The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-satisfiability-state-any-key-formul-8aa8

stable pending witness
2026-05-29 08:41:42 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain satisfiability. State any key formula.
64 chars

Generation

Satisfiability is the problem of determining whether there exists an assignment of truth values to variables that makes a given logical formula true. A formula is **satisfiable** if at least one such assignment exists, and **unsatisfiable** if no assignment makes it true. The Boolean Satisfiability Problem (SAT) typically deals with formulas in **Conjunctive Normal Form (CNF)**: a conjunction of clauses where each clause is a disjunction of literals, expressed as **(l₁₁ ∨ l₁₂ ∨ ...) ∧ (l₂₁ ∨ l₂₂ ∨ ...) ∧ ...**, where each *lᵢⱼ* is a variable or its negation. SAT was the first problem proven to be NP-complete, making it foundational in computational complexity theory.
25 tokens in · 207 tokens out · 3870 ms · $0.0032

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
3876.9 ms
Base LLM
3870.1 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0032

Trail

08:41:42 received prompt_chars=64 verifiers=['scripture_anchors', 'theology_doctrine']
08:41:42 red_gate decision=pass reason=no disqualifying input patterns detected
08:41:45 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=25 tokens_out=207 latency_ms=3870.1 cost_usd=0.0032
08:41:45 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:41:45 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:41:45 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:41:45 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:41:45 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:41:45 signed hash_algo=sha256 hash=sha256:dc250bc10d1f048c230d6b7dd6a9c1d7434e41375fbed3c64914e8bfa84cdd43

Content hash

sha256:dc250bc10d1f048c230d6b7dd6a9c1d7434e41375fbed3c64914e8bfa84cdd43

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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