The Mechanism · Gated-generation receipt

gen-explain-proof-by-contradiction-as-you-would-to-a-capable-stu-abee

stable pending witness
2026-05-29 05:45:01 UTC · anthropic/claude-sonnet-4-5

Prompt

Explain proof by contradiction as you would to a capable student, in 3-4 sentences.
83 chars

Generation

Proof by contradiction works by assuming the opposite of what you want to prove is true, then showing this assumption leads to a logical impossibility or contradiction. Since our logical reasoning was valid, the contradiction reveals that our initial assumption must have been false—meaning the original statement must be true. For example, to prove √2 is irrational, we assume it *is* rational (can be written as a fraction), then show this leads to a contradiction, forcing us to conclude √2 must be irrational after all.
28 tokens in · 112 tokens out · 3805 ms · $0.0018

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
3812.1 ms
Base LLM
3804.6 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0018

Trail

05:45:01 received prompt_chars=83 verifiers=['scripture_anchors', 'theology_doctrine']
05:45:01 red_gate decision=pass reason=no disqualifying input patterns detected
05:45:04 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=28 tokens_out=112 latency_ms=3804.6 cost_usd=0.0018
05:45:04 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:45:04 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:45:04 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:45:04 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:45:04 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:45:04 signed hash_algo=sha256 hash=sha256:1a304f0694f4ef804b6a8dc807c90a904865f274abe21b4882bc63b6e57ace4c

Content hash

sha256:1a304f0694f4ef804b6a8dc807c90a904865f274abe21b4882bc63b6e57ace4c

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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