QIT Primer — unmarked photonic channel

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VISUAL SYSTEM · MINI AI LABS

Near-black laboratory. Cyan live · bronze Λ-ghost · mint lock. No type on stills. Record: CITY-LABS-VISUAL-SYSTEM-20260915.

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Quantum Information Theory Primer — E47 spectral core. Mini AI Labs visual system.

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VISUAL SYSTEM · MINI AI LABS

Near-black laboratory. Cyan live · bronze Λ-ghost · mint lock. No type on stills.

Record: CITY-LABS-VISUAL-SYSTEM-20260915.

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QUANTUM REPRESENTATION BRIDGE · 2026-08-09

Canonical monograph: The Kartekeya Intertwining Bridge Theorem

Let $G_E=K^2$ and let $U$ be unitary. The transported quantum system is

$$ G_D=UG_EU^\dagger,\qquad P_D=UP_EU^\dagger,\qquad \rho_D=U\rho_EU^\dagger. $$

Then $e^{-tG_D}U=Ue^{-tG_E}$, $P_DU=UP_E$, and $\operatorname{Tr}(P_D\rho_D)=\operatorname{Tr}(P_E\rho_E)$. The variational energy is also invariant: $\langle U\psi|G_D|U\psi\rangle=\langle\psi|G_E|\psi\rangle$.

This supplies the exact substrate-change theorem. It does not identify an independently observed physical system with E47 unless that system's measured or modeled operator satisfies the intertwining certificate.

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Constrained-QFT, relational-time, and RG synthesis · 13 August 2026

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The plate’s quantum-field lift is routed through Professor’s Cube Exhibit — Shared-Carrier S₃ Symmetry Bridge, Bohm–Madelung Kernel Hamiltonian Identity, ARR-C005 · Time-Chain Identity, and ARR-C006 · Coherence RG Fixed Points.

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The constrained state sector is written

$$ \widehat H\Psi=0, $$

and the internal clock obeys

$$ d\tau=\psi_C\,dt,\qquad \frac d{d\tau}=\psi_C^{-1}\frac d{dt}. $$

The coherence coupling evolves by

$$ \frac{dg_\Omega}{d\ln b}=(2-d_C)g_\Omega-A g_\Omega^2, $$

with the synthesis calibration $A=(2-d_C)/\Omega_c$ giving the machine-verified fixed point $g_\Omega^*=\Omega_c=47/125$.

📚 Corpus publication release · 2026-08-09

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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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E47 / Base-5 visual validation packet · 2026-07-31

Formal Python monograph · Complete archive

The Base-5 layer preserves exact rational payloads while the E47 quantum architecture retains its own typed carrier, selector, projector, channel, and propagator. In particular,

$$ \Omega_c=\frac{47}{125}=0.376_{10}=0.142_5, $$