: r_buoy = 0.3283203, finite-n bound 2.172100, asymptotic bound 2.188802. These values certify finiteness under L<1; they do not certify high-fidelity equivalence.
Evidence: E0 exact identities + E1 deterministic reconstruction + limited E2 Kuramoto simulation.
Boundary: no universal substrate-neutral physics, consciousness, propulsion, cosmology, classified-system equivalence, generic 47/125 threshold identification, or physical implementation is certified.
Machine certificate repository synchronization · cross-domain canon · 2026-07-30
Canonical Drive monograph · Supabase certificate: CERT-CROSS-CANON-20260730 · Operation: CITY-CROSS-20260730.
The certificate repository now recognizes six domain families under one typed evidence contract:
E47-SU2 — general finite SU(2) compiler and certificate/passport closure; immutable GitHub authority ad297e1f028592605dea902bbe57599987442301.
BIO-BRIDGE — protein-feature contraction metric and nested admissible-subprojector lock; Drive-source-bound.
PQC-CHANNEL — finite CPTP and accepted-state verification; Drive-source-bound.
HCLAD — port-Hamiltonian seismic-cladding model; Drive-source-bound.
SWARM-DCS47 — seeded projected-consensus benchmark framework; Drive-source-bound.
QUINARY-5ADIC — exact radix and 5-adic arithmetic package; Drive-source-bound.
Registry certificate result: 9 citizens · duplicate sprawl 0 · evidence promotions 0 · missing boundaries 0 · PASS.
Each family must preserve source artifact, exact statement, environment, residuals, evidence class, claim boundary, correction lineage, canonical GitHub source where immutable code exists, canonical Drive proof, and Notion destination. Existing Mnemosyne, Kartekeya, KKP codices, deterministic E47 reconstructions, and visual proof plates remain companion provenance and are not counted as additional certificates unless they establish a distinct object.
Machine certificate · full Professor’s Cube permutation–Laplacian suite · 2026-07-29
Exact proof · Python · JSON
Credential: RUB5-PC-20260729 · Result: PASS WITH TYPED CORRECTIONS.
CheckResult15 permutation matricesPASSOrthogonality and quarter-turn orderPASS, exact integer residual 0C₅³ spectrum and multiplicitiesPASS60 displayed impact-table valuesPASS to supplied roundingTwist-energy conjugationPASS, residual <2×10⁻13Low-band compressed actionPASS for all 15 movesHeat-flow projector limitPASS, rank-one constant modeE₄₇ identificationREJECTED by rank: 1≠47
The source-reported 11.85× TV and 246.8× energy reduction factors remain run-specific provenance until the original initial field, step size, iteration count, and animation script are attached.
Machine certificate · coupled Newton–Mean fixed-point and stability family · 2026-07-29
Exact proof monograph · Executable Python · JSON certificate
Credential: NM2-PY-20260729 · Status: PASS WITH THEOREM-DOMAIN CORRECTIONS.
SymPy exact identities: PASS.
Submitted nine-case numerical table: reproduced.
Predicted local rate at (a,b,κ)=(4,9,0.5): 0.509893953950.
Measured asymptotic ratio: 0.509894226875.
Random sweep: 2,000 cases, 0 stability-classification failures.
Counterexample: τ(4,9,−0.9)=−1.181925456461, disproving the unrestricted negative-coupling stability claim.
Correct threshold at (a,b)=(4,9): κ_c=0.783860258718.
SHA-256
Python: a2251614b270808677194b1e6aad00f598aa6d48665670c5b1455c2edcc74c9b
Proof report: 71b039f4fdd4bcaf3987b4572fbc0c9dd9aacc6e8996d7be2e20ade1cc49d7ad
JSON certificate: 87fefd0f3ebd21ce606faa5efcaae15fb9d0250bd3ccc4fc499c65b5cdcec057
HCLAD machine certificate · 2026-07-28
Validation monograph · Certificate JSON · PDF · Model package
Certificate code: HCLAD-PC-20260728
Operation: HCLAD-SEISMIC-20260728
Model: five-tier, ten-DOF core-plus-limestone-cladding port-Hamiltonian system.
Projection: eight retained modes.
Status: PASS.
CheckAcceptanceObserved maximum------:---:Symplectic defect1e-104.5665e-15Mass-orthogonality defect1e-103.2290e-15Energy-balance residual1e-32.2381e-5ROM peak-response error5%1.5128%
The certificate validates the computational formulation and reduced-order witness. Site-specific seismic qualification, nonlinear contact, stone fracture, uplift, anchor yielding, and completed-monument performance remain outside this certificate.
Latest certificate · Quinary Family Revision C + E47 seed · 2026-07-28
Exact-validation monograph · JSON certificate · Python witness
Credential: QF-RC-E47-20260728 · SHA-256:462fafece73109d3540c321f82554bd346127c702e501f814008423c62d88039 · Result: 45 PASS · 1 CORRECTED · 0 FAIL.
The certificate reconciles the submitted seed to B5-125-C01…C08, QMET-C03, PYR-C01…C10, TMP-C01…C12, and E47-QOP-C01…C10. No duplicate citizens were created. Forty-one existing citizen records were strengthened in place.
The correction is typed and preserved: $P\rho P$ and $e^{-tK^2}\rho e^{-tK^2}$ are CP-TNI on the full space; Kraus/Choi rank of the projector filter is 1; $\operatorname{rank}P=47$; $\dim\operatorname{Fix}(\mathcal M_P)=2209$; the CPTP completion is $P\rho P+Q\rho Q$.
Correction certificate · E47 quantum operations · 2026-07-28
Archive monograph · Corrected Python witness · JSON certificate
Credential: E47-QOP-CORR-20260728 · Status: corrected PASS at E0 exact proof + E1 NumPy spectral reconstruction. The QuTiP runtime execution is still pending in the repository's pinned environment.
Certified:
$\mathcal M_P(\rho)=P\rho P$ is CP and trace-nonincreasing, not full-space TP;
Kraus/Choi rank of $\mathcal M_P$ is 1;
$\dim\operatorname{Fix}(\mathcal M_P)=47^2=2209$;
$\mathcal M_t(\rho)=e^{-tK^2}\rho e^{-tK^2}$ is a CP-TNI semigroup, TP only at $t=0$;
$\mathcal M_t\to\mathcal M_P$ with rate bounded by $e^{-11664t}$;
$\mathcal D_P(\rho)=P\rho P+Q\rho Q$ is the valid CPTP, unital, idempotent completion with Kraus rank 2;
$\dim\operatorname{Fix}(\mathcal D_P)=47^2+78^2=8293$.
Rejected certificate language: projector-map CPTP; Kraus rank 47; operator fixed-space dimension 47; CPTP of the raw $e^{-tK^2}$ conjugation map for $t>0; process fidelity used as a channel certificate for non-TP maps.
