The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-mathematical-induction-answer-co-d7c7

stable pending witness
2026-05-29 07:34:55 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of mathematical induction? Answer concisely in 2-3 sentences.
86 chars

Generation

Mathematical induction is a fundamental proof technique that establishes the truth of infinitely many statements by proving just two things: a base case and that each case implies the next. It's essential for proving properties about natural numbers, sequences, and recursive structures throughout mathematics and computer science. This method transforms seemingly impossible infinite verifications into manageable, finite proofs.
28 tokens in · 75 tokens out · 3309 ms · $0.0012

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
3315.3 ms
Base LLM
3308.5 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0012

Trail

07:34:55 received prompt_chars=86 verifiers=['scripture_anchors', 'theology_doctrine']
07:34:55 red_gate decision=pass reason=no disqualifying input patterns detected
07:34:58 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=28 tokens_out=75 latency_ms=3308.5 cost_usd=0.0012
07:34:58 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:34:58 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:34:58 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:34:58 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:34:58 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:34:58 signed hash_algo=sha256 hash=sha256:884a6a5f1232e47ff30e4349ca7a94468437049ab984cfc5a74de85a6068cf27

Content hash

sha256:884a6a5f1232e47ff30e4349ca7a94468437049ab984cfc5a74de85a6068cf27

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.

Bring another teaching · Run a discernment