The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-rate-distortion-function-state-6f84

stable pending witness
2026-05-29 08:04:14 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the rate-distortion function. State any key formula.
78 chars

Generation

The rate-distortion function R(D) characterizes the minimum bit rate (information) required to represent a source with a given average distortion D. It represents the fundamental tradeoff between compression efficiency and reconstruction quality, showing that higher compression (lower rate) necessarily leads to greater distortion. For a source X and reconstruction X̂ with distortion measure d(x,x̂), the rate-distortion function is: **R(D) = min I(X;X̂)** where the minimization is over all conditional distributions p(x̂|x) subject to E[d(X,X̂)] ≤ D, and I(X;X̂) is the mutual information between source and reconstruction.
28 tokens in · 165 tokens out · 4769 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
4776.1 ms
Base LLM
4769.2 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0026

Trail

08:04:14 received prompt_chars=78 verifiers=['scripture_anchors', 'theology_doctrine']
08:04:14 red_gate decision=pass reason=no disqualifying input patterns detected
08:04:19 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=28 tokens_out=165 latency_ms=4769.2 cost_usd=0.0026
08:04:19 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:04:19 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:04:19 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:04:19 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:04:19 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:04:19 signed hash_algo=sha256 hash=sha256:ff0d72b839d6aeacaa60411741f867086cefac656bff7ce13567afb71c1b7a9a

Content hash

sha256:ff0d72b839d6aeacaa60411741f867086cefac656bff7ce13567afb71c1b7a9a

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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