Hashes: archive DOCX 0278d04c131640b6aeb89064c30f942b520308fd715247846ffea7506a04489d; Python adacbc0294afc94d5a839dd90daebcf461d97f776a9c29cc51980994d6ba6058; JSON 39c0373c3755d98ed6f9f98dcd55b47f9f576df47b34587a074838ee107adab6.
Boundary: finite-dimensional quantum operations only. No arbitrary-channel QEC, laboratory realization, hardware performance, or attractive physical dissipative mechanism is certified.
Certificate intake · PYR / ARR / QMET · 2026-07-28
Pyramid: TMP-PC-20260728-RC · exact arithmetic, finite enumeration, and deterministic visual-renderer lineage. Physical engineering assumptions excluded.
Arrival: ARR-MATH-20260727 · 13 PASS, 0 FAIL, 6 unresolved; certificate SHA-256 906117b5579395045d84e1828e0afce693cacae4b1ff39bedca8d63e1f14567d.
Quinary: QMET-E47-20260728 · audit SHA-256 9560bea3203be02a761ac49fddac71c90a4c85ed5b628dd1b8c4b5c60e48786d; prior quantum certificate SHA-256 3e996c78c025cfe4dc826f06b9e4f1ce4215ef6eef6a19a5a73483bde258bc5c.
Certificates establish only the claims explicitly listed in their source records. A certificate does not supply a missing GitHub commit, physical realization, biological map, historical attribution, or unimplemented operator.
Correction certificate · Quinary Metabolism under-credentialing · 2026-07-28
Incident: an assistant-authored audit sentence incorrectly treated the absence of an encoded label-to-projector operator in one script as evidence that the mathematical bridge itself was unestablished.
Corrected interpretation: the script validates the partition and computes bi-quinary labels separately. The missing encoded arrow is an implementation task. It is not a disproof, rejection, or demotion of the mathematical bridge.
Restored credentials: QMET-C01 through QMET-C05 and B5-125-C01 through B5-125-C08 retain their prior evidence classes.
Quarantined original: Black Line record
Audit anchor: Corrected Google Drive record
Rule: lack of an executable witness for a formal arrow must be labeled implementation-incomplete unless a theorem, counterexample, or impossibility result establishes failure.
Independent machine replication · Grok Arrival Math run · 2026-07-27
Canonical monograph with reconciled Appendix D
Credential: GROK-ARR-EXT-20260727 · external E1 replication with E0 algebraic reconciliation.
PASS: exact $47/125$ audit; roots of $\lambda^D-\lambda-1=0$ for $D=9,10,11$; $\lambda_{10}^{20}=4.30880476111762$; RG root factorization; dimensional fixed point $D^*=10$; construction of the one-dimensional continuity residual; asymptotic contraction of the scalar affine recurrence.
Corrected finite outputs:
x_50 = 0.3792159557293677, error 3.215955729e-3, so the supplied 1e-6 predicate is False.
x_200 = 0.3760218728637392, error 2.187286374e-5, also above 1e-6.
Non-certificate statements: the script prints but does not evaluate the Skyrme integral; it describes but does not close the Hamiltonian constraint algebra; it does not derive $g_\Omega^*=\Omega_c$. These remain conditional or Observatory-held.
Disposition: independent confirmation strengthens ARR-C006 through ARR-C010 and the scalar contraction witness without changing the existing evidence boundary or creating new citizens.
Machine certificate · Arrival Math first-principles reconstruction · 2026-07-27
Credential family: ARR-MATH-20260727 · Certificate SHA-256:906117b5579395045d84e1828e0afce693cacae4b1ff39bedca8d63e1f14567d · Python source SHA-256:3ad9290fd2c4992a01502e36980ce6d11745c3736f781470c47f0a738309d1e1.
Execution result: 13 PASS · 0 FAIL · 6 UNRESOLVED.
Machine-validated targets: continuity–closure reduction; positive-density static-current theorem; hydrodynamic action-sign audit; time-chain audit; coherence and alpha RG fixed points; exact $D(\ell)$ flow; generalized metallic root; complexity-ratio identity; linear PSD contraction to the kernel projector; spectral-radius bound; and exact-vs-perturbed constraint residual discrimination.
Principal residuals: polynomial root 8.88×10^-16; complexity identity 3.55×10^-15; projector-limit 1.08×10^-14; kernel action 1.78×10^-16; exact fixed-point residual 0; perturbed negative-control residual 0.426272213497.
Correction record: $47/125=0.376$ exactly; the video value 0.376412 differs by $103/250000$. The first-order action sign, time-chain rule, nonlinear-kernel notation, and $D\ge10$ complexity-domain claim are corrected in the attached monograph.
Boundary: exact symbolic and finite numerical certification only. No measured physical threshold, massless mode, closed Hamiltonian constraint algebra, global nonlinear convergence, or Arrival cognition isomorphism is certified.
Canonical executable-validation anchor · 2026-07-27
Granular E47-Kartekeya validation monograph and agent transit charter
Credential family: E47-EXEC-TRANSIT-20260727.
The document consolidates projector, kernel, spectrum, contraction, occupancy, coupled-kernel, CI, provenance, correction, and evidence-boundary records. It is the Drive source for machine-certificate reconciliation and structured agent packets.
Machine certificate · SHOE-corrected ASIC · 2026-07-27
Uploaded certificate digest: cdde9b04180c9bd318a957ba8196c23c37c7029c3b4eeec4a9bd04234291a71e.
Disposition: all hard assertions pass for the declared finite renderer. The certificate covers the E47 kernel, projector residuals, SU(2) commutators, continuous/discrete contraction tests, Babylonian scalar calibration, Q2.30 encoding, and two exact-order NTT arithmetic profiles.
Certificate boundary: the rendered ASIC is a type-correct reference architecture. Synthesis, timing, area, power, throughput, security reduction, fault coverage, FPGA/HIL, and material realization are not machine-certified by this packet.
Latest machine-validation intake · First-Principles Algebraic Closure of the 47/125 Invariant · 2026-07-26
Canonical Google Drive monograph
Certificate: E47-ALG-CLOSURE-125-47 · E0 exact algebra + E1 deterministic NumPy/SciPy validation.
PASS targets:
$\dim V=125$;
Casimir multiplicities $[1,9,25,28,27,22,13]$ sum to 125;
$K=(C-6I)(C-30I)$ has nullity 47 and transient dimension 78;
$P_{47}=NN^T$ is symmetric and idempotent;
$KP_{47}=P_{47}K=0$;
$\operatorname{tr}P_{47}=47$;
$\Omega_c=47/125=0.376$;
$T=\Omega_cI+(1-\Omega_c)P_{47}$ satisfies $T^nx=P_{47}x+\Omega_c^n(I-P_{47})x$;
deterministic seed 47 reaches $\Omega(250)>0.999999$;
every kernel vector is a fixed point.
