Latest certified intake · Hyperbolic–Liquid Fractal Buoy Formalism · 2026-07-30

Canonical independent-run monograph

Credential family: HLFB-20260730

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

Executive synthesis

The Drive corpus resolves into six principal families:

  1. Classical fractal and multifractal mathematics: self-similar sets, box-counting and spectral dimensions, recursive functions, Mandelbrot dynamics, generalized dimensions, and multifractal spectra.
  2. Hyperbolic harmonic geometry: Poincaré-ball embeddings, negative-curvature geodesics, Laplace–Beltrami eigenmodes, recursive harmonic identity, and boundary-attractor language.
  3. Fractal quantum systems: Schrödinger equations with scale-dependent or lacunary potentials, multifractal wavefunctions, Anderson localization, spectral statistics, and candidate quantum-chaotic behavior.
  4. Python simulation laboratories: recursive Fourier fields, scaling fits, toy invariants, Kuramoto coherence, ring winding, Mandelbrot visualizations, symmetry-breaking potentials, and recursive feedback loops.
  5. Canonical K47/125 algebra: exact $E_{47}$ projector and contraction results used as a proposed selector or invariant monitor.
  6. Open extensions: identity, cognition, cosmology, holography, quantum-code geometry, and engineering interpretations.