Fractals and Hyperbolic Geometry — unmarked hyperbolic disk
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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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TIGHTENING RECONCILIATION · 2026-08-14
The existing Hyperbolic–Liquid Fractal family is bound to Hyperbolic–Liquid Fractal Buoy Formalism — Independent Python Runs, Certificate Reconciliation, and Cross-System Archive Monograph and Python Hyperbolic Liquid Fractal Certification.
Registry keys HLFB-IND-20260730 and HLFB-PY-20260730 remain separate independent-run witnesses. Existing hashes are preserved: 3745bcfec1a6e06a for the independent validation source and ecae22e2e1dfab96984619e5fb8e85e79cd986e545f8a6292f0184aacbeef6fb for the Python certificate. No new child page was created and no empirical or physical evidence class is promoted by this archive repair.
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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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Canonical independent-run monograph
Credential family: HLFB-20260730
HLFB-PY-20260730 — seed 47, 28/28 PASS, SHA-256 ecae22e2e1dfab96984619e5fb8e85e79cd986e545f8a6292f0184aacbeef6fb.HLFB-IND-20260730 — seed 42, Python 3.12.3, NumPy 2.4.4, PASS with explicit calibration.Run B calibration: r_buoy=0.3283203, finite-n bound 2.172100, asymptotic bound 2.188802. This confirms finiteness under L<1, not tight or high-fidelity equivalence.
Validated packet: Poincaré metric witnesses; hyperbolic exponential growth; self-similar dimension and log-log recovery; controlled approximate intertwining; Lipschitz invariant transfer; semiconjugacy/conjugacy witnesses; Weyl spectral stability; projector-family convergence; finite quantum evolution/filter/projector witnesses.
Evidence: E0 + E1, with limited E2 for parameter-dependent Kuramoto and field simulations.
Boundary: no physical manifold identification, universal substrate-neutrality, consciousness, propulsion, cosmology, classified-system equivalence, or generic 47/125 threshold claim is promoted.
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Canonical research boundary
This page consolidates the Google Drive corpus on fractals, multifractals, hyperbolic geometry, recursive harmonic structures, fractal quantum models, Python simulations, and quantum-computational obligations.
Fractal geometry describes scaling and self-similarity. Hyperbolic geometry describes spaces of negative curvature. They are mathematically compatible but not interchangeable. Recursive branching can often be represented efficiently in hyperbolic space; it does not by itself prove that the underlying physical or informational manifold has negative curvature.
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Audit date: July 17, 2026
Status key: ✅ established mathematics or exact finite computation · ◇ structural formalism · △ conditional or open bridge · ○ speculative interpretation
The Drive corpus resolves into six principal families: