The Mechanism · Gated-generation receipt

gen-define-satisfiability-and-give-one-short-worked-example-b992

stable pending witness
2026-05-29 02:55:35 UTC · anthropic/claude-sonnet-4-5

Prompt

Define satisfiability and give one short worked example.
56 chars

Generation

# Satisfiability **Definition:** A logical formula is **satisfiable** if there exists at least one assignment of truth values to its variables that makes the formula true. If no such assignment exists, the formula is **unsatisfiable**. ## Worked Example **Formula:** (P ∨ Q) ∧ (¬P ∨ R) ∧ (¬Q ∨ ¬R) Let's test the assignment: P = True, Q = False, R = True - **(P ∨ Q)** = (True ∨ False) = **True** ✓ - **(¬P ∨ R)** = (False ∨ True) = **True** ✓ - **(¬Q ∨ ¬R)** = (True ∨ False) = **True** ✓ Overall: True ∧ True ∧ True = **True** **Conclusion:** The formula is **satisfiable** (we found a satisfying assignment).
18 tokens in · 251 tokens out · 4106 ms · $0.0038

The four gates

RED
pass
no disqualifying input patterns detected
FLOOR
pass
output above protective minimum; no mismatches
WAY
pass
no declared way_path (Way check NA); no coercion language
EXECUTION
deferred
no witnesses available (Witness Roll not yet constituted)

Verifier results

scripture_anchors NOT_APPLICABLE
0 Scripture citation(s) extracted
theology_doctrine NOT_APPLICABLE
no doctrine keyword patterns detected

Metrics

Total latency
4113.1 ms
Base LLM
4105.9 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0038

Trail

02:55:35 received prompt_chars=56 verifiers=['scripture_anchors', 'theology_doctrine']
02:55:35 red_gate decision=pass reason=no disqualifying input patterns detected
02:55:39 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=18 tokens_out=251 latency_ms=4105.9 cost_usd=0.0038
02:55:39 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
02:55:39 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
02:55:39 floor_gate decision=pass reason=output above protective minimum; no mismatches
02:55:39 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
02:55:39 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
02:55:39 signed hash_algo=sha256 hash=sha256:c32470e91e796a53840d0e8af3dccdb4c147d229b558e2b1607ea0d95a8c21d7

Content hash

sha256:c32470e91e796a53840d0e8af3dccdb4c147d229b558e2b1607ea0d95a8c21d7

SHA256 over the canonical JSON (excluding this field). Tamper detection. Ed25519 signing planned for v2 once the operator’s signing key is provisioned on disk.

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