Coherence Collapse Analysis: A Universal Failure Mode in Complex Coordinating Systems

 Coherence Collapse Analysis (CCA) is a measurement substrate and vocabulary for correlation-driven fragility in complex systems. When constraints governing system behaviour become correlated, effective diversity collapses toward unity: k_eff = 
  k/(1+ρ(k−1)) → 1 as ρ → 1. The formula is the Kish (1965) design effect, and the same effective-count construction has been reached independently in survey sampling, political science (Laakso–Taagepera), ecology (Hill numbers), and portfolio
  theory.

  The durable result is the map's Möbius structure: k_eff is strictly monotone decreasing in ρ and saturates at 1/ρ. Scale cannot restore diversity that correlation has already collapsed — at ρ=0.1 the ceiling is 10 effective constraints, at ρ=0.5
  it is 2, however many are added. This is substrate-independent and requires no calibration. The paper also derives a stability condition (α/k ≥ d), three closed-form collapse timescales, a singularity boundary, and a chaos–healthy–rigidity phase
  decomposition, and describes a 128-sensor GPU-timing strain gauge used as a correlation-measurement instrument.

  Version 5 is a corrections version and withdraws several claims made in version 3. Eighteen defects are enumerated with evidence and dispositions in the accompanying corrections note, with a machine witness reproducing every algebraic defect. The
  load-bearing ones:

  - The stability criterion erred in the permissive direction — the published form certified as stable systems whose defence function is strictly decreasing. Corrected from α/k_eff to α/k ≥ d.
  - Both results previously offered as hardware validation of k_eff are identity checks: they compute the identity and compare it against itself, and would return the same agreement for any formula. k_eff is an identity and admits no empirical
  confirmation.
  - The institutional application does not consult k_eff at all; re-scored against a pre-specified outcome definition it performs below chance, and is reported here as a negative result.
  - The cross-domain generality claim is withdrawn: applying one formula to three datasets shows it can be applied, not that it holds.
  - "Software-induced coherence collapse" is withdrawn as a measurement artifact, established by pre-registered replication on the original hardware.

  Scope, stated plainly. L-01 establishes that the class of marginal-preserving undetectable patterns is non-empty — an existence result with no measure; the "~40%/60%" figures of earlier versions followed from one illustrative parameterization and
  are withdrawn. The Lean 4 development establishes internal consistency and bears on external validity not at all. The Monte Carlo section is a sampler self-consistency check, not a validation.

  The paper carries nine falsification conditions, each with an observable, a threshold, and a procedure. Their current status is reported rather than smoothed: two have fired against the framework, three are unmet, one is unresolved, one passes, 
  and three were newly entered by the fires themselves. Version 3's three stated conditions could not fire and are withdrawn rather than reworded.

  CCA is not a validated predictive framework and not a safety guarantee. Its central safety intuition — that accumulating independent constraints starves deception — does not follow from the geometry presented: simulation shows that under the
  paper's own assumptions, constraints shrink feasible volume without shrinking deception preferentially. That asymmetry is assumed, not derived, and is the alignment problem itself.