SCBE/HYDRA: Tarski Sheaf for Temporal Consensus and Policy Propagation

Purpose

This formalism models triadic/tetradic temporal nodes as a lattice-valued sheaf and verifies whether local intent variants can be glued into a globally consistent policy state.

Model

• Temporal nodes: triadic (Ti, Tm, Tg) or tetradic (Ti, Tm, Tg, Tp).
• Stalk lattice: finite chain (default Boolean {0,1} where 0=noise, 1=valid intent).
• Restrictions: monotone edge maps (identity by default, optional twisted/adversarial maps).
• Tarski operator: Phi(x)_v = x_v ∧ (meet of incoming restricted neighbor values).

TH^0 is represented as the set of fixed points of Phi.

Why this helps SCBE/HYDRA

1. Consensus verification: a state is globally valid iff it is a fixed point.
2. Obstruction detection: violations are counted by local node failures against incoming meets.
3. Fail-to-noise enforcement: iterative descent of Phi projects inconsistent states toward bottom/noise.
4. Adversarial path testing: twisted restrictions (e.g., Boolean complement edges) reveal braiding obstructions.

End-to-end mapping dimensions

1. Mathematical: finite lattice + monotone maps + Tarski fixed points.
2. Governance: local policy intents are accepted only when gluable globally.
3. Security: adversarial twists produce detectable obstructions and trigger degradation to noise.
4. Operational: deterministic, testable Python implementation with bounded convergence.

Stakeholder impact

• AI governance teams: auditable consistency checks across temporal variants.
• Security teams: explicit obstruction detection on adversarial routes.
• MLOps/platform teams: predictable fail-safe projection behavior for release gating.
• Pilot buyers: interpretable explanation for why model-policy states are accepted/rejected.