The Mechanism · Gated-generation receipt

gen-state-error-correcting-codes-precisely-and-explain-why-it-ma-b30d

stable pending witness
2026-05-29 04:50:23 UTC · anthropic/claude-sonnet-4-5

Prompt

State error-correcting codes precisely and explain why it matters in 2-3 sentences.
83 chars

Generation

# Error-Correcting Codes **Precise Definition:** An error-correcting code is a mapping C: Σᵏ → Σⁿ (where n > k) that encodes k information symbols into n symbols by adding redundancy, such that the minimum Hamming distance d between any two codewords allows detection of up to d-1 errors and correction of up to ⌊(d-1)/2⌋ errors. **Why It Matters:** Error-correcting codes are essential for reliable digital communication and storage because physical channels inevitably introduce noise and errors. Without them, technologies like satellite communications, QR codes, CDs/DVDs, and RAM would be completely impractical—every scratched disk would be unreadable and every wireless transmission would be corrupted. They enable the modern digital world by mathematically guaranteeing data integrity despite imperfect physical media.
27 tokens in · 203 tokens out · 5887 ms · $0.0031

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
5899.3 ms
Base LLM
5886.7 ms
Verifiers
0.2 ms
Gates
0.1 ms
Cost
$0.0031

Trail

04:50:23 received prompt_chars=83 verifiers=['scripture_anchors', 'theology_doctrine']
04:50:23 red_gate decision=pass reason=no disqualifying input patterns detected
04:50:29 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=27 tokens_out=203 latency_ms=5886.7 cost_usd=0.0031
04:50:29 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:50:29 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:50:29 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:50:29 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:50:29 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:50:29 signed hash_algo=sha256 hash=sha256:966e68dcecfe2e0835b891da3082ce0d8f844c58c6d6ebdacda64fc708439151

Content hash

sha256:966e68dcecfe2e0835b891da3082ce0d8f844c58c6d6ebdacda64fc708439151

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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