The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-law-of-excluded-middle-state-an-74f6

stable pending witness
2026-05-29 08:29:50 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the law of excluded middle. State any key formula.
76 chars

Generation

The law of excluded middle is a fundamental principle in classical logic stating that for any proposition P, either P is true or its negation (not-P) is true—there is no third option. It asserts that every proposition must have exactly one of two truth values: true or false. **Key formula:** P ∨ ¬P (read as "P or not-P") This principle is accepted in classical logic but rejected by some non-classical systems like intuitionistic logic, where a proposition is considered true only if it can be constructively proven.
27 tokens in · 124 tokens out · 3717 ms · $0.0019

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
3724.6 ms
Base LLM
3716.7 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0019

Trail

08:29:50 received prompt_chars=76 verifiers=['scripture_anchors', 'theology_doctrine']
08:29:50 red_gate decision=pass reason=no disqualifying input patterns detected
08:29:54 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=27 tokens_out=124 latency_ms=3716.7 cost_usd=0.0019
08:29:54 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:29:54 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:29:54 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:29:54 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:29:54 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:29:54 signed hash_algo=sha256 hash=sha256:c059cf9927b0b2937bd081ef4d4f4e8b89f30b86ef1e2b302fa7d1e97ca5bd49

Content hash

sha256:c059cf9927b0b2937bd081ef4d4f4e8b89f30b86ef1e2b302fa7d1e97ca5bd49

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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