The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-lagrangian-formulation-state-an-2b79

stable pending witness
2026-05-29 06:55:15 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the Lagrangian formulation. State any key formula.
76 chars

Generation

The Lagrangian formulation is an approach to classical mechanics that describes a system's dynamics using the Lagrangian function L = T - V, where T is kinetic energy and V is potential energy. The system's motion is determined by the principle of least action through the **Euler-Lagrange equation**: **d/dt(∂L/∂q̇ᵢ) - ∂L/∂qᵢ = 0** where qᵢ represents generalized coordinates and q̇ᵢ their time derivatives. This formulation is often more powerful than Newton's laws because it works in any coordinate system and automatically incorporates constraints.
29 tokens in · 157 tokens out · 4255 ms · $0.0024

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
4262.1 ms
Base LLM
4255.3 ms
Verifiers
0.2 ms
Gates
0.1 ms
Cost
$0.0024

Trail

06:55:15 received prompt_chars=76 verifiers=['scripture_anchors', 'theology_doctrine']
06:55:15 red_gate decision=pass reason=no disqualifying input patterns detected
06:55:19 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=157 latency_ms=4255.3 cost_usd=0.0024
06:55:19 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:55:19 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:55:19 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:55:19 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:55:19 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:55:19 signed hash_algo=sha256 hash=sha256:ae64c56749c8ac854fb0759faefbca26b3fc78de68494684b3869be3d9c2f8f3

Content hash

sha256:ae64c56749c8ac854fb0759faefbca26b3fc78de68494684b3869be3d9c2f8f3

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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