1.1 KiB
1.1 KiB
ADR-CE-001: Sheaf Laplacian Defines Coherence Witness
Status: Accepted Date: 2026-01-22 Parent: ADR-014 Coherence Engine Architecture
Context
Traditional AI systems use probabilistic confidence scores to gate decisions. These scores:
- Can be confidently wrong (hallucination)
- Don't provide structural guarantees
- Are not provable or auditable
Decision
Sheaf Laplacian defines coherence witness, not probabilistic confidence.
The coherence energy E(S) = Σ w_e|r_e|² provides a mathematical measure of structural consistency where:
- r_e = ρ_u(x_u) - ρ_v(x_v) is the edge residual
- w_e is the edge weight
- Zero energy means perfect global consistency
Consequences
Benefits
- Mathematical proof of consistency, not statistical guess
- Every decision has computable witness
- Residuals pinpoint exact inconsistency locations
Risks
- Restriction map design requires domain expertise
- Initial setup more complex than confidence thresholds
References
- Hansen & Ghrist (2019), "Toward a spectral theory of cellular sheaves"
- ADR-014: Coherence Engine Architecture