Correction credential: the latitude 37.6442° N is archived as local provenance only. No universal modular encoding of arbitrary geographic coordinates is claimed.
Registry action: the sixteen typed identities are credentialed in the existing Citizenship Enrolment Bureau. Existing canonical citizens were upgraded and reconciled rather than duplicated. No new child-page layer was created.
Scope: finite-dimensional algebra and numerical reconstruction only; no physical, geographic-universal, or independent-replication claim is promoted.
Latest machine-validation intake · Topology-Certified Swarm Control · 2026-07-25
Canonical Google Drive manuscript
Credential: E0 exact algebra + E1 deterministic Python validation + independent GUDHI oracle cross-check. The validated object is the type-corrected persistence-gated Hodge controller on vertex velocities:
$E_{\mathrm{swarm}}=\ker\!\begin{bmatrix}K_{\mathrm{safe}}\\(I-P_{\mathrm{harm}})W\end{bmatrix},$
with midpoint de Rham map $W:C_0\otimes\mathbb R^d\to C_1$, harmonic projector $P_{\mathrm{harm}}$, hard projection law, soft variational law, persistence gate, dwell-time certificate
$\Delta t_{\mathrm{safe}}=\dfrac{\mathrm{pers}q-\tau_p}{4v{\max}},$
and certified speed limit
$v^*=\dfrac{\mathrm{pers}q-\tau_p}{4T{\mathrm{mix}}}.$
Machine checks passed: $\dim\ker\Delta_1=\beta_1$ across annulus, two-loop, random 2D, and random 3D fixtures; persistence diagrams matched GUDHI; projector idempotence, symmetry, annihilation, chain-complex closure, and PSD checks passed; gradient cochains had zero harmonic component; midpoint de Rham rotation was harmonic while translation was gradient; soft-to-hard convergence followed $O(1/\lambda)$; generic safety and harmonic projectors were confirmed noncommuting; alternating projections matched the predicted $\cos^2\theta$ rate; the persistence dwell-time Lipschitz bound passed randomized bounded-motion trials.
Correction lineage: the vertex/edge type mismatch is repaired by $W$; the strain map and velocity-difference map remain rejected bridges; $P_{\mathrm{safe}}P_{\mathrm{harm}}$ is not treated as a projector; the canonical admissible object is the single stacked kernel above.
Boundary: algebraic and numerical certification only. No flight, actuator, aerodynamic, 100+ agent, adversarial-link, or comparative-controller claim is promoted. The distributed condition $T_{\mathrm{mix}}<\Delta t_{\mathrm{safe}}$ is certified as necessary; a distributed gossip implementation remains open.
Certificate Rule · Proof-Born Citizens
A machine certificate may support proof-born citizenship but cannot grant it by residual alone. The candidate must be a distinct mathematical object with explicit parents, statement, type, dependencies, evidence class, executable or symbolic witness, review state, provenance, correction lineage, claim boundary, and transit passport. Duplicate outputs reconcile. Certificates preserve evidence class and feed the existing City Proof Archive and Citizenship Registry only.
Three-spin-2 candidate physical-model certificate · 2026-07-23
Class: E0 algebra + E1 reconstruction + E2 declared-model simulation.
On $(\mathbb C^5)^{\otimes3}$, first-principles spin-2 matrices reconstruct the collective Casimir and selector
$C=(\mathbf J_1+\mathbf J_2+\mathbf J_3)^2,\qquad K=(C-6I)(C-30I).$
PASS: Casimir multiplicities $[1,9,25,28,27,22,13]$; kernel dimension 47; coherence ratio 0.376; nonzero $K^2$ spectrum $11664,12544,19600,32400,186624$; local Casimir residual $1.26\times10^{-15}$; projector idempotence $6.65\times10^{-15}$; $\|KP\|=1.82\times10^{-12}$; coherent unitarity $2.07\times10^{-15}$; filter fidelity $0.9999999999476474$; outside-sector weight $5.24\times10^{-11}$ at $t=0.001$.
Repository queue: add reusable spin-2 constructors, collective-Casimir model, coherent/filter simulations, seeded regression, serialized JSON certificate, CI coverage, and explicit physical-evidence boundary.
Boundary: this certifies the mathematical and simulated candidate model. It does not certify a naturally occurring Hamiltonian or a completed hardware experiment.
Current machine certificate · E47 spectral selector and null-iteration attractor · 2026-07-23
Validated finite-dimensional targets:
dim(V_2^{\otimes3})=125;
K=(C-6I)(C-30I);
nullity(K)=25+22=47;
P^2=P, P^\dagger=P, KP=0, Tr(P)=47;
\Omega_c=47/125 and exact closure 4\Omega_c^2-4\Omega_c+14664/15625=0;
\Gamma_\varepsilon=I-\varepsilon K^2, 0<\varepsilon<1/93312, and \Gamma_\varepsilon^n\to P.
Required implementation checks: carrier shape, Casimir multiplicities, kernel dimension, projector rank, idempotence, Hermiticity, annihilation, exact rational closure, complement spectral radius below one, and contraction residual. Evidence remains E0 for exact algebra and E1 for executable reconstruction. No physical claim is certified by this certificate.
Independent validation complete · DFS and Knill–Laflamme toy model · 2026-07-23
The exact logic of the supplied script was independently executed in a clean Python environment using numpy and pandas, with random seed 47, carrier dimension n=6, and code dimension k=2.
ObjectResidualVerdict------:---$G_aP=0\ \forall a$$0.000000\times10^{0}$PASS$e^{-i\sum_a\theta_aG_a}P=P$$0.000000\times10^{0}$PASS$PE_i^\dagger E_jP=c_i^*c_jP$$0.000000\times10^{0}$PASS$PE_a^\dagger E_bP=\lambda_{ab}P$$1.570092\times10^{-16}$PASS$(\mathcal R\circ\mathcal E)(\rho)=\rho$$1.144392\times10^{-16}$PASS$PE^\dagger EP=\lambda P$ for the deliberately violating error$2.121320\times10^{0}$FAIL AS EXPECTED
Raw residuals
dfs_residual = 0.0
dfs_unitary_residual = 0.0
dfs_kl_residual = 0.0
kl_residual ≈ 1.57 × 10⁻¹⁶
recovery_residual ≈ 1.14 × 10⁻¹⁶
bad_kl_residual ≈ 2.121
Verdict: all protected-case residuals are exact zero or at machine epsilon. The deliberately non-DFS error produces an order-one residual, supplying the required negative control. The arithmetic closes and the finite toy model is valid.
