The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-volume-of-solids-of-revolution-stat-7936

stable pending witness
2026-05-29 04:14:33 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain volume of solids of revolution. State any key formula.
80 chars

Generation

A solid of revolution is created by rotating a 2D region around an axis (usually the x-axis or y-axis), forming a 3D object. To find its volume, we use either the **disk method** or the **washer method**, depending on whether the solid is filled or hollow. **Key formulas:** - Disk method (rotating around x-axis): **V = π∫[a to b] [f(x)]² dx** - Washer method (for hollow solids): **V = π∫[a to b] ([R(x)]² - [r(x)]²) dx** where R(x) is the outer radius and r(x) is the inner radius.
28 tokens in · 163 tokens out · 5956 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
5968.0 ms
Base LLM
5956.4 ms
Verifiers
0.3 ms
Gates
0.1 ms
Cost
$0.0025

Trail

04:14:33 received prompt_chars=80 verifiers=['scripture_anchors', 'theology_doctrine']
04:14:33 red_gate decision=pass reason=no disqualifying input patterns detected
04:14:39 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=28 tokens_out=163 latency_ms=5956.4 cost_usd=0.0025
04:14:39 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:14:39 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:14:39 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:14:39 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:14:39 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:14:39 signed hash_algo=sha256 hash=sha256:dc778b63f9114f782bc84b9903578de2d85bfbd899b6d5b1ce279ac147acb7c0

Content hash

sha256:dc778b63f9114f782bc84b9903578de2d85bfbd899b6d5b1ce279ac147acb7c0

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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