The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-noisy-channel-theorem-state-any-0f1b

stable pending witness
2026-05-29 03:02:29 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the noisy-channel theorem. State any key formula.
75 chars

Generation

The noisy-channel theorem (Shannon's theorem) states that for any communication channel with noise, there exists a maximum rate called the channel capacity C at which information can be transmitted with arbitrarily low error probability. The key formula is **C = B logâ‚‚(1 + S/N)**, where C is capacity in bits per second, B is bandwidth in Hz, and S/N is the signal-to-noise ratio. As long as the transmission rate is below this capacity, error-free communication is theoretically possible using appropriate error-correction codes. Attempting to transmit above this rate will inevitably result in errors that cannot be fully corrected.
28 tokens in · 142 tokens out · 3879 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
3887.0 ms
Base LLM
3878.9 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0022

Trail

03:02:29 received prompt_chars=75 verifiers=['scripture_anchors', 'theology_doctrine']
03:02:29 red_gate decision=pass reason=no disqualifying input patterns detected
03:02:32 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=28 tokens_out=142 latency_ms=3878.9 cost_usd=0.0022
03:02:32 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
03:02:32 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
03:02:32 floor_gate decision=pass reason=output above protective minimum; no mismatches
03:02:32 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
03:02:32 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
03:02:32 signed hash_algo=sha256 hash=sha256:6993384f4617d552c40a700ffe68d9bfb39ce05dac1fb7c8fa1b5371bbe850fc

Content hash

sha256:6993384f4617d552c40a700ffe68d9bfb39ce05dac1fb7c8fa1b5371bbe850fc

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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