The Mechanism · Gated-generation receipt

gen-state-capacitor-charging-in-an-rc-circuit-precisely-and-expl-6e57

stable pending witness
2026-05-29 08:33:26 UTC · anthropic/claude-sonnet-4-5

Prompt

State capacitor charging in an RC circuit precisely and explain why it matters in 2-3 sentences.
96 chars

Generation

# Capacitor Charging in an RC Circuit **Precise Statement:** The voltage across a capacitor in an RC circuit charges according to V(t) = V₀(1 - e^(-t/RC)), where V₀ is the source voltage, R is resistance, C is capacitance, and RC is the time constant τ. **Why It Matters:** This exponential behavior determines how quickly circuits respond to voltage changes, which is critical for timing applications, signal filtering, and power supply design. The time constant τ = RC tells engineers exactly how fast a circuit will reach steady-state—after 5τ, the capacitor is ~99% charged, making this essential for predicting circuit behavior in everything from camera flashes to computer memory.
29 tokens in · 168 tokens out · 5822 ms · $0.0026

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
5829.3 ms
Base LLM
5822.0 ms
Verifiers
0.4 ms
Gates
0.1 ms
Cost
$0.0026

Trail

08:33:26 received prompt_chars=96 verifiers=['scripture_anchors', 'theology_doctrine']
08:33:26 red_gate decision=pass reason=no disqualifying input patterns detected
08:33:32 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=168 latency_ms=5822.0 cost_usd=0.0026
08:33:32 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:33:32 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:33:32 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:33:32 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:33:32 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:33:32 signed hash_algo=sha256 hash=sha256:4c0a16b89ab02e14767646e0a00b1a25d8bb5e6bdbd58ef7a2306e3637164ecc

Content hash

sha256:4c0a16b89ab02e14767646e0a00b1a25d8bb5e6bdbd58ef7a2306e3637164ecc

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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