The Mechanism · Gated-generation receipt

gen-explain-mathematical-induction-as-you-would-to-a-capable-stu-6f2f

stable pending witness
2026-05-29 04:28:41 UTC · anthropic/claude-sonnet-4-5

Prompt

Explain mathematical induction as you would to a capable student, in 3-4 sentences.
83 chars

Generation

Mathematical induction is a proof technique for statements involving positive integers, working like an infinite chain of dominoes. First, you prove the statement is true for the initial case (usually n=1)—this is like tipping the first domino. Then you prove that *if* the statement is true for some arbitrary case k, it *must* be true for the next case k+1—ensuring each domino knocks over the next one. These two steps together guarantee the statement is true for all positive integers, just as all the dominoes will fall.
28 tokens in · 119 tokens out · 4285 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
4295.2 ms
Base LLM
4284.5 ms
Verifiers
0.2 ms
Gates
0.1 ms
Cost
$0.0019

Trail

04:28:41 received prompt_chars=83 verifiers=['scripture_anchors', 'theology_doctrine']
04:28:41 red_gate decision=pass reason=no disqualifying input patterns detected
04:28:46 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=28 tokens_out=119 latency_ms=4284.5 cost_usd=0.0019
04:28:46 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:28:46 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:28:46 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:28:46 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:28:46 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:28:46 signed hash_algo=sha256 hash=sha256:98adeeb75784f1043937ce69d19038e8fbe7921164643cc2d913af10d5840023

Content hash

sha256:98adeeb75784f1043937ce69d19038e8fbe7921164643cc2d913af10d5840023

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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