The Mechanism · Gated-generation receipt

gen-define-hamming-distance-and-give-one-short-worked-example-1a15

stable pending witness
2026-05-29 08:53:44 UTC · anthropic/claude-sonnet-4-5

Prompt

Define Hamming distance and give one short worked example.
58 chars

Generation

# Hamming Distance **Definition:** The Hamming distance between two strings of equal length is the number of positions at which the corresponding symbols are different. In other words, it counts the minimum number of substitutions needed to change one string into the other. ## Worked Example Find the Hamming distance between "**karolin**" and "**kathrin**" ``` k a r o l i n k a t h r i n ✓ ✗ ✗ ✗ ✓ ✓ ``` Comparing position by position: - Position 1: k = k ✓ - Position 2: a = a ✓ - Position 3: r ≠ t ✗ - Position 4: o ≠ h ✗ - Position 5: l ≠ r ✗ - Position 6: i = i ✓ - Position 7: n = n ✓ **Hamming distance = 3** (three positions differ)
19 tokens in · 244 tokens out · 4269 ms · $0.0037

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
4276.5 ms
Base LLM
4269.1 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0037

Trail

08:53:44 received prompt_chars=58 verifiers=['scripture_anchors', 'theology_doctrine']
08:53:44 red_gate decision=pass reason=no disqualifying input patterns detected
08:53:49 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=19 tokens_out=244 latency_ms=4269.1 cost_usd=0.0037
08:53:49 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:53:49 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:53:49 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:53:49 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:53:49 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:53:49 signed hash_algo=sha256 hash=sha256:437921e10bc4c856ef34c2c8b1e1652c0ecc30f4d238881d5c360e4338915f5a

Content hash

sha256:437921e10bc4c856ef34c2c8b1e1652c0ecc30f4d238881d5c360e4338915f5a

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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