CAUSAL CHAIN AUDIT: PAPER 03 (Coherence Metric)

1. LOGICAL FLOW ANALYSIS

Thesis: Structural Integrity follows Phase Transition Physics (|P - Pc|^gamma).
Mapping: $P$ (Control Parameter) = Constraints. $\chi$ (Order Parameter) = Coherence.
Observation: 1968-1973 was a synchronized phase transition.
Prediction: Cross-domain coupling (percolation) explains the sync.

Formula Mismatch:
- Papers 1 & 2 use Exponential Decay ($\chi \sim e^{-\lambda t}$).
- Paper 3 uses Power Law / Criticality ($\chi \sim |P-P_c|^\gamma$).
- Problem: These are mutually exclusive functions for the same data. You cannot fit the same curve to both well unless the range is very limited.
- Fix: Define the relationship. Does Exponential Decay describe the Control Parameter ($P(t)$), which then drives the Power Law response in $\chi$?
  - Hypothesis: $P(t) \sim e^{-\lambda t}$ (Constraints decay exponentially).
  - Result: $\chi(P)$ follows power law.
  - Action: Explicitly link the two models.

Claim	Type	Status	Source/Note
”9 Domains Analyzed”	Empirical	[COMPUTED]	JSON has >9. Safe.
”Inflection 1968-1973”	Statistical	[VERIFIED]	JSON `t0_mean` = 1968.9. Matches well.
”p < 10^-6”	Statistical	[FAILED]	JSON `ks_pvalue` = 0.0033 ($10^{-3}$).
”R^2 = 0.87 on polarization”	Statistical	[MISSING]	JSON does not list “Polarization”. Lists “Trust” ($R^2=0.82$) or “GSS Trust” ($R^2=0.77$).

Unify the Math: The shift from Exponential (P1/P2) to Power Law (P3) is jarring. Frame P3 as the “Deeper Mechanism” explaining why the exponential decay in P2 leads to rupture.
Correct P-Values: Standardize on the computed $10^{-3}$ unless new runs improve it.
Cite Specifics: Replace “Polarization” data claim with a variable actually in the JSON (e.g., “Trust in Government”).