The Mechanism · Gated-generation receipt

gen-explain-elliptic-curve-cryptography-as-you-would-to-a-capabl-f009

stable pending witness
2026-05-29 07:05:53 UTC · anthropic/claude-sonnet-4-5

Prompt

Explain elliptic-curve cryptography as you would to a capable student, in 3-4 sentences.
88 chars

Generation

Elliptic-curve cryptography (ECC) is based on the mathematical difficulty of solving the "discrete logarithm problem" on elliptic curves—essentially, if you add a point on the curve to itself many times to get a new point, it's extremely hard to figure out how many times you added it. This one-way mathematical operation allows you to create a public key from a private key, but makes it computationally infeasible to reverse the process. ECC provides the same security as older systems like RSA but with much smaller key sizes, making it faster and more efficient—a 256-bit ECC key offers similar security to a 3072-bit RSA key.
32 tokens in · 151 tokens out · 4466 ms · $0.0024

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
4479.4 ms
Base LLM
4466.3 ms
Verifiers
0.2 ms
Gates
0.1 ms
Cost
$0.0024

Trail

07:05:53 received prompt_chars=88 verifiers=['scripture_anchors', 'theology_doctrine']
07:05:53 red_gate decision=pass reason=no disqualifying input patterns detected
07:05:57 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=32 tokens_out=151 latency_ms=4466.3 cost_usd=0.0024
07:05:57 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:05:57 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:05:57 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:05:57 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:05:57 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:05:57 signed hash_algo=sha256 hash=sha256:59e954b5ab0450ad036dca7ad2d09e229ab6bc04eae06aee928a498ae43ef844

Content hash

sha256:59e954b5ab0450ad036dca7ad2d09e229ab6bc04eae06aee928a498ae43ef844

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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