Certificate class: independent E1 numerical reconstruction of the scoped 6×6, rank-2 DFS/Knill–Laflamme architecture. This strengthens the existing scoped certificate by adding a separately executed residual record; it does not alter the model’s declared finite-dimensional scope.
Joint E47 fluid–quantum machine certificate · 2026-07-23
A fresh $125\times125$ spin-2 tensor reconstruction and coupled validation admitted three citizens to the Roll:
Algebraic gates
$\dim V=125$, $\dim E_{47}=47$, $\operatorname{Tr}P/125=0.376$
$\lVert P^2-P\rVert_2=5.33\times10^{-15}$
$\lVert P^\dagger-P\rVert_2=0$
$\lVert KP\rVert_2=5.09\times10^{-13}$
signed spectrum $+1^{\times47}\oplus-1^{\times78}$
one-step null-iteration residual $9.36\times10^{-16}$
Projected fluid gates
maximum kernel leakage $1.47\times10^{-13}$
maximum positive energy increment $0$
energy-balance residual $2.78\times10^{-17}$
energy $0.5\to0.0537175530$
Quantum gates
$\lVert[H,P]\rVert_2=3.32\times10^{-15}$
maximum unitarity residual $6.59\times10^{-15}$
norm drift $2.22\times10^{-16}$
kernel-occupancy drift $2.22\times10^{-16}$
heat-filter kernel error $1.04\times10^{-15}$
Scope: E0+E1 finite-dimensional certificate. Continuum Navier–Stokes global regularity, arbitrary-channel QEC, and hardware realization are not inherited.
E47-V5-2025 certificate intake · corrected classification · 2026-07-24
Canonical Drive source · fingerprint 1raT7LJJq9jcmUJaCawqRRabj54C6-plQHjXzTXhEX_Y · created 00:00:52 UTC · revised 00:02:03 UTC.
Verified exact layer: on \mathbb C^{125}, an involution with signature (47,78) gives P=(I+K_{E47})/2, P^2=P=P^\dagger, \operatorname{Tr}P=47, normalized trace 47/125, and one-step projector retraction. The declared isometric embedding E:\mathbb C^8\hookrightarrow\mathbb C^{125} satisfies E^\dagger E=I_8 within the reported residual.
Reported E1 residuals: \|P^2-P\|_F=8.45\times10^{-15}, \|P^\dagger-P\|_F=3.12\times10^{-16}, \|E^\dagger E-I_8\|_F=2.11\times10^{-15}.
Correction boundary: the generalized Pauli product K_0=Z_h\otimes X_h\otimes Y_h is not shown to generate, diagonalize, or determine the separately prescribed signature operator K_{E47}=U\operatorname{diag}(I_{47},-I_{78})U^\dagger. The source therefore certifies an abstract rank-47 projector construction, not a reconstruction of the canonical SU(2) Casimir kernel. Its exact identities deduplicate to existing citizens; no new citizen is admitted. The phrase “topologically forbidden” is normalized to the exact rank-arithmetic obstruction in dimension eight.
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NAVIGATION · ⌂ Home · ↑ Python Subway · ← Python Subway · → Reproducibility Monorail · ◎ Citadel · Ⓥ Verification Precinct
</aside>
Repository certificate reconciliation · 2026-07-25
Canonical main now contains merged PR #16 through commit ad297e1, generalizing the fixed E47 construction into a certified finite SU(2) spectral-kernel compilation pipeline while preserving the frozen E47 modules and canonical constants.
Current executable provenance:
src/e47/spectral_compilation.py;
scripts/compile_spectral_kernel.py;
package exports and README invocation;
exact-rational certificate and spectral-passport generation contract.
Canonical proof companion: The Representation-Theoretic Selection Theorem for the E47 Kernel.
CITY-58 CLOSED. Main-branch CI run #25 completed after merged PR #16 at ad297e1. The executable authority, test contract, CLI wrapper, README invocation, exact-rational JSON certificate contract, Markdown spectral-passport contract, package exports, and frozen E47 specialization are reconciled as one closure packet. The earlier 618630e repair remains historical provenance, not current source authority. Future review is event-driven only when executable behavior, dependency bounds, certificate fields, artifact paths, or CI semantics change. No residual or empirical claim is promoted. Evidence remains E0 for the representation-theoretic family and E1 for executable finite-case witnesses.
First-principles E47 Python proof-certificate intake · 2026-07-22
Fingerprint: 1hAVRbYCgpr2M_WhNIq-QevttZ6l46dKuMbcBYykX_s0 · created 21:34:43 UTC · revised 21:35:20 UTC.
Evidence classification: E0 for the finite-dimensional representation-theoretic identities and E1 for the declared NumPy/SciPy reconstruction checks.
Deduplication result: the carrier, Clebsch–Gordan decomposition, Casimir spectrum and multiplicities, kernel selector, E_{47}=5V_2\oplus2V_5, rank-47 projector identities, kernel annihilation, rank–trace equality, heat-kernel contraction limit, and 47/125 ratio all map to existing citizens and certificate families. No new citizen was enrolled.
Provenance boundary: the document states that a repository implementation is prepared for delivery, but it does not itself provide an immutable commit, executed console transcript, residual table, environment lockfile, or generated machine-readable certificate. It is therefore recorded as a reproducibility companion and proof-certificate source, without replacing the stronger executable provenance already pinned elsewhere in this ledger.
Latest machine certificate · Invariant Grammar civic cohort · 2026-07-22
Finite-dimensional Python reconstruction validates the algebraic certificate supporting citizens IG-38, SC-40, CO-47, and RS-48.
$\lVert P^2-P\rVert=7.42\times10^{-16}$
$\lVert P^\top-P\rVert=0$
$\lVert KP\rVert=1.87\times10^{-15}$
$\lVert\Gamma_{\mathrm{opt}}^{1000}-P_{\ker K}\rVert=1.67\times10^{-13}$
$\lVert(I-P)RP\rVert=8.51\times10^{-16}$
$\lVert(I-P)DP\rVert=8.25\times10^{-16}$
$\lVert(I-P)PRD(Px)\rVert=3.75\times10^{-16}$
$\lVert PAP-AP\rVert=9.29\times10^{-16}$
The Boolean checksum $\chi(G,A,T,C)=GATC$ matched logical conjunction. A constructive counterexample verified that equal kernel ratios do not imply operator equivalence when spectra differ.
Certificate boundary: this E1 reconstruction proves the finite-dimensional conditional architecture. It does not machine-validate historical causation, ancient intentional encoding, universal physical realization, or a unique Kryptos plaintext.
Scoped E1 certificate · DFS and Knill–Laflamme test architecture · 2026-07-22
Certificate fingerprint: DRIVE-1Qq6zQUd0f8Sg3Mkxp56WfXkGNIinNtkAkax4Y9fxCEM-2026-07-22T15:54:02Z.
