d803bfe2b1
git-subtree-dir: vendor/ruvector git-subtree-split: b64c21726f2bb37286d9ee36a7869fef60cc6900
38 lines
1.1 KiB
Markdown
38 lines
1.1 KiB
Markdown
# ADR-CE-001: Sheaf Laplacian Defines Coherence Witness
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**Status**: Accepted
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**Date**: 2026-01-22
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**Parent**: ADR-014 Coherence Engine Architecture
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## Context
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Traditional AI systems use probabilistic confidence scores to gate decisions. These scores:
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- Can be confidently wrong (hallucination)
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- Don't provide structural guarantees
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- Are not provable or auditable
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## Decision
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**Sheaf Laplacian defines coherence witness, not probabilistic confidence.**
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The coherence energy E(S) = Σ w_e|r_e|² provides a mathematical measure of structural consistency where:
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- r_e = ρ_u(x_u) - ρ_v(x_v) is the edge residual
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- w_e is the edge weight
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- Zero energy means perfect global consistency
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## Consequences
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### Benefits
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- Mathematical proof of consistency, not statistical guess
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- Every decision has computable witness
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- Residuals pinpoint exact inconsistency locations
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### Risks
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- Restriction map design requires domain expertise
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- Initial setup more complex than confidence thresholds
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## References
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- Hansen & Ghrist (2019), "Toward a spectral theory of cellular sheaves"
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- ADR-014: Coherence Engine Architecture
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