The Mechanism · Gated-generation receipt

gen-define-the-law-of-excluded-middle-and-give-one-short-worked-8848

stable pending witness
2026-05-29 03:38:30 UTC · anthropic/claude-sonnet-4-5

Prompt

Define the law of excluded middle and give one short worked example.
68 chars

Generation

# Law of Excluded Middle The **law of excluded middle** states that for any proposition P, either P is true or its negation (not-P) is true. There is no third option. Formally: **P ∨ ¬P** (P or not-P) ## Example **Proposition P:** "It is raining right now." By the law of excluded middle: - Either "It is raining right now" (P is true) - OR "It is not raining right now" (¬P is true) One of these **must** be true. There's no middle ground where it's neither raining nor not-raining—even if we're uncertain which is the case, one of them is definitively true.
20 tokens in · 173 tokens out · 4986 ms · $0.0027

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
4994.5 ms
Base LLM
4986.2 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0027

Trail

03:38:30 received prompt_chars=68 verifiers=['scripture_anchors', 'theology_doctrine']
03:38:30 red_gate decision=pass reason=no disqualifying input patterns detected
03:38:35 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=20 tokens_out=173 latency_ms=4986.2 cost_usd=0.0027
03:38:35 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
03:38:35 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
03:38:35 floor_gate decision=pass reason=output above protective minimum; no mismatches
03:38:35 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
03:38:35 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
03:38:35 signed hash_algo=sha256 hash=sha256:a2f95b825c870da71a1eee406f820756f1f389fd013fc78d37360b98e1d62810

Content hash

sha256:a2f95b825c870da71a1eee406f820756f1f389fd013fc78d37360b98e1d62810

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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