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SUBCLAIMS PROMOTED UNDER CITY PHYSICAL-CLAIM PROTOCOL. Within Einstein gravity, if a vacuum-sector stress tensor is declared as $T_{\mu\nu}^{(E)}=-\rho_E g_{\mu\nu}$, then its equivalent cosmological-constant contribution $\Lambda_E=8\pi G\rho_E$ is a [T] physical-model theorem. Therefore, under the additional declared ansatz $\rho_E=\rho_0(47/125)$, the algebraic descendant $\Lambda_E=8\pi G\rho_0(47/125)$ is a [C] conditional physical-model corollary. Not promoted: derivation of the vacuum-sector ansatz from the finite E47 theorem, the continuum map $C\mapsto\Delta_g$, Lorentzian/nondegenerate metric emergence, or determination of $\rho_0$ from nature.
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The new canonical corpus monograph is now linked here: Recursive Intelligence / Kouns–Killion Paradigm — Corpus Publication Monograph and Evidence Atlas.
It places this page’s branch in the shared publication spine while retaining its own evidence class and validation obligations.
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Canonical artifact: Recursive Intelligence / Kouns–Killion Paradigm — Corpus Publication Monograph and Evidence Atlas.
This publication pass reconciles the E47 exact core, executable certificates, Rubik/C₅³ carrier, AQSFT and quantum-information lifts, L_IG and Babylonian computational formalism, radix-invariant pyramid geometry, hyperbolic/fractal extensions, PQC/hardware proposals, and Mathematical City provenance.
Evidence rule: E0 exact proof, E1 executable reconstruction, E2 simulation, E3 external benchmark, E4 experiment, and H0 hardware remain claim-level classes. The monograph preserves corrections and does not transfer evidence between branches.
Publication route: core theorem → computational companion → Rubik/C₅³ paper → L_IG formal-language paper → historical-computational dossier → radix/geometry paper → applications prospectus.
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Exact finite layer: $\dim V=125$, $\dim\ker[(C-6I)(C-30I)]=47$, $P_{47}^2=P_{47}=P_{47}^\dagger$, and $KP_{47}=0$. A regenerated generic-basis witness gives projector, conjugation, and finite AQSFT product-kernel residuals at floating-point scale.
Cryptographic boundary: a public concrete spectral operator yields its selected projector and kernel in polynomial time; a fixed public E47/ISSR instance is not a hardness assumption. The finite proof therefore does not imply post-quantum secrecy.
Conditional hybrid route: ML-KEM/MLWE may establish a secret seed $\sigma$ that derives a unitary $U_\sigma$; E47 then acts only as a keyed transform/filter. Any confidentiality theorem is carried by the stated ML-KEM/KDF/AEAD reduction, with protocol and implementation obligations remaining open.
Canonical monograph: E47–AQSFT Spectral Cryptography — Multi-Silo Reconciliation Monograph.
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$V_2^{\otimes3}\to C\to K\to E_{47}\to P_{47}\to H_K=K^\dagger K\to e^{-tH_K}\to P_{47}.$
$\operatorname{Tr}\left(P_{47}\frac{I}{125}\right)=\frac{47}{125}=\Omega_c.$
$\mathcal V=\rho_E P_{47}+\rho_\perp(I-P_{47}),\qquad \mathcal V|{E{47}}=\rho_E I_{47}.$
$T_{\mu\nu}^{(E)}=-\rho_E g_{\mu\nu},\qquad \Lambda_E=8\pi G\rho_E.$
For $\rho_E=\rho_0\Omega_c$,
$\Lambda_E=8\pi G\rho_0\frac{47}{125}.$
The finite spectral carrier, projector, rank, trace, contraction, covariance, and composite-kernel identities are machine validated. The arrows $C\mapsto\Delta_g$, $g_{\mu\nu}=\langle\partial_\mu\phi,\partial_\nu\phi\rangle$, $T_{\mu\nu}=-\rho_Eg_{\mu\nu}$, and the determination of $\rho_0$ remain conditional continuum and physical lifts.