The Mechanism · Gated-generation receipt

gen-state-congruence-criteria-precisely-and-explain-why-it-matte-e1a3

stable pending witness
2026-05-29 04:00:19 UTC · anthropic/claude-sonnet-4-5

Prompt

State congruence criteria precisely and explain why it matters in 2-3 sentences.
80 chars

Generation

# Congruence Criteria **Precise Statement:** Two triangles are congruent if they satisfy any of these conditions: - **SSS**: All three pairs of corresponding sides are equal - **SAS**: Two pairs of sides and the included angle are equal - **ASA**: Two pairs of angles and the included side are equal - **AAS**: Two pairs of angles and a non-included side are equal - **HL** (right triangles only): Hypotenuse and one leg are equal **Why It Matters:** Congruence criteria allow us to prove triangles are identical in shape and size without measuring all six parts, which is essential for geometric proofs and practical applications. These minimal conditions guarantee that all other corresponding parts are automatically equal (CPCTC), making geometric reasoning efficient and rigorous.
26 tokens in · 184 tokens out · 5317 ms · $0.0028

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
5325.2 ms
Base LLM
5316.6 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0028

Trail

04:00:19 received prompt_chars=80 verifiers=['scripture_anchors', 'theology_doctrine']
04:00:19 red_gate decision=pass reason=no disqualifying input patterns detected
04:00:24 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=26 tokens_out=184 latency_ms=5316.6 cost_usd=0.0028
04:00:24 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:00:24 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:00:24 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:00:24 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:00:24 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:00:24 signed hash_algo=sha256 hash=sha256:23aca434cdfc71a6d3adda08722c7e94e880da7f33f0d70d4b95976d2d4160af

Content hash

sha256:23aca434cdfc71a6d3adda08722c7e94e880da7f33f0d70d4b95976d2d4160af

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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