Coherence Selection Experiment — Success (P-Sweep + Gaussian Weighting w(s)) | Invariant Record

INVARIANT RECORD HTML EDITION ARU INTELLIGENCE INC. SEALED-FIELD TOY MODEL EXPERIMENT SUCCESS LOG OFFLINE-COMPATIBLE NO EXTERNAL LIBRARIES

DECEMBER 24, 2025

COHERENCE SELECTION EXPERIMENT — SUCCESS

A sealed-path demonstration showing dominance stability under nonlinearity (p-sweep) and structural weighting w(s), including the critical non-tautological signature: selection persists even when crystallization fails.

Commitment Integral

C = ∫ w(s) · |Θ(s)|^p ds

Crystallization

C ≥ C₀ (C₀=5)

Selection

b* = argmax C_b

NONLINEARITY DISCRIMINATES (P-SWEEP)

FAILURE MODE OBSERVED (NON-TAUTOLOGY)

SELECTION STABLE UNDER STRUCTURE w(s)

Primary Outputs

Base run + Gaussian-weight run

Base Run

w(s)

uniform (1)

p

2.0

C values

[10.000000, 3.750000, 1.498657]

Crystallized?

[True, False, False]

Selected

Worldline 1 (Sustained)

Gaussian Weight Run

w(s)

Gaussian (center=5, σ=2), normalized

p

2.0

C values

[4.952481, 1.859063, 0.382164]

Crystallized?

[False, False, False]

Selected

Worldline 1 (Sustained)

Non-tautology signature: the sustained branch remains the selected worldline even when the threshold event (crystallization) is suppressed by structural weighting. Selection and crystallization separate cleanly.

Figure A — Θ(s) Across Branches

Sustained vs wavering vs decaying

Figure B — Commitment C vs p (P-Sweep)

Nonlinearity amplifies stability

Figure C — Structural Weighting w(s)

Gaussian envelope centered at s=5

TERMINAL GLYPH

Θ → |Θ|^p → ∫ → C → argmax → ACTUALITY

© 2025 Daniel Jacob Read IV • All Rights Reserved • ARU Intelligence Inc.

Index Terms

coherence selection, p-sweep nonlinearity, gaussian structural weighting w(s), commitment integral, dominance ordering, threshold crystallization, sealed-path toy model, computational experiment, worldline selection, failure mode (non-tautology), invariant record, ARU Intelligence Inc