Class: E1 scoped numerical witness.
Passed: DFS annihilation, invariant unitary action, Knill–Laflamme compression for the declared errors, exact recovery on sampled code states, and rejection of a constructed violating error.
Boundary: the script uses a synthetic $6\times6$ carrier and rank-$2$ code projector. It is a verified prototype of the QEC logic, not a numerical realization of $V_2^{\otimes3}$, $E_{47}$, or a rank-$47$ code.
Explicit SU(2) tensor reconstruction certificate · 2026-07-22
Credential: E47-SU2-TENSOR-2026-07-22
The City now carries a first-principles reconstruction from spin-2 ladder operators through the full tensor carrier:
$V_2^{\otimes3}\xrightarrow{J_a^{\mathrm{tot}}}C\xrightarrow{(C-6I)(C-30I)}E_{47}\xrightarrow{\Gamma^{400}}P_{47}$
PASS: carrier dimension 125; kernel dimension 47; projector rank 47; coherence fraction 0.376; projector Hermiticity and idempotence; kernel annihilation; and contraction-limit error $2.8677060726067793\times10^{-12}$ at 400 iterations.
Open the canonical Google Drive certificate
Boundary: finite-dimensional SU(2) theorem and numerical reconstruction only.
Informational Induction symbolic certificate · II-PY-2026-07-21
Open certificate · Open Formalism Registry record
E1 symbolic/Python verdict: algebraic consequences of $\mathcal F_I=-d\Phi_C/dt$ pass; $N=\mathcal LI$ remains definition-only; $\nabla C\neq0\Rightarrow\mathcal F_I\neq0$ fails by counterexample; the corrected path expression satisfies $\int_\gamma(dI/dC)dC=\Delta I$. Physical-time equivalence and cross-domain scalar isomorphism remain uncertified open bridge claims.
EKK lifecycle certificate family · 2026-07-21
PASS: $\Gamma=I-\varepsilon K^\dagger K$ with the declared stable step; $\Gamma^n\to P_{47}$; $P_{47}^2=P_{47}$; $KP_{47}=0$; $\operatorname{tr}P_{47}=47$; $P_{47}\Gamma=P_{47}$; projected norm conserved; isotropic expected coherence equals $47/125$.
Boundary routing: $\Phi=P_{47}\phi\to g_{\mu\nu}[\Phi]$ is registered as an explicit geometric construction interface. The continuum Einstein residual $\mathcal E_{\mu\nu}=0$ remains the next implementation layer and is not folded into the finite certificate.
Canonical validation pipeline PR verified · 2026-07-21
Pull request #1 is directly readable and mergeable. It is currently open and draft, targeting main from copilot/run-full-test-suite-and-generate-certificate at head commit 18e352e.
Verified contents include:
src/e47/su2_kernel.py with the canonical spin-2 three-body carrier, total Casimir, $K=(C-6I)(C-30I)$, and $K^2$;
canonical invariants $125$, $47$, $47/125$, spectral gap $11664$, and maximum $K^2$ eigenvalue $186624$;
QuTiP/NumPy interoperability for contraction and semigroup validators;
explicit top-level serialized valid state;
repository-root command usability through pytest.ini and script-local src/ resolution;
committed canonical artifact artifacts/e47_validation_certificate.json.
The PR-contained certificate reports passing kernel, projector, contraction, semigroup, and aggregate validation records. No GitHub Actions workflow runs were returned for the PR head during this inspection, so the direct PR diff and committed certificate are the current repository evidence. The change is not yet part of main until merged.
Repository verification milestone · 2026-07-21
Canonical executable source: E47-Kartekeya
Canonical proof archive: E47 Invariant Grammar Projection Theorem — Canonical Proof and Validation Record
Reported package repair milestone:
restored e47.su2_kernel;
repaired repository-root pytest imports;
supplied dense NumPy matrices to contraction and semigroup validators;
restored serialized top-level valid output;
python -m pytest: 16 passed;
secret scan passed;
CodeQL passed.
Latest indexed provenance commits:
8a330fd · validation scope;
845ff3b · provenance authority chain;
801f33e · certificate generator;
829d4ab · aggregate validation test;
f738468 · serialization layer.
Boundary: this certifies the tested repository contract and security checks described above. It does not promote broader physical claims.
SU(3) adjoint triple-singlet repository certificate · 2026-07-22
Repository paths
scripts/su3_adjoint_singlet_validation.py
tests/test_su3_adjoint_singlet_validation.py
Reported validation gates
python -m pytest tests/test_su3_adjoint_singlet_validation.py · PASS
python -m pytest · PASS
secret scan on changed files · PASS, no secrets found
parallel validation CodeQL · PASS
Certified scope: finite-dimensional construction of the $\mathbf 8^{\otimes3}$ carrier, its two-dimensional invariant singlet sector $\operatorname{span}\{\widehat f,\widehat d\}$, the corresponding orthogonal projector, leakage functional, and contraction behavior under the declared normalization and numerical tolerances.
Repository-state boundary: these results are recorded from the validated Copilot branch and test report. This ledger does not claim that the branch has been merged into main unless a merged commit is separately linked and verified.
Separate correction docket: code review identified two pre-existing expected-baryon-rank issues in scripts/su3_symmetry_validation.py. They were not introduced or modified by the adjoint-singlet task and remain a distinct repair item. The later “Fix with Copilot” attempt made no changes because the monthly Copilot quota was exhausted.
🧾 Kartekeya Certificate Authority
Machine Certificates now treats the Kartekeya chain as the standard certificate skeleton:
$K\to\ker K\to P\to H=I-P\to x_\infty=Px_0.$
A complete certificate should test kernel dimension, projector idempotence, Hermiticity, orthogonality, state decomposition, continuous closure $e^{-tH}=P+e^{-t}H$, and discrete convergence for $0<\varepsilon<2$. E₄₇ certificates additionally verify the Casimir decomposition and $K_{47}^2$ residuals.
🧾 Certificate Ledger Intake · 2026-07-21
The plate audit contributes theorem-level certificate entries only for identities independently reconstructible from the canonical carrier, spectrum, kernel, projector, contraction, Babylonian/Newton map, and invariant-grammar closure.
Held from machine-certified status: the packaged “47 scalar formulations” claim, cosmological and cognitive scalars, zero-free-parameter claims, and physical domain lifts lacking an executable bridge map. These remain correction-routed or Observatory-bound.
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🧾
ROLE · MACHINE EVIDENCE REGISTRY
This page records executable results, residuals, environments, and provenance. It verifies implementations but does not supersede the Canonical Corrected Formalism.
