The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-modular-inverses-answer-concisel-14fe

stable pending witness
2026-05-29 02:57:54 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of modular inverses? Answer concisely in 2-3 sentences.
80 chars

Generation

Modular inverses are essential for solving linear congruences and performing division in modular arithmetic, which ordinary division cannot handle. They are fundamental to modern cryptography, particularly in RSA encryption where they enable secure encoding and decoding of messages. A modular inverse of *a* mod *n* exists only when *a* and *n* are coprime, making it a key concept in number theory applications.
29 tokens in · 90 tokens out · 2738 ms · $0.0014

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
2746.8 ms
Base LLM
2738.4 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0014

Trail

02:57:54 received prompt_chars=80 verifiers=['scripture_anchors', 'theology_doctrine']
02:57:54 red_gate decision=pass reason=no disqualifying input patterns detected
02:57:57 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=90 latency_ms=2738.4 cost_usd=0.0014
02:57:57 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
02:57:57 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
02:57:57 floor_gate decision=pass reason=output above protective minimum; no mismatches
02:57:57 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
02:57:57 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
02:57:57 signed hash_algo=sha256 hash=sha256:6b25c158bc689c4da3c9fa5ed5e8a3a97b7c24eee8df08f7102c717ae746b7a3

Content hash

sha256:6b25c158bc689c4da3c9fa5ed5e8a3a97b7c24eee8df08f7102c717ae746b7a3

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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