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TEST DESCRIPTION: Contact Point 2 — Singh's delta^2 = 3/8 vs TLT-019
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Author: Jonathan Shelton
Date: 2026-03-21
Status: PRE-REGISTERED (test description written BEFORE coding)
Protocol: Outcome-agnostic. Observe what happens at t/T = 3/8 = 0.375.
Project: 4D Research (24-cell focal point)

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1. WHAT WE ARE TESTING
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Singh (2025, arxiv 2508.10131) derives fermion mass ratios from the
exceptional Jordan algebra J3(O_C) with a universal parameter:

  delta^2 = 3/8 = 0.375

This parameter sets the eigenvalue spread (q-delta, q, q+delta) for
all charged fermion sectors. It is derived from algebra, not fitted.

Our TLT-019 test verified:
  - Optimal decoherence ratio: t/T ~ 0.3 (peak differentiation)
  - Collapse boundary: t/T = 0.5 (exact, theory.txt)
  - Scale-independent (identical at M=10 through M=500)

Singh's 3/8 = 0.375 sits BETWEEN our optimal (0.3) and collapse (0.5).

QUESTION: Does t/T = 0.375 show any special feature in the TLT-019
framework that would connect our wave-interference decoherence to
Singh's algebraic eigenvalue spread?

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2. WHAT WE EXPECT TO SEE (pre-registered)
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  A. If 0.375 shows NO special feature — just a point on the declining
     slope between 0.3 (optimal) and 0.5 (collapse) — then the numerical
     proximity is coincidental and the frameworks are not connected at
     this level.

  B. If 0.375 shows a LOCAL feature (inflection point, secondary peak,
     mode transition) that 0.300 does not — then there is a structural
     connection between the decoherence ratio and the Jordan eigenvalue
     spread that warrants investigation.

  C. If 0.375 produces a QUALITATIVELY different pattern (different
     symmetry, different peak count, different spatial organization) —
     then 3/8 may be a distinct physical regime, not just a parameter value.

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3. WHAT WOULD FALSIFY
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  - If the region around 0.375 is featureless (smooth monotonic decline
    from 0.3 to 0.5), this contact point is a numerical coincidence.

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4. WHAT WOULD CONFIRM
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  - A local feature at or near t/T = 0.375 that is absent at 0.350 and
    0.400 would be non-trivial evidence of a connection.
  - If the feature involves a change in the NUMBER of distinct intensity
    classes (not just their magnitudes), it connects to Singh's eigenvalue
    COUNT (3 eigenvalues from 3 generations).

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5. METHODOLOGY
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  ENGINE: IDENTICAL to TLT-019 (pulsed N=3 wave interference, 2D FDTD).
  This is NOT the 4D engine. It is the established 2D engine from
  the audited TLT test suite.

  SWEEP: t/T from 0.30 to 0.45, step 0.005 (31 values)
  This brackets both our optimal (0.3) and Singh's delta^2 (0.375)
  with dense sampling.

  GRID: Same as TLT-019 (M=100 verified sufficient for scale-independence)

  MEASUREMENTS (same as TLT-019):
    - Number of distinct intensity classes (n_classes)
    - Number of local maxima (n_maxima)
    - Coefficient of variation (CV) of peak intensities
    - Spatial frequency of dominant mode (k_dom)
    - Pattern symmetry order

  KEY VALUES TO EXAMINE:
    t/T = 0.300 (our verified optimal)
    t/T = 0.375 (Singh's delta^2 = 3/8)
    t/T = 0.382 (1/phi^2, already falsified in TLT-019)
    t/T = 0.400 (control: round number between 3/8 and 1/2)

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6. RUNTIME ESTIMATE
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  31 values x ~2 min each = ~1 hour on Hetzner.

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7. CONNECTION TO PRIOR TESTS
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  TLT-019: Established t/T ~ 0.3 optimal, 0.5 collapse, falsified phi^2.
  THIS TEST: Specifically probes t/T = 3/8 from Singh's Jordan algebra.

  No engine modifications. Same code, new sweep range.

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