The Mechanism · Gated-generation receipt

gen-explain-modular-inverses-as-you-would-to-a-capable-student-i-6a37

stable pending witness
2026-05-29 02:46:12 UTC · anthropic/claude-sonnet-4-5

Prompt

Explain modular inverses as you would to a capable student, in 3-4 sentences.
77 chars

Generation

# Modular Inverses A modular inverse of a number *a* modulo *n* is another number *b* such that when you multiply them together, you get 1 (mod *n*) — in other words, *ab* ≡ 1 (mod *n*). Think of it like finding a reciprocal in regular arithmetic (where 5 × 1/5 = 1), except we're working with remainders after division by *n*. For example, the modular inverse of 3 modulo 7 is 5, because 3 × 5 = 15 ≡ 1 (mod 7). Not every number has a modular inverse — it only exists when *a* and *n* are coprime (share no common factors besides 1).
29 tokens in · 189 tokens out · 4210 ms · $0.0029

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
4217.1 ms
Base LLM
4209.6 ms
Verifiers
0.3 ms
Gates
0.0 ms
Cost
$0.0029

Trail

02:46:12 received prompt_chars=77 verifiers=['scripture_anchors', 'theology_doctrine']
02:46:12 red_gate decision=pass reason=no disqualifying input patterns detected
02:46:16 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=189 latency_ms=4209.6 cost_usd=0.0029
02:46:16 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
02:46:16 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
02:46:16 floor_gate decision=pass reason=output above protective minimum; no mismatches
02:46:16 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
02:46:16 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
02:46:16 signed hash_algo=sha256 hash=sha256:e0fc7963361eb1e3a5bf2089dbad0326d9098449a2e432ea460ecf6f8961dc3d

Content hash

sha256:e0fc7963361eb1e3a5bf2089dbad0326d9098449a2e432ea460ecf6f8961dc3d

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