Mathematical Rigor
Bounded Lattice Semantics
Conventional policy engines suffer from conflicting rule precedence, circular definitions, and order-dependent evaluation bugs. MGC solves policy conflict by structuring governance verdicts as a formal bounded meet-semilattice:
Status(v) = Local(v) ⊓ ⨅_{u ∈ Parents(v)} Inherited(u)
Order: DENY ⊏ REVIEW ⊏ MONITOR ⊏ PERMIT
Under this algebraic structure, DENY is the strict zero element (⊥). If any ancestor in an artifact's derivation history is encumbered by an active blocking condition, no downstream child can escape it without cryptographic discharge by an authorized authority.
curl -X POST https://app.materialcondition.com/api/evaluate \
-H "Authorization: Bearer $MGC_API_KEY" \
-H "Content-Type: application/json" \
-d '{
"target_entity": "urn:sha256:7b91c04f981e...",
"depth_limit": 64
}'
{
"status": "EVALUATED",
"overall_verdict": "DENY",
"lattice_meet": "LOCAL_PERMIT ⊓ INHERITED_DENY = DENY",
"blocking_encumbrance": {
"condition_id": "MGC-2026-004",
"root_ancestor": "urn:sha256:d8a2048f...",
"lineage_depth": 2,
"required_authority": "ADJUDICATOR"
}
}