The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-norton-s-theorem-state-any-key-form-0bce

stable pending witness
2026-05-29 08:35:04 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain Norton's theorem. State any key formula.
66 chars

Generation

Norton's theorem states that any linear electrical network with voltage sources, current sources, and resistances can be replaced by an equivalent circuit consisting of a single current source in parallel with a single resistance. The Norton current (I_N) is the short-circuit current flowing through the terminals, and the Norton resistance (R_N) is the equivalent resistance seen from the terminals when all independent sources are deactivated. **Key formula:** I_N = V_oc / R_N, where V_oc is the open-circuit voltage across the terminals, or equivalently, R_N = R_th (Norton resistance equals Thévenin resistance).
25 tokens in · 141 tokens out · 3741 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
3748.0 ms
Base LLM
3741.2 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0022

Trail

08:35:04 received prompt_chars=66 verifiers=['scripture_anchors', 'theology_doctrine']
08:35:04 red_gate decision=pass reason=no disqualifying input patterns detected
08:35:08 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=25 tokens_out=141 latency_ms=3741.2 cost_usd=0.0022
08:35:08 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:35:08 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:35:08 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:35:08 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:35:08 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:35:08 signed hash_algo=sha256 hash=sha256:e96b9d13e1e64a1a958cb0d2851dfee9d7fad7a2940714f47e88a262843c555f

Content hash

sha256:e96b9d13e1e64a1a958cb0d2851dfee9d7fad7a2940714f47e88a262843c555f

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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