The Mechanism · Gated-generation receipt

gen-explain-ramsey-theory-basics-as-you-would-to-a-capable-stude-7bcd

stable pending witness
2026-05-29 04:34:24 UTC · anthropic/claude-sonnet-4-5

Prompt

Explain Ramsey theory basics as you would to a capable student, in 3-4 sentences.
81 chars

Generation

Ramsey theory studies how order inevitably emerges in sufficiently large structures—essentially proving that complete disorder is impossible. The classic example is the party problem: at any party of 6 people, you're guaranteed to find either 3 mutual friends or 3 mutual strangers. The key insight is finding threshold sizes (Ramsey numbers) where patterns must appear, even though pinpointing these exact thresholds is notoriously difficult—for instance, we still don't know the minimum party size that guarantees 5 mutual friends or 5 mutual strangers.
30 tokens in · 126 tokens out · 4636 ms · $0.002

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
4646.3 ms
Base LLM
4636.0 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.002

Trail

04:34:24 received prompt_chars=81 verifiers=['scripture_anchors', 'theology_doctrine']
04:34:24 red_gate decision=pass reason=no disqualifying input patterns detected
04:34:29 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=30 tokens_out=126 latency_ms=4636.0 cost_usd=0.002
04:34:29 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:34:29 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:34:29 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:34:29 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:34:29 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:34:29 signed hash_algo=sha256 hash=sha256:4fb2950eb971f2abe3cd0d73cc5f1803d4fef4f883e83a33c3d304cc31612dda

Content hash

sha256:4fb2950eb971f2abe3cd0d73cc5f1803d4fef4f883e83a33c3d304cc31612dda

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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