The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-material-implication-state-any-key-8636

hold
2026-05-29 07:38:30 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain material implication. State any key formula.
70 chars

Generation

Material implication is a logical connective that represents "if-then" statements, where a conditional statement is considered false only when the antecedent (the "if" part) is true and the consequent (the "then" part) is false. The key formula is **p → q**, which is logically equivalent to **¬p ∨ q** (either not-p or q). This means that when p is false, the implication is automatically true regardless of q's truth value—a feature that can seem counterintuitive but is fundamental to classical logic. Material implication differs from everyday causal reasoning because it's purely truth-functional, not requiring any meaningful connection between p and q.
25 tokens in · 154 tokens out · 4389 ms · $0.0024

The four gates

RED
pass
no disqualifying input patterns detected
FLOOR
pass
output above protective minimum; no mismatches
WAY
wait
output contains coercion language: ['regardless of']
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
4397.0 ms
Base LLM
4388.9 ms
Verifiers
0.2 ms
Gates
0.1 ms
Cost
$0.0024

Trail

07:38:30 received prompt_chars=70 verifiers=['scripture_anchors', 'theology_doctrine']
07:38:30 red_gate decision=pass reason=no disqualifying input patterns detected
07:38:34 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=25 tokens_out=154 latency_ms=4388.9 cost_usd=0.0024
07:38:34 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:38:34 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:38:34 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:38:34 way_gate decision=wait reason=output contains coercion language: ['regardless of']
07:38:34 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:38:34 signed hash_algo=sha256 hash=sha256:edf9e6f49dbdf97656a87a6bf64fc962fb678c34561fa560f874b91295ae90ab

Content hash

sha256:edf9e6f49dbdf97656a87a6bf64fc962fb678c34561fa560f874b91295ae90ab

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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