Ring 049: sacred physics conformance — hard tolerance verification for all 6 constants

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Ring 049: Sacred Physics Hard Tolerance Verification

Phase: HARDEN | Layer: PHYSICS | Parent: #126

Problem

specs/math/sacred_physics.t27 defines 6 constants (PHI, PHI_INV, TRINITY, GAMMA_LQG, G_MEASURED, OMEGA_LAMBDA) with hard tolerances, but the conformance vector conformance/sacred_physics_vectors.json does not verify all 6 constants at maximum precision (GF32).

Goal

Create exhaustive conformance vectors for all 6 sacred constants at GF32 precision, including the fundamental identity phi^2 + phi^-2 = 3.

Constants and tolerances

PHI = 1.618033988749895  tolerance: 1e-15
PHI_INV = 0.618033988749895  tolerance: 1e-15
TRINITY = 3.0  tolerance: 0.0  (exact)
GAMMA_LQG = 0.2360679775  tolerance: 1e-10
G_MEASURED = 6.67430e-11  tolerance: 1e-15
OMEGA_LAMBDA = 0.685  tolerance: 1e-3

Identity verification

test trinity_identity {
  // phi^2 + 1/phi^2 = 3 (exact)
  assert abs(PHI * PHI + PHI_INV * PHI_INV - TRINITY) < 1e-12,
}

test barbero_immirzi {
  // GAMMA_LQG = phi^-3
  assert abs(GAMMA_LQG - pow(PHI, -3)) < 1e-10,
}

Specs to modify

• specs/math/sacred_physics.t27 - add identity tests
• conformance/sacred_physics_vectors.json - extend to v2 schema

Acceptance criteria

• Trinity identity phi^2 + phi^-2 = 3 verified to 1e-12
• Barbero-Immirzi = phi^-3 verified
• All 6 constants within hard tolerance
• Schema v2 format

Seal requirements

• seal --save specs/math/sacred_physics.t27
• seal --save conformance/sacred_physics_vectors.json

Dependencies

• Ring 028 (sacred physics gen) - sealed
• Ring 038 (Ring 038: conformance vector schema v2 — add phi_distance and verdict fields #133) - conformance schema v2

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Branch: ring/049-sacred-physics | Commit: feat(ring-049): sacred physics hard tolerance verification [SEED-49]