The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-error-correcting-codes-state-any-ke-8792

stable pending witness
2026-05-29 07:41:55 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain error-correcting codes. State any key formula.
72 chars

Generation

Error-correcting codes add redundant information to data so that errors introduced during transmission or storage can be detected and corrected. The code's ability to correct errors depends on its **minimum distance** d, which is the smallest number of bit positions in which any two valid codewords differ. A key relationship is given by the **Singleton bound**: for a code with n total bits, k data bits, and minimum distance d, we have **d ≤ n - k + 1**. Codes can correct up to t = ⌊(d-1)/2⌋ errors.
27 tokens in · 132 tokens out · 3638 ms · $0.0021

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
3647.1 ms
Base LLM
3637.7 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0021

Trail

07:41:55 received prompt_chars=72 verifiers=['scripture_anchors', 'theology_doctrine']
07:41:55 red_gate decision=pass reason=no disqualifying input patterns detected
07:41:59 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=27 tokens_out=132 latency_ms=3637.7 cost_usd=0.0021
07:41:59 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:41:59 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:41:59 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:41:59 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:41:59 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:41:59 signed hash_algo=sha256 hash=sha256:1ab21390f2bee59df5a1957279eceef7e42ea244c8d5bfae33820285aa46609b

Content hash

sha256:1ab21390f2bee59df5a1957279eceef7e42ea244c8d5bfae33820285aa46609b

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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