The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-darcy-s-law-state-any-key-formula-a2c4

stable pending witness
2026-05-29 06:39:27 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain Darcy's law. State any key formula.
61 chars

Generation

Darcy's law describes the flow of fluid through a porous medium, stating that the flow rate is proportional to the pressure gradient and inversely proportional to the fluid viscosity. The key formula is: **Q = -KA(dh/dl)** where Q is the volumetric flow rate, K is the hydraulic conductivity of the porous medium, A is the cross-sectional area, and dh/dl is the hydraulic gradient (change in hydraulic head over distance). This fundamental principle is widely used in groundwater hydrology, petroleum engineering, and soil mechanics to predict fluid movement through permeable materials.
27 tokens in · 139 tokens out · 5517 ms · $0.0022

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
5523.4 ms
Base LLM
5516.8 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0022

Trail

06:39:27 received prompt_chars=61 verifiers=['scripture_anchors', 'theology_doctrine']
06:39:27 red_gate decision=pass reason=no disqualifying input patterns detected
06:39:33 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=27 tokens_out=139 latency_ms=5516.8 cost_usd=0.0022
06:39:33 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:39:33 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:39:33 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:39:33 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:39:33 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:39:33 signed hash_algo=sha256 hash=sha256:993c27cb3f6c4574d4a71940bb9859b803cf1e84ee1874579a846a37964b032c

Content hash

sha256:993c27cb3f6c4574d4a71940bb9859b803cf1e84ee1874579a846a37964b032c

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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