The Mechanism · Gated-generation receipt

gen-state-the-handshake-lemma-precisely-and-explain-why-it-matte-02da

stable pending witness
2026-05-29 05:23:25 UTC · anthropic/claude-sonnet-4-5

Prompt

State the handshake lemma precisely and explain why it matters in 2-3 sentences.
80 chars

Generation

# Handshake Lemma **Precise Statement:** In any undirected graph, the sum of all vertex degrees equals twice the number of edges, or equivalently: ∑(deg(v)) = 2|E|. **Why it matters:** This fundamental result proves that every graph must have an even number of odd-degree vertices, which is crucial for determining whether Eulerian paths exist and for solving many graph-theoretic problems. It also provides a simple sanity check for graph data and connects local properties (vertex degrees) to global structure (edge count).
28 tokens in · 127 tokens out · 3575 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
3583.3 ms
Base LLM
3575.4 ms
Verifiers
0.3 ms
Gates
0.1 ms
Cost
$0.002

Trail

05:23:25 received prompt_chars=80 verifiers=['scripture_anchors', 'theology_doctrine']
05:23:25 red_gate decision=pass reason=no disqualifying input patterns detected
05:23:29 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=28 tokens_out=127 latency_ms=3575.4 cost_usd=0.002
05:23:29 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:23:29 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:23:29 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:23:29 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:23:29 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:23:29 signed hash_algo=sha256 hash=sha256:3b06d00dc8e0acffcc4a8bf4c00cd5906c1c91d6b28e0dc628481e25dfa280b0

Content hash

sha256:3b06d00dc8e0acffcc4a8bf4c00cd5906c1c91d6b28e0dc628481e25dfa280b0

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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