The Mechanism · Gated-generation receipt

gen-explain-coordinate-geometry-as-you-would-to-a-capable-studen-63cc

stable pending witness
2026-05-29 03:53:00 UTC · anthropic/claude-sonnet-4-5

Prompt

Explain coordinate geometry as you would to a capable student, in 3-4 sentences.
80 chars

Generation

Coordinate geometry connects algebra and geometry by placing shapes on a grid where every point has an address given by coordinates (x, y). This lets you use equations to describe geometric objects—for example, a circle becomes an equation like x² + y² = r², and a line becomes y = mx + b. The real power is that you can now solve geometry problems using algebra: finding distances with formulas, calculating slopes, proving shapes are parallel or perpendicular, and locating intersection points by solving equations simultaneously.
27 tokens in · 109 tokens out · 3711 ms · $0.0017

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
3717.8 ms
Base LLM
3710.6 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0017

Trail

03:53:00 received prompt_chars=80 verifiers=['scripture_anchors', 'theology_doctrine']
03:53:00 red_gate decision=pass reason=no disqualifying input patterns detected
03:53:04 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=27 tokens_out=109 latency_ms=3710.6 cost_usd=0.0017
03:53:04 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
03:53:04 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
03:53:04 floor_gate decision=pass reason=output above protective minimum; no mismatches
03:53:04 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
03:53:04 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
03:53:04 signed hash_algo=sha256 hash=sha256:32edd5e7f24e40a38b8b9a7f9f5de2afec16d8d8d499fed9805999e53ac85a01

Content hash

sha256:32edd5e7f24e40a38b8b9a7f9f5de2afec16d8d8d499fed9805999e53ac85a01

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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