The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-conic-sections-state-any-key-formul-dec7

stable pending witness
2026-05-29 08:42:56 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain conic sections. State any key formula.
64 chars

Generation

Conic sections are curves formed by intersecting a plane with a double cone, resulting in four basic shapes: circles, ellipses, parabolas, and hyperbolas. Each shape has distinct properties and applications in physics, engineering, and astronomy. **Key formulas:** - **Circle:** x² + y² = r² - **Ellipse:** x²/a² + y²/b² = 1 - **Parabola:** y² = 4px or x² = 4py - **Hyperbola:** x²/a² - y²/b² = 1 These can all be represented by the general second-degree equation: Ax² + Bxy + Cy² + Dx + Ey + F = 0.
25 tokens in · 178 tokens out · 3780 ms · $0.0027

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
3792.8 ms
Base LLM
3780.1 ms
Verifiers
0.2 ms
Gates
0.1 ms
Cost
$0.0027

Trail

08:42:56 received prompt_chars=64 verifiers=['scripture_anchors', 'theology_doctrine']
08:42:56 red_gate decision=pass reason=no disqualifying input patterns detected
08:43:00 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=25 tokens_out=178 latency_ms=3780.1 cost_usd=0.0027
08:43:00 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:43:00 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:43:00 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:43:00 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:43:00 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:43:00 signed hash_algo=sha256 hash=sha256:283c84276a1023fb51862d5239bdcaa9f2208cb3906e4503b780415125d26463

Content hash

sha256:283c84276a1023fb51862d5239bdcaa9f2208cb3906e4503b780415125d26463

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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