The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-quadratic-residues-answer-concis-6043

stable pending witness
2026-05-29 02:50:28 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of quadratic residues? Answer concisely in 2-3 sentences.
82 chars

Generation

Quadratic residues are fundamental to number theory and cryptography, determining which integers can be expressed as perfect squares modulo n. They form the basis for important algorithms like the Legendre symbol and quadratic reciprocity law, which provide efficient methods for solving equations and testing primality. Their properties are also crucial for modern cryptographic systems, including encryption schemes and zero-knowledge proofs.
29 tokens in · 84 tokens out · 2428 ms · $0.0013

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
2439.3 ms
Base LLM
2428.2 ms
Verifiers
0.2 ms
Gates
0.1 ms
Cost
$0.0013

Trail

02:50:28 received prompt_chars=82 verifiers=['scripture_anchors', 'theology_doctrine']
02:50:28 red_gate decision=pass reason=no disqualifying input patterns detected
02:50:30 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=84 latency_ms=2428.2 cost_usd=0.0013
02:50:30 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
02:50:30 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
02:50:30 floor_gate decision=pass reason=output above protective minimum; no mismatches
02:50:30 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
02:50:30 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
02:50:30 signed hash_algo=sha256 hash=sha256:f18eaedde27b833847e387de67ef42720adb25fd0959f0c6c4ea5a712ef0bbc4

Content hash

sha256:f18eaedde27b833847e387de67ef42720adb25fd0959f0c6c4ea5a712ef0bbc4

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