The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-primitive-roots-answer-concisely-45ef

stable pending witness
2026-05-29 06:19:43 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of primitive roots? Answer concisely in 2-3 sentences.
79 chars

Generation

Primitive roots modulo n are generators of the multiplicative group of integers modulo n, meaning their powers produce all numbers coprime to n. They are fundamental in number theory for constructing cyclic groups and have important applications in cryptography, particularly in systems like Diffie-Hellman key exchange and discrete logarithm-based encryption.
27 tokens in · 75 tokens out · 9543 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
9550.1 ms
Base LLM
9543.2 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0012

Trail

06:19:43 received prompt_chars=79 verifiers=['scripture_anchors', 'theology_doctrine']
06:19:43 red_gate decision=pass reason=no disqualifying input patterns detected
06:19:52 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=27 tokens_out=75 latency_ms=9543.2 cost_usd=0.0012
06:19:52 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:19:52 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:19:52 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:19:52 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:19:52 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:19:52 signed hash_algo=sha256 hash=sha256:d7ee2d2b99d1bff62dbef30bf78ed240187b8f9a03ac4d220b6c8d38bd4c7d20

Content hash

sha256:d7ee2d2b99d1bff62dbef30bf78ed240187b8f9a03ac4d220b6c8d38bd4c7d20

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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