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Consistency Checks

Status: CANONICAL

Cross-Repository Consistency

All SSZ repositories must produce consistent results. The following checks are performed:

1. Ξ Value Consistency

Every repo that computes Ξ must agree at standard test points:

r/r_s Ξ_weak Ξ_strong Used in
1.0 0.500 0.802 metric-pure, unified
1.595 0.313 0.313 all repos (intersection)
3.0 0.167 0.259 qubits, unified
10.0 0.050 0.150 segcalc, lensing
100.0 0.005 — all repos

2. D Value Consistency

r/r_s D_SSZ D_GR Δ
1.0 0.555 0.000 ∞
1.595 0.611 0.611 0.0%
3.0 0.794 0.816 2.7%
10.0 0.952 0.949 0.3%
100.0 0.995 0.995 0.0%

3. PPN Consistency

  • β = 1 in all repos
  • γ = 1 in all repos
  • Lensing: α = 2r_s/b (PPN) in all relevant repos
  • Shapiro: factor (1+γ) = 2 in all relevant repos

4. Regime Boundary Consistency

  • Blend zone: 1.8 ≤ r/r_s ≤ 2.2 (not 90-110!)
  • C² continuity verified at both boundaries
  • No formula mixing without explicit blend

Repo Scope Index

Each repository has a defined scope:

Repo Scope Ξ Formula PPN?
ssz-qubits Weak field r_s/(2r) NO
ssz-metric-pure Strong field min(1-exp(-φr_s / r), Ξ_max) YES
maxwell Blend Hermite C² YES
Unified-Results All regimes Full YES
segcalc All regimes Full YES
freq-curv-validation Weak field r_s/(2r) YES
ssz-lensing Weak-to-strong Full YES

Rule: If a repo only covers weak field, don't compare its Ξ values to a strong-field repo — they use different formulas by design.

Common "False Alarm" Patterns

1. Factor-2 Discrepancy

Symptom: Lensing/Shapiro result is 50% of GR Cause: Using Ξ-only (g_tt) instead of PPN (g_tt + g_rr) Fix: Apply (1+γ) factor

2. r*/r_s Mismatch (1.387 vs 1.595)

Symptom: Two different intersection points Cause: Different Ξ formulas have different D_SSZ = D_GR comparison points Reality: Both are correct only with their source context:

  • r*/r_s ≈ 1.595: decay/global form Xi_A(x)=1-exp(-phi/x)
  • r*/r_s ≈ 1.387: saturation/local form Xi_B(x)=1-exp(-phi*x)

3. Regime Formula Mismatch

Symptom: Ξ values differ between repos at same r/r_s Cause: Different repos use different regime formulas Fix: Check which regime each repo covers (see scope table above)

Guardrails ≠ "Repos are wrong"

The repos are physically correct and internally consistent. Guardrails prevent:

  • Cross-repo confusion from comparing different-scope results
  • Silent wrong-method application
  • Future misunderstandings when extending the framework

Guardrails = Documentation hardening, not error correction.

© 2025–2026 Carmen N. Wrede, Lino P. Casu