Theorems — Security
Every theorem derives from Axiom-0. Classical results emerge as degenerate limits.
5 theorems across 5 modules
Catalog
| ID | Name | Module |
|---|---|---|
T-SEC-1 | Trust Fidelity Duality | trust_fidelity |
T-SEC-2 | Trust Integrity Bound | trust_integrity |
T-SEC-3 | Security Entropy Bound | security_entropy |
T-SEC-4 | Anomaly Return Time | anomaly_return |
T-SEC-5 | Trust Seam Closure | trust_fidelity |
Trust Fidelity
Source: closures/security/trust_fidelity.py
T-SEC-1: Trust Fidelity Duality
- Function:
trust_fidelity_duality() - Module:
trust_fidelity - Statement: Trust T and threat drift θ satisfy T + θ = 1 — the duality identity applied to security signals
- Proof Status: PROVEN (structural identity)
- Key Result: Security fidelity inherits F + ω = 1 exactly
T-SEC-5: Trust Seam Closure
- Function:
trust_seam_closure() - Module:
trust_fidelity - Statement: The trust account must balance between successive observations — debits (anomalies) and credits (validated returns) must reconcile within tol_seam
- Proof Status: PROVEN (seam budget identity)
Trust Integrity
Source: closures/security/trust_integrity.py
T-SEC-2: Trust Integrity Bound
- Function:
trust_integrity_bound() - Module:
trust_integrity - Statement: Trust integrity composite TIC cannot exceed trust fidelity T (TIC ≤ T). One compromised signal channel destroys multiplicative trust coherence regardless of how many channels remain clean.
- Proof Status: PROVEN (integrity bound IC ≤ F)
- Key Result: One weak security channel (e.g., unverified PII) kills composite trust via geometric slaughter
Security Entropy
Source: closures/security/security_entropy.py
T-SEC-3: Security Entropy Bound
- Function:
security_entropy() - Module:
security_entropy - Statement: The Bernoulli field entropy H of the security trace measures uncertainty across signal channels. Higher entropy indicates mixed or ambiguous threat signals.
- Proof Status: PROVEN (kernel invariant)
Anomaly Return
Source: closures/security/anomaly_return.py
T-SEC-4: Anomaly Return Time
- Function:
anomaly_return_time() - Module:
anomaly_return - Statement: τ_A measures how long until anomalous signals return to baseline trust. If τ_A = ∞_rec (no return), the signal is permanently classified as BLOCKED with zero budget credit.
- Proof Status: PROVEN (return time diagnostic)
- Key Result: Persistent anomalies yield ∞_rec — permanent detention in the threat register
Security Signal Channels
| Channel | Measures | Range |
|---|---|---|
file_integrity | File hash validation | [0,1] |
malware_confidence | Malware detection score | [0,1] |
phishing_score | Fraud/phishing probability | [0,1] |
auth_strength | Authentication robustness | [0,1] |
pii_protection | PII data protection level | [0,1] |
network_trust | Network trust indicator | [0,1] |
Validation Status Mapping
| Status | Regime | Condition |
|---|---|---|
TRUSTED | Stable | All signals high, ω < 0.038 |
SUSPICIOUS | Watch | Mixed signals, 0.038 ≤ ω < 0.30 |
BLOCKED | Collapse | Clear threat, ω ≥ 0.30 |
NON_EVALUABLE | — | Insufficient signal data |
Generated by the Headless Contract Gateway (HCG) · Domain: security · UMCP v2.2.5