Proofs

Finite-dimensional construction of E₄₇ = ker K on V₂⊗³. dim V = 125, dim ker K = 47, Ωc = 47/125. All kernel checks pass in the Kartekeya certificate.

P₄₇² = P₄₇ = P₄₇†, KP₄₇ = 0, Tr P₄₇ = 47. Idempotence residual 4.91e-14. Rank and trace certified in the same machine run as the kernel.

Iterative contraction to Ωc with kernel-fixed residual 5.29e-15 and asymptotic projector residual 9.84e-11 after 398 iterations.

Semigroup law residual 2.40e-15, positivity 4.63e-16, kernel-fixed 1.01e-13. Completely positive, trace-non-increasing filter on the complement of E₄₇.

Theorem plate in Kartekeya: linearized Einstein sector as an intertwiner on the E₄₇ kernel. Next obligation remains the nontrivial Einstein sector.

Exact statement of the E₄₇ projection flow on the carrier. Companion plate to the core spectral certificate.

FPSK reconstruction of the kernel from Casimir roots with no fitted parameters. Drive certificate plus Notion plate E47-FPSK-20260809.

Latest Proof Forge dual-validation bundle, 13 Sep 2026. Canonical live edge of the algebraic core.

MC-E47-CORPUS-REPRO-20260912. Deduplicated corpus closure with machine-readable JSON and zip bundle.

Canonical theorem sheet, monograph, and city-registry crosswalk for exact-to-machine-precision certification of the E₄₇ spectrum.

Certified plate bound to GitHub commit ad297e1. City journal of spectral science issue.

Shared-carrier S₃ symmetry on the 5×5×5 cube (dim 125). Machine validation plus quantum-simulation dossier.

Kernel selection program with three machine-validated identities and a QuTiP cascade simulation plate.

Executable SU(3) adjoint identities in Kartekeya. Companion to the SU(2) triple-tensor engine.

compile_spectral_kernel.py --spin 2 --copies 3 --select 2 5. CI-regenerated certificate and passport.

Group-theoretic spectral graph tomography: Kronecker closure of the E₄₇ human-network lift. Radial Schrödinger companion certificate.

Invariant-grammar spectral parity certificates v1 and v2 for the universal translator lab.

E47_Channel_Operations_Correction_Certificate_2026-07-28. Precinct-certified channel identities.

Linear model machine certificate cited from the Open Questions Observatory.

Quinary_Family_Revision_C_E47_certificate.json — base-5 family identities.

Machine certificate closing the base-5 Planck / Einstein / Faraday identities.

Post-quantum self-preserving intelligence: identity, RSC, PQSPI ASIC, IEEE dossier. Hardware synthesis remains open.

Bio-Recursive Mobility Network and validation framework. Origin vector of the work; experimental collaborators invited.

Explicit next proof obligation in the Kartekeya repo. Linearized intertwiner is closed; the nontrivial sector is not.