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EIDOLON · FLY THE FIELD
Take flight · EIDOLON — Scalar Flight Lab
Explore islands, follow a flow course, practice precision hover, or join a murmuration.
Start with Explore → S–47 scalar craft → Archipelago, then select Take flight.
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EIDOLON — Scalar Flight Lab · interactive flight simulation
EIDOLON — Scalar Flight Lab · interactive flight simulation
Simulation. Four flight modes, two vehicles, and three landscapes. Desktop, touch, and gamepad controls. Open Take flight for the full-screen experience.
The flight experience uses model-based dynamics. Exact E47 results, numerical checks, and application hypotheses retain their own supporting records.
The Mathematical City · 125 → 47
An executable research architecture for invariant computation.
The Mathematical City is the public research atlas for Recursive Intelligence, the Kouns–Killion K47/125 framework, and E47 invariant computation. Explore exact SU(2) representation theory, Casimir spectral projectors, executable Python validation, quantum operator models, machine certificates, corrections, and reproducible mathematical research.
$\Omega_c=47/125=0.376$ · $\rho_=15/17$ · $\varepsilon_=1/99144$
Structure is discovered. Invariance is selected. Everything else is tested.
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KARTEKEYA
Canonical E47 machine · executable object
Live 125-state carrier → spectral selector → 47-dimensional invariant → Clebsch–Gordan register → contraction → certificates.
Coprocessor, not a mythic die.
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FPV20C DUAL VALIDATION · 2026-09-13
The six new proof-born citizens were consolidated into one first-principles operator chain and validated twice: deterministic Python and a 14-qubit statevector purification. Classical residuals: Euler $4.44\times10^{-16}$, exact Taylor $2.22\times10^{-16}$, Fourier $5.85\times10^{-16}$, Dirichlet-incidence $1.78\times10^{-15}$, Kirchhoff $3.55\times10^{-15}$, purity $3.47\times10^{-18}$. Quantum realization: $|\Psi_{47}\rangle=47^{-1/2}\sum_{j=0}^{46}|j\rangle_S|j\rangle_A$ on 7+7 qubits gives $\rho_S=P_{47}/47$, $\operatorname{rank}\rho_S=47$, purity $1/47$, and $S(\rho_S)=\ln47$ to machine precision. Certificate MC-PF-FPV20C-DUALVAL-20260913 is live in Supabase. Boundary remains E0+E1 only; no hardware or empirical promotion.
City Murmuration — Proof Forge FPV20 Citizen-Proving Flight C · 2026-09-13
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PROOF FORGE OPEN · 2026-09-13
The City now forges 20 first-principles proofs per borough per day, each Python-validated at E0/E1. Day-0 batch: 120/120 PASS. Seven new citizens enrolled with legacy lineage; PREC-C05/C07/C08 and QOP C01–C10 reconciled in place.
City Murmuration — Proof Forge Day 2026-09-13 · Prec Citizens + 20×6 First-Principles Batch · Proof Forge Drive · Day packet
Independent reconstruction recovered $\mathrm{rank}\,P=47$ from $\chi_{\{6,30\}}(C)$ with Casimir dimensions $(1,9,25,28,27,22,13)$. Grid Laplacian kernel remains $1\ne 47$. No E3/E4/H0 promotion.
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