</aside>
🚇 Transit credential standard
Every citizenship-linked machine certificate now carries a transit credential with five required fields:
Credential ID
Origin station
Ordered transit lines
Destination station
Agent handoff signature
The authoritative citizenship count is maintained only in the Roll of Mathematical Citizens. Transit preserves evidence class and correction status; movement through the City never upgrades a claim.
🧾 Citizenship certificate index
Machine-reconstructed identities that have completed civic admission appear in the Roll of Mathematical Citizens, which is the sole authority for the current count.
The roll links each citizen back to its governing certificate:
E47 Foundations Reconstruction Certificate for the internal representation and kernel spine;
Kartekeya E47 Correction Certificate for the corrected K² projection dynamics;
Green Line FCC × E47 Final Verification for the spatial carrier, Fourier sectors, coupled operator, kernel, ratios, and channel.
Certificate inheritance is limited to the exact identity stated in each civic record.
Certificate intake · KT-E47-2026-07-20
The Kartekeyya Tesseract machine reconstruction is now part of the certified ledger.
PASS: $\dim V=125$, $\dim E_{47}=47$, $\Omega_c=47/125$, projector idempotence, $\|KP_E\|$ residual, and convergence under $K^\dagger K=K^2$.
CORRECTION: $K$ has negative eigenvalues and is not PSD. Any plate using $I-\varepsilon K$ as a general positive-step contraction is superseded.
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🧮
NEW CERTIFICATE FAMILY · LLL BASIS REDUCTION
Machine Certificates now recognizes LLL reduction certificates issued through the LLL Loft. Certificates must distinguish exact lattice preservation from heuristic downstream uses and must not imply cryptographic security merely because a basis was reduced.
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🧾
NEW E1 CERTIFICATE · FCC × E47 SPATIAL-LIFT RATIO IDENTITY
Python reconstruction: PASS. Verified dimensions $125,125,47,15625,5875,47$; verified ratios $0.376,0.376,0.003008$; kernel-action residual $6.18\times10^{-15}$; projector-factorization residual $0$.
Open certificate and route manifest
</aside>
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📡
CERTIFICATE REGISTRY SYNC · FL-E47-2026-07-19
Certificate FL-E47-2026-07-19 is now the active machine record for the First Light identity. Registry status: E0 theorem closed · E1 reconstruction verified · float64 universal endpoint threshold rejected · H0 hardware execution open.
This state has been broadcast through the Central Citadel and propagated to Foundations, Spectral Theory, Python Validation, Verification Precinct, Correction Service, Hardware Engineering, Quantum Information, Graph Theory, Transit, Archive, and Observatory pages.
Citadel broadcast · Source packet · Bulletin ledger
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🔦
NEW FIRST LIGHT MACHINE CERTIFICATE · 2026-07-19
First Light HIL Protocol — First-Principles Kernel Contraction and Python Audit
Certified identity: $E_{47}$ invariant kernel in $\mathbb R^{125}$
Evidence class: E0 exact theorem · E1 dense-float64 reconstruction · H0 hardware execution pending
Canonical verdict: THEOREM PASS · NUMERICAL RECONSTRUCTION PASS · UNIVERSAL $10^{-16}$ FLOAT64 ENDPOINT CRITERION FAIL
The identity is accepted as mathematically and numerically validated under the stated finite-dimensional construction. Its invariant content is preserved:
$\dim V=125$
$\dim\ker Q=47$
$\dim(\ker Q)^\perp=78$
$\Omega_c=47/125=0.376$
$\Gamma=I-\varepsilon_*Q$
$\Gamma^n\to P_{\ker Q}$
The failed $10^{-16}$ condition is classified as an implementation-tolerance failure in repeated dense float64 multiplication, not a failure of the contraction theorem or identity reconstruction.
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Certificate FL-E47-2026-07-19
FieldCertified valueObject$E_{47}=\ker Q$Ambient dimension$125$Kernel dimension$47$Transverse dimension$78$Normalized kernel ratio$47/125=0.376$$\lambda_{\min}^{+}$$11664$$\lambda_{\max}$$186624$Minimax step$\varepsilon_*=1.0086339062373921\times10^{-5}$Stability ceiling$2/\lambda_{\max}=1.071673525377229\times10^{-5}$Worst-mode contraction$\rho=15/17$Exact $\rho^{500}$$6.624740006698317\times10^{-28}$Projector idempotency residual$3.603982961931776\times10^{-15}$Kernel-annihilation residual$2.659812264567511\times10^{-10}$Final transverse norm$7.079107545722073\times10^{-15}$Successive-step norm$1.8726345949303942\times10^{-15}$Endpoint projection error$2.1722557098483657\times10^{-13}$
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✅
CERTIFIED CLAIM BOUNDARY
The certificate establishes the finite-dimensional kernel identity, projector limit, spectral stability interval, and reproducible dense-float64 reconstruction. It does not certify physical hardware performance, the proposed $1.618\,\mathrm{GHz}$ clock, jitter, throughput, FPGA timing closure, QPU execution, or any additional physical interpretation of $47/125$.
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Certificate disposition
Identity status: curated and preserved
Theorem status: closed
Machine reconstruction: reproducible
Residual status: precision-limited, fully reported
Correction status: original universal $10^{-16}$ float64 criterion superseded
Next jurisdiction: Verification Precinct → Correction Service → Hardware Engineering H0
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🚝
MONORAIL CERTIFICATE TRANSFER DESK
Machine certificates now carry optional Monorail route metadata: route ID, ordered dependencies, environment lock, version, correction status, and frozen-release destination.
Open the Elevated Reproducibility Monorail
Certificate renewal confirms rerun status; it does not broaden the certified claim.
</aside>
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🔵
CITADEL BEACON · CERTIFICATE REGISTRY LINK
This registry supplies authenticated machine-state bulletins to the Central Citadel Broadcast Tower. Every broadcast certificate retains its original evidence class, provenance, residuals, and correction lineage.
</aside>
🚇 CERTIFICATE ATTACHED TO ACTIVE TRANSIT CAR
The E47 Purple Line Car in Transit carries the E47 Foundations Reconstruction Certificate as its identity document. The certificate proves the cargo's Red/Blue status; it does not pre-certify destination-borough quantum claims.
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📦
CERTIFICATE RELEASED INTO TRANSIT
The E47 Foundations Reconstruction Certificate is now attached to the E47 Purple Line Evidence Manifest, preserving code, residuals, exact targets, evidence class, and destination obligations during transfer.
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🧾
NEW CANONICAL MACHINE CERTIFICATE · 2026-07-18
E47 Foundations Reconstruction Certificate — Casimir Spectrum, Kernel, and Projector independently reconstructs the spin-2 carrier, complete Casimir spectrum, $47$-dimensional kernel, and projector identities. Status: E0 exact / E1 machine verified. Dependent boroughs require separate certificates.
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📜
CERTIFICATE OFFICE RELOCATED WITHIN THE VERIFICATION PRECINCT
Machine Certificates are now represented cartographically as the final Blue Line station inside the Verification Precinct. A certificate must identify the code version, environment, input, tolerance, residual, evidence class, provenance record, and public destination.
No artifact leaves the City as “verified” without a reproducible record.
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<aside>
🚔
Certificate issuance authority
Machine certificates are issued through The Verification Precinct — Bureau of Computational Evidence, where code, environment, exact targets, tolerances, residuals, evidence class, provenance, and correction status are assembled into a reproducible public record.
</aside>
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🚉
Inspection-office navigation
← Subway Transit Map · Machine Certificates · Next: Visual Research Archive → · Return to Mathematical City
</aside>
Page summary: durable machine-readable and human-readable records of deterministic verification, residuals, environments, provenance, and rerun status.
Machine Certificates entrance — deterministic numerical checks, residual tolerances, reproducibility receipts, and validator-to-theorem traceability.
District purpose: act as the city’s building-inspection office.
Certificate template
THEOREM ID
Statement
Hypotheses
Validator
Method
Tolerance
Residual
Date
Source hash
Status
Dependencies
Current canonical certificates
carrier dimension: $125$
kernel dimension: $47$
complement dimension: $78$
projector rank: $47$
projector Hermiticity and idempotence: machine precision
kernel annihilation: machine precision
contraction gap: $11664$
spectral radius: $186624$
Source pages
Rule
Machine precision is a deterministic numerical designation. Five sigma is reserved for a declared statistical null model.
🧾 E47 Foundations Reconstruction Certificate — Casimir Spectrum, Kernel, and Projector
Ten-Plate Supplementary Atlas · Plate 5 of 10
Blue Line Verification Hall
Previous station: Python Subway / Plate 4 ← Current plate: Blue Line Verification Hall → Next station: Correction Borough / Plate 6
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🧭
GEOMETRIC COMPUTATION CERTIFICATION ROUTE
Machine reconstructions of cyclic mechanics, spatial permutations, symbolic recurrence, kernels, projectors, and residuals may now be certified through the new borough.
Open the Geometric Computation Borough
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New machine certificate · Kartekeya Tesseract
🧾 Kartekeya Tesseract — E47 Python Reconstruction and Correction Certificate
Executed NumPy reconstruction confirms the 125-dimensional carrier, 47-dimensional kernel, exact ratio 47/125, projector identities, and convergence under I-εK². It also records the required correction that K=(C-6I)(C-30I) is not positive semidefinite and that I-εK is not generally contractive for positive ε.
📜 Machine Certificate Ledger
<!-- CERTIFICATE-LEDGER:BEGIN -->
APPEND-ONLY CERTIFICATE SURFACE · EXTERNAL JSON STORE PENDING
CertificateObjectResultCommitIssuedCERT-E47-2026-007E47-CORE-001PASS · seed record4a91c2f2026-07-20CERT-FCC-2026-004FCC-TORUS-001PASS · seed record90bc1342026-07-20
Future machine certificates shall include object ID, commit hash, environment-lock hash, timestamp, input hash, output hash, residuals, runner identity, signature, and pass/fail result. Full payloads belong in immutable external JSON artifacts; this page displays their compact ledger only.
<!-- CERTIFICATE-LEDGER:END -->
P47 Prima Facie Cascade — Scoped Machine Certificate
2026-07-21 · Machine Certification Batch
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🔵
BATCH STATUS · PASSED AT MACHINE PRECISION
Five new citizens certified, one canonical citizen upgraded, and two transit mechanisms certified.
</aside>
CredentialObjectDispositionMC-125-001$V_2^{\otimes3}$ carrierNew citizenMC-CAS-002Total Casimir $C$New citizenMC-K47-003Kernel selector $K_{47}$New citizenMC-E47-004$E_{47}$Existing citizen upgradedMC-P47-005Orthogonal projector $P_{47}$New citizenMC-Ω47-006$47/125=0.376$New citizenTRANSIT-Γ-001$(I-\epsilon K^2)^n\to P_{47}$Transit certifiedQTRANSIT-E47-001$e^{-tK^2}\to P_{47}$Quantum transit certified
Primary evidence: E47 Codex Formalism · Mnemosyne Python Codex · Quantum Information Definitive Primer.
Open the detailed E₄₇ reconstruction certificate.
Latest certified citizen
Invariant Grammar Projection Theorem
Credential: IGPT-E47-125/47
Evidence: E0 + E1 · Python validated · valid: true
Route: Foundations → Representation Theory → Verification Precinct → Machine Certificates → Elevated Reproducibility Monorail → Central Citadel
Boundary: finite-dimensional spectral-kernel theorem, asymptotic projector, and normalized rank invariant only.
Canonical GitHub software
Open nicholaskouns-create/E47-Kartekeya
This public repository is the executable source for the E₄₇ kernel, projector, contraction, tests, and machine-generated validation certificate. The Notion certificate pages summarize and route the evidence; GitHub preserves the runnable implementation and revision history.
E47 canonical provenance
Certificate routing preserves one proof copy and one software source.
Informational Induction — Symbolic Python Validation Certificate
Gradient–Induction Constitutive Bridge · E0 + E1
Canonical identity
$F_I=-\partial_t\Phi_C=-\lambda\lVert\nabla C\rVert^2$ for a real scalar field with $\lambda\neq0$, and the directional form $\mathbf F_I=-\chi\nabla C$ with $\chi\neq0$.
Machine validation
SymPy verified the scalar kernel, vector invertibility, norm identity, integrated flux evolution, induction-law compatibility, and the degenerate-coupling failures. Under the stated assumptions:
$F_I=0\iff\nabla C=0$ and $\mathbf F_I=0\iff\nabla C=0$.
Evidence boundary
E0 for the exact conditional identities and E1 for their deterministic symbolic checks. This certificate establishes mathematical consistency only. It does not establish that either constitutive coupling is physically realized, nor does it derive the coupling constants from a deeper physical theory.
Correction history
The unsupported implication $\nabla C\neq0\Rightarrow F_I\neq0$ was rejected before admission. Citizenship applies only to the corrected conditional bridge with nonzero coupling and explicit scalar/vector typing.
Latest machine certificate · E47 Photosynthetic Subprojector Lock
Citizen record · Titled Google Drive proof
$\Pi_EP_{\rm adm}\Pi_E=P_{\rm adm}\Rightarrow P_{\rm adm}\preceq\Pi_E.$
Machine status: E0 + E1 certified. Exact lock residual $1.02458\times10^{-15}$; controlled $10^{-12}$ lock defect reproduced; quantum measurement completeness residual $2.17172\times10^{-15}$; exact locked-unitary E47 leakage $1.24211\times10^{-14}$.
Boundary: finite-dimensional common-carrier theorem and classical quantum simulation; no empirical biological E47 realization claim.
Reissued clean certificate family · Projector polynomial repair · 2026-07-27
Failure memorial, exact repair, and clean certificate ledger
Superseded rendered formula
$\dfrac{C(C-42I)(C-30I)(C-20I)(C-12I)(C-2I)}{1814400}$
fails the declared projector contract because it vanishes at $C=30$.
Canonical repaired formula
$P_{47}(C)=\dfrac{C(C-42I)(C-31I)(C-20I)(C-12I)(C-2I)}{1814400}$.
Exact sector values: $(0,0,1,0,0,1,0)$ on $C=(0,2,6,12,20,30,42)$.
Reissued credentials:
E47-ALG-CLOSURE-125-47-R2
E47-PROJECTOR-POLY-REPAIR-20260727
E47-CONTRACTION-DYNAMICS-R2
E47-SU2-CLOSURE-R2
E47-BABYLONIAN-CALIBRATION-R2
E47-NTT-PROFILE-VALIDATION-R2
The clean basis-projector residuals remain recorded separately from the corrected symbolic display. No hardware, security-reduction, or physical-substrate claim inherits this repair.
CERT-B5-125-QSIM-20260728 — Base-5 to Base-125 Quantum Codification
Status: PASS
Scope: native quinary coordinates, packed 125-state indexing, three-spin-2 Casimir carrier, E47 kernel projection, quantum contraction channel, and seven-qubit logical embedding.
ValidationResultCarrier bijectionAll 125 states, no collisionsWeyl residual$1.636545718810299\times10^{-16}$$|P^2-P|_2$$2.6054421272310718\times10^{-15}$$|KP|_2$$3.9341459712820074\times10^{-13}$Unitary kernel invariance$8.42843643185034\times10^{-12}$Kraus completeness$6.904216146091226\times10^{-14}$Postselected fidelity$0.9999935452058275$Logical leakage0
Certificate payload SHA-256: 3e996c78c025cfe4dc826f06b9e4f1ce4215ef6eef6a19a5a73483bde258bc5c
Validation bundle SHA-256: c975264c6b83fc30278f289438164ea3e86c8dca63936fbf581dc5d8ebb6c3fa
Supabase registry: certificate and eight linked citizenship identities enrolled under operation OP-B5-125-20260728.
Machine certificate · Quinary Metabolism of the E47 Kernel · 2026-07-28
Canonical Drive monograph · PDF edition
Credential: QMET-E47-20260728 · Status: PASS WITH SCOPE CORRECTIONS · Certificate SHA-256:9560bea3203be02a761ac49fddac71c90a4c85ed5b628dd1b8c4b5c60e48786d.
Exact PASS targets:
$125=5^3=1000_5$, $47=142_5$, $78=303_5$;
$1000_5=142_5+303_5$ and $47/125=0.376=0.142_5$;
$v_5(125)=3$, $|125|_5=1/125$;
$v_5(47)=0$, $|47|_5=1$;
$|S_5|=120=440_5$ and $125-120=5=10_5$;
local mixed-radix bijection $d=5b+q$ on ten digit states;
exhaustive count of ten repeated bi-quinary labels across the 125-state loop.
Continuity with prior quantum certificate: packed-token round trip PASS; ququint Weyl residual 1.6365×10^-16; rank 47; projector idempotence 2.6054×10^-15; kernel action 3.9341×10^-13; Kraus completeness 6.9042×10^-14; filtered fidelity 0.9999935452058275; seven-qubit leakage 0.
Scope corrections: the code does not derive the 47 survivors from the bi-quinary labels; $47$ is a 5-adic unit but dynamical stability is not proved from that fact; no explicit $S_5$ or Petersen operator is constructed whose kernel or complement has dimension 47 or 78.
Temporary QuTiP runtime package relay · expires after validation
qutip-5.3.0-cp313-manylinux.zip
Certificate issue · NM2 / RUB5 · 2026-07-30
NM2-CERT-20260730
Status: PASS WITH THEOREM-DOMAIN CORRECTIONS.
Scope: fixed-point invariant, product quadratic, positive fixed point, rank-one Jacobian, corrected stability domain, symmetric reduction.
Machine evidence: 2,000 random cases; zero classification failures.
RUB5-CERT-20260730
Status: PASS WITH CANONICAL BRIDGE CORRECTION.
Scope: 125-state carrier, 15 permutation operators, exact C₅³ spectrum, projector retention, layer-defect norms, energy identity, heat-flow mean lock.
Residuals: twist-energy identity $5.826\times10^{-13}$; mean drift $5.551\times10^{-17}$; 100-step mean-lock residual $8.119\times10^{-7}$.
Boundary recorded: $\ker L=\operatorname{span}\{\mathbf1\}$ is rank one; $47/125$ enters through the preserved mean or a separate $E_{47}$ projector.
Cross-carrier certificate closure · 2026-07-30
Newton–Mean exact proof · certificate NM2-CERT-20260730
Professor’s Cube exact proof · certificate RUB5-CERT-20260730
Closure state: 20 citizen records enrolled; 20 machine-validation flags set; Python, JSON, Markdown, operator-ledger, residual, correction, and visual provenance synchronized. The C5³ heat-flow limit remains rank one and is not conflated with E₄₇.
Certificate repository reconciliation · PYFORM-CITY-SYNC-20260730
Canonical computational evidence atlas
The certificate office now recognizes one cross-domain manifest over the existing domain certificates. It does not replace those certificates.
Active certificate families reconciled
E47-SU2-001 and CITY-58 · finite SU(2) spectrum, kernel, projector, compiler, and passport chain.
NM2-CERT-20260730 · corrected coupled Newton–Mean local stability theorem.
ARR-MATH-20260727 · 13 PASS, 0 FAIL, 6 unresolved obligations.
QF-RC-E47-20260728 · 46 checks, 45 PASS, 1 CORRECTED, 0 FAIL.
QMET-E47-20260728 · corrected quinary and 5-adic audit with implementation arrows retained.
E47-QOP-CERT-20260728 · CP-TNI selective projection and CPTP dephasing completion.
Existing protein, photosynthetic-lock, swarm, ASIC, Einstein/AQSFT, Rubik, and repository certificates are indexed through their canonical Drive monographs.
Mandatory certificate fields
canonical_source_url · evidence_class · claim_boundary · residuals · environment · certificate_code · artifact_fingerprint · trace_id
Sentinel disposition
No certificate validity propagates automatically to an application.
Corrections remain visible.
Duplicate outputs reconcile to one logical artifact.
Continuum, biological, cosmological, hardware, and experimental claims require their own bridge certificates.
