The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-tangent-lines-to-a-curve-state-any-af32

stable pending witness
2026-05-29 03:56:34 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain tangent lines to a curve. State any key formula.
74 chars

Generation

A tangent line to a curve at a given point is a straight line that just touches the curve at that point and has the same direction (slope) as the curve at that instant. It represents the best linear approximation to the curve near that point. The key formula for the tangent line at point $(x_0, y_0)$ on a curve $y = f(x)$ is: $$y - y_0 = f'(x_0)(x - x_0)$$ where $f'(x_0)$ is the derivative of $f$ at $x_0$, which gives the slope of the tangent line.
28 tokens in · 148 tokens out · 3512 ms · $0.0023

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
3517.5 ms
Base LLM
3511.6 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0023

Trail

03:56:34 received prompt_chars=74 verifiers=['scripture_anchors', 'theology_doctrine']
03:56:34 red_gate decision=pass reason=no disqualifying input patterns detected
03:56:38 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=28 tokens_out=148 latency_ms=3511.6 cost_usd=0.0023
03:56:38 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
03:56:38 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
03:56:38 floor_gate decision=pass reason=output above protective minimum; no mismatches
03:56:38 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
03:56:38 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
03:56:38 signed hash_algo=sha256 hash=sha256:3467f3a5ba74229f20627022d99101540ab4740915217044bddb6360fc21adef

Content hash

sha256:3467f3a5ba74229f20627022d99101540ab4740915217044bddb6360fc21adef

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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