The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-capacitor-charging-in-an-rc-circuit-897c

stable pending witness
2026-05-29 08:41:22 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain capacitor charging in an RC circuit. State any key formula.
85 chars

Generation

When a capacitor charges in an RC circuit, current initially flows at its maximum value and then decreases exponentially as the capacitor voltage builds up. The voltage across the capacitor increases from zero toward the source voltage, following an exponential curve that approaches the final value asymptotically. The charging process is characterized by the time constant τ = RC, where the capacitor reaches approximately 63% of the source voltage after one time constant. The voltage across the capacitor at any time is given by **V(t) = V₀(1 - e^(-t/RC))**, where V₀ is the source voltage.
29 tokens in · 138 tokens out · 6392 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
6398.4 ms
Base LLM
6391.8 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0022

Trail

08:41:22 received prompt_chars=85 verifiers=['scripture_anchors', 'theology_doctrine']
08:41:22 red_gate decision=pass reason=no disqualifying input patterns detected
08:41:28 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=138 latency_ms=6391.8 cost_usd=0.0022
08:41:28 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:41:28 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:41:28 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:41:28 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:41:28 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:41:28 signed hash_algo=sha256 hash=sha256:7a7b33fb68c0be025f18f673d9c350eb39c7e8e25bf727c6e96600055e95895d

Content hash

sha256:7a7b33fb68c0be025f18f673d9c350eb39c7e8e25bf727c6e96600055e95895d

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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