The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-elliptic-curve-cryptography-state-a-b8a1

stable pending witness
2026-05-29 02:27:26 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain elliptic-curve cryptography. State any key formula.
77 chars

Generation

Elliptic-curve cryptography (ECC) is a public-key encryption approach based on the algebraic structure of elliptic curves over finite fields. It relies on the computational difficulty of the elliptic curve discrete logarithm problem: given points P and Q on an elliptic curve, finding the integer k such that Q = kP is computationally infeasible for large k. The key formula defining an elliptic curve is: **y² = x³ + ax + b** (where 4a³ + 27b² ≠ 0) ECC provides equivalent security to traditional methods like RSA but with much smaller key sizes, making it more efficient for modern applications.
29 tokens in · 158 tokens out · 4705 ms · $0.0025

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
4713.2 ms
Base LLM
4705.1 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0025

Trail

02:27:26 received prompt_chars=77 verifiers=['scripture_anchors', 'theology_doctrine']
02:27:26 red_gate decision=pass reason=no disqualifying input patterns detected
02:27:31 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=158 latency_ms=4705.1 cost_usd=0.0025
02:27:31 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
02:27:31 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
02:27:31 floor_gate decision=pass reason=output above protective minimum; no mismatches
02:27:31 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
02:27:31 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
02:27:31 signed hash_algo=sha256 hash=sha256:750175c19cc4ca1f7d4748973efe1da55047c1d18418e73dc6a73a80d3977207

Content hash

sha256:750175c19cc4ca1f7d4748973efe1da55047c1d18418e73dc6a73a80d3977207

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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