The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-source-coding-theorem-state-any-9132

stable pending witness
2026-05-29 08:06:52 UTC · anthropic/claude-sonnet-4-5

Prompt

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

Generation

The source coding theorem, also known as Shannon's first theorem, establishes the fundamental limit for lossless data compression. It states that a discrete memoryless source with entropy H(X) can be compressed to an average code length arbitrarily close to H(X) bits per symbol, but no compression scheme can achieve an average length less than H(X) without losing information. The key formula is the entropy: **H(X) = -Σ p(x) log₂ p(x)**, where p(x) is the probability of symbol x. This theorem guarantees that optimal codes achieve an average length L satisfying H(X) ≤ L < H(X) + 1.
26 tokens in · 158 tokens out · 4430 ms · $0.0024

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
4442.6 ms
Base LLM
4430.4 ms
Verifiers
0.2 ms
Gates
0.1 ms
Cost
$0.0024

Trail

08:06:52 received prompt_chars=75 verifiers=['scripture_anchors', 'theology_doctrine']
08:06:52 red_gate decision=pass reason=no disqualifying input patterns detected
08:06:56 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=26 tokens_out=158 latency_ms=4430.4 cost_usd=0.0024
08:06:56 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:06:56 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:06:56 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:06:56 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:06:56 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:06:56 signed hash_algo=sha256 hash=sha256:a6e08c3bd2a6fb53eebdc4f3882238861ed86b16562fb1be7551f26d40d9d0bb

Content hash

sha256:a6e08c3bd2a6fb53eebdc4f3882238861ed86b16562fb1be7551f26d40d9d0bb

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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