The Mechanism · Gated-generation receipt

gen-state-proof-by-contradiction-precisely-and-explain-why-it-ma-7295

stable pending witness
2026-05-29 04:52:30 UTC · anthropic/claude-sonnet-4-5

Prompt

State proof by contradiction precisely and explain why it matters in 2-3 sentences.
83 chars

Generation

# Proof by Contradiction **Precise Statement:** To prove a statement P, assume ¬P (P is false), then derive a logical contradiction. Since our logical system must be consistent, ¬P must be false, therefore P must be true. **Why It Matters:** Proof by contradiction is essential because some statements are extremely difficult or impossible to prove directly—it's often easier to assume the opposite and show that leads to an absurdity. This technique has established many fundamental mathematical results, including the irrationality of √2, the infinitude of primes, and Cantor's theorem on the uncountability of real numbers, which would be significantly harder to prove by direct methods.
25 tokens in · 153 tokens out · 4820 ms · $0.0024

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
4828.1 ms
Base LLM
4820.3 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0024

Trail

04:52:30 received prompt_chars=83 verifiers=['scripture_anchors', 'theology_doctrine']
04:52:30 red_gate decision=pass reason=no disqualifying input patterns detected
04:52:35 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=25 tokens_out=153 latency_ms=4820.3 cost_usd=0.0024
04:52:35 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:52:35 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:52:35 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:52:35 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:52:35 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:52:35 signed hash_algo=sha256 hash=sha256:c30a537de483411d95d93a4f1e04a36608dfcbb73dbc714c4a7daf05d9c263f7

Content hash

sha256:c30a537de483411d95d93a4f1e04a36608dfcbb73dbc714c4a7daf05d9c263f7

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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