The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-congruence-criteria-answer-conci-a23a

stable pending witness
2026-05-29 08:17:11 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of congruence criteria? Answer concisely in 2-3 sentences.
83 chars

Generation

Congruence criteria (SSS, SAS, ASA, AAS, and HL) provide the minimum conditions needed to prove that two triangles are congruent without having to verify all six corresponding parts. These criteria are essential tools in geometric proofs, allowing mathematicians to establish that triangles are identical in shape and size by checking only three specific measurements. This makes geometric reasoning more efficient and forms the foundation for proving many other geometric theorems and properties.
29 tokens in · 100 tokens out · 4254 ms · $0.0016

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
4261.0 ms
Base LLM
4254.3 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0016

Trail

08:17:11 received prompt_chars=83 verifiers=['scripture_anchors', 'theology_doctrine']
08:17:11 red_gate decision=pass reason=no disqualifying input patterns detected
08:17:15 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=100 latency_ms=4254.3 cost_usd=0.0016
08:17:15 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:17:15 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:17:15 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:17:15 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:17:15 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:17:15 signed hash_algo=sha256 hash=sha256:c06aa4185b88ab1160f7487187ba0e31b14d36d52c51c11ae73d6b2a6802e363

Content hash

sha256:c06aa4185b88ab1160f7487187ba0e31b14d36d52c51c11ae73d6b2a6802e363

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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