I₁ · STATE INTEGRITY
No unauthorized state mutation
Every state transition must pass the full 5-gate validation pipeline. Any failure causes a complete revert — no partial state persists.
S_new = f(S_old, event)
⟹ event fully validated
Violation → Transfer = REJECT
I₂ · COMPLIANCE INTEGRITY
All rules must be TRUE
The compliance engine is a total blocking function. C(e) = ⋀ᵢ rᵢ(e). First FALSE terminates — no bypass path exists.
C(e) = 1 → ALLOW
C(e) = 0 → BLOCK
Violation → BLOCK + RESTRICTED
I₃ · IDENTITY INTEGRITY
Status(IR) = VALID required
If ID ≥ 1, only VALID identity permits transfer. UNKNOWN is blocking — fail-safe by design. ZKP compatible.
VALID ↔ time<EXP ∧ REV=0
UNKNOWN → BLOCK
Violation → Transfer = REJECT
I₄ · GOVERNANCE INTEGRITY
Override needs sig + quorum
No minority can execute restricted overrides. ⌈2/3 × N⌉ quorum required for EMERGENCY_ROLLBACK. Legal basis hash mandatory.
k ≥ ⌈2/3 × N⌉
+ Verify(SIG) = TRUE
Violation → Override = REJECT
I₅ · DOWNGRADE RESISTANCE
Hashes invariant across chains
Destination chain verifies ComplianceHash, GovHash, ID level, and jurisdiction. Any mismatch blocks transfer before minting.
CH_dest = CH_origin
GH_dest = GH_origin
Violation → REJECT, no mint
I₆ · LEGAL BINDING
Asset references legal hash
Legal Mirror anchors governing document via LH = H(doc ‖ J ‖ v). Document may be off-chain; only hash is on-chain. Tamper → different LH.
LH = H(document ‖ J ‖ v)
Missing → Certification FAIL
Cross-chain: LH preserved
I₇ · SCHEMA INTEGRITY
H(ser(Asset)) = stored hash
Canonical serialization: fixed field order, UTF-8, big-endian. Any field change produces a different hash. Unknown fields rejected.
H(ser(Asset)) = StoredHash
ser(·): fixed order + encoding
Mismatch → Implementation INVALID
I₈ · BOUNDED EXECUTION
All modules run in O(n) or O(1)
Compliance O(|C|), fees O(|m|), governance O(|N|), cross-chain O(1). No unbounded loops. Deterministic gas in smart contract environments.
T(compliance) = O(|C|)
T(cross-chain) = O(1)
Exceeded → Transaction REJECT
I₉ · DEPLOYMENT INTEGRITY
Deployment must not weaken
No institutional customization may weaken any invariant. All nine invariants above must hold in every production deployment.
∀ deployment D:
D preserves I₁ through I₈
Violation → Certification INVALID
I₁₀ · PROFILE INVARIANT
All profiles A–F preserve I₁–I₉
Smart contract, account-based, object model, permissioned, sovereign, hybrid — every profile is bound by the full invariant set.
∀ P ∈ {A,B,C,D,E,F}:
P preserves I₁–I₉
Violation → Certification REVOKED
I₁₁ · CERTIFICATE INTEGRITY
CID commits to all asset components — any change produces a different certificate
The Cross-Chain Certificate Identifier binds State, Compliance, Governance, Jurisdiction, and Legal Mirror into a single hash. Under collision resistance, forging a valid CID for modified inputs is computationally infeasible. This is the cryptographic backbone of cross-chain regulatory continuity.
CID = H(I ‖ SH ‖ CH ‖ GH ‖ t) where SH=H(ser(S)), CH=H(ser(C)), GH=H(ser(G))
(S,C,G,J,L) ≠ (S',C',G',J',L') ⟹ CID_new ≠ CID_prev Violation → Transfer REJECT, no minting