The Mechanism · Gated-generation receipt

gen-state-satisfiability-precisely-and-explain-why-it-matters-in-48db

stable pending witness
2026-05-29 08:38:48 UTC · anthropic/claude-sonnet-4-5

Prompt

State satisfiability precisely and explain why it matters in 2-3 sentences.
75 chars

Generation

# Satisfiability **Definition**: A logical formula is *satisfiable* if there exists at least one interpretation (assignment of truth values to its variables) that makes the formula true. Otherwise, it is *unsatisfiable*. **Why it matters**: Satisfiability is fundamental because many problems in computer science, mathematics, and engineering can be reduced to checking whether a logical formula is satisfiable—including hardware/software verification, planning, scheduling, and constraint solving. The Boolean satisfiability problem (SAT) is also the first problem proven to be NP-complete, making it central to computational complexity theory and our understanding of what can be efficiently computed.
25 tokens in · 144 tokens out · 3381 ms · $0.0022

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
3387.9 ms
Base LLM
3381.0 ms
Verifiers
0.3 ms
Gates
0.1 ms
Cost
$0.0022

Trail

08:38:48 received prompt_chars=75 verifiers=['scripture_anchors', 'theology_doctrine']
08:38:48 red_gate decision=pass reason=no disqualifying input patterns detected
08:38:51 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=25 tokens_out=144 latency_ms=3381.0 cost_usd=0.0022
08:38:51 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:38:51 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:38:51 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:38:51 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:38:51 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:38:51 signed hash_algo=sha256 hash=sha256:761a167ac64d7ce6c275e77e354a2003dfb71e7118ecb22ba237f3c02d41f156

Content hash

sha256:761a167ac64d7ce6c275e77e354a2003dfb71e7118ecb22ba237f3c02d41f156

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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