The Mechanism · Gated-generation receipt

gen-state-similar-triangles-precisely-and-explain-why-it-matters-db6b

stable pending witness
2026-05-29 04:48:53 UTC · anthropic/claude-sonnet-4-5

Prompt

State similar triangles precisely and explain why it matters in 2-3 sentences.
78 chars

Generation

# Similar Triangles Theorem **Precise Statement:** Two triangles are similar if and only if their corresponding angles are congruent AND their corresponding sides are proportional (in the same ratio). **Why It Matters:** The precise correspondence is crucial—you must identify *which* vertices/angles/sides match up before applying similarity. Without specifying this correspondence, you cannot correctly use proportional relationships to solve for unknown lengths. For example, in △ABC ~ △DEF, you know AB/DE = BC/EF = AC/DF, but if you mismatch the correspondence, your calculations will be wrong.
25 tokens in · 138 tokens out · 4406 ms · $0.0021

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
4415.9 ms
Base LLM
4406.1 ms
Verifiers
0.2 ms
Gates
0.1 ms
Cost
$0.0021

Trail

04:48:53 received prompt_chars=78 verifiers=['scripture_anchors', 'theology_doctrine']
04:48:53 red_gate decision=pass reason=no disqualifying input patterns detected
04:48:58 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=25 tokens_out=138 latency_ms=4406.1 cost_usd=0.0021
04:48:58 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:48:58 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:48:58 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:48:58 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:48:58 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:48:58 signed hash_algo=sha256 hash=sha256:4a327d4e4b70d5d3841e370f0524fae942389c80c0766b27d36cb8daa5e01bc7

Content hash

sha256:4a327d4e4b70d5d3841e370f0524fae942389c80c0766b27d36cb8daa5e01bc7

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.

Bring another teaching · Run a discernment