The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-handshake-lemma-state-any-key-f-283a

stable pending witness
2026-05-29 05:20:01 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the handshake lemma. State any key formula.
69 chars

Generation

The handshake lemma states that in any graph, the sum of all vertex degrees equals twice the number of edges. This is because each edge connects two vertices, so it contributes 1 to the degree of each of its endpoints, making it counted twice in the total sum. The key formula is: **∑ deg(v) = 2|E|**, where the sum is over all vertices v and |E| is the number of edges. A useful corollary is that every graph has an even number of odd-degree vertices.
28 tokens in · 122 tokens out · 3595 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
3606.2 ms
Base LLM
3594.9 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0019

Trail

05:20:01 received prompt_chars=69 verifiers=['scripture_anchors', 'theology_doctrine']
05:20:01 red_gate decision=pass reason=no disqualifying input patterns detected
05:20:05 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=28 tokens_out=122 latency_ms=3594.9 cost_usd=0.0019
05:20:05 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:20:05 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:20:05 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:20:05 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:20:05 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:20:05 signed hash_algo=sha256 hash=sha256:a30535396d68c14149266b1cff2b5b555aa31f980d70d315bd8011ea7799b81b

Content hash

sha256:a30535396d68c14149266b1cff2b5b555aa31f980d70d315bd8011ea7799b81b

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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