The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-phasor-analysis-state-any-key-formu-c98e

stable pending witness
2026-05-29 03:47:56 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain phasor analysis. State any key formula.
65 chars

Generation

Phasor analysis is a technique for analyzing AC circuits in steady state by representing sinusoidal voltages and currents as rotating complex numbers (phasors). A sinusoidal signal **v(t) = V_m cos(ωt + φ)** is transformed into a phasor **V = V_m ∠φ** or **V = V_m e^(jφ)**, where the time-dependent part e^(jωt) is implicit. This converts differential equations in the time domain into algebraic equations in the frequency domain, greatly simplifying circuit analysis. The key relationship is **v(t) = Re{V e^(jωt)}**, which allows conversion between time-domain signals and phasors.
26 tokens in · 170 tokens out · 6352 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
6359.5 ms
Base LLM
6352.4 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0026

Trail

03:47:56 received prompt_chars=65 verifiers=['scripture_anchors', 'theology_doctrine']
03:47:56 red_gate decision=pass reason=no disqualifying input patterns detected
03:48:03 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=26 tokens_out=170 latency_ms=6352.4 cost_usd=0.0026
03:48:03 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
03:48:03 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
03:48:03 floor_gate decision=pass reason=output above protective minimum; no mismatches
03:48:03 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
03:48:03 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
03:48:03 signed hash_algo=sha256 hash=sha256:485f0248a0ca8007891387e84d38cea1ee8d5aa995851930530baccdca33b22e

Content hash

sha256:485f0248a0ca8007891387e84d38cea1ee8d5aa995851930530baccdca33b22e

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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