The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-a-hash-table-state-any-key-formula-de60

stable pending witness
2026-05-29 02:43:19 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain a hash table. State any key formula.
62 chars

Generation

A hash table is a data structure that stores key-value pairs and provides fast lookup, insertion, and deletion operations. It uses a hash function to compute an index (hash code) from a key, determining where to store the value in an underlying array. The key formula is **index = hash(key) mod table_size**, which maps the hash value to a valid array position. Hash tables typically achieve O(1) average-case time complexity for basic operations, though collisions (when different keys map to the same index) must be handled using techniques like chaining or open addressing.
25 tokens in · 124 tokens out · 3967 ms · $0.0019

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
3974.3 ms
Base LLM
3966.7 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0019

Trail

02:43:19 received prompt_chars=62 verifiers=['scripture_anchors', 'theology_doctrine']
02:43:19 red_gate decision=pass reason=no disqualifying input patterns detected