Empirical

Coherence Cliff

Scaling Evidence for Sheaf Diagnostics

Demonstrated500 graphs, 7 scales, 5-50 nodes. Sheaf diagnostic vs. 12 baselines. Headline R² is internal consistency — predictor and ground truth are near-identical functionals of the same restriction matrices; on fully external data (BABEL live pipelines) a Hamming convention-distance baseline ties (ρ=0.423) or wins (ρ=0.39 vs 0.14). Pre-registered dissociation experiment unrun.
Key result

The demonstrated finding is baseline collapse: depth-3 testing 0.28 → 0.04 and best conventional 0.83 → 0.52 as size grows 5 → 50. The sheaf line holds R² > 0.96 but is structurally favored (see status); cohomological invariants alone score near zero (dim H¹ 0.093, coherence fee 0.000).

Falsification

A bounded-depth testing strategy that maintains accuracy at scale

Formal anchors
A13The Sheaf ConditionA21Coherence Cost ModelA28Sense Gluing

Abstract

Documents the regime change where conventional testing breaks down as composition size grows. Six convention dimensions grounded in real standards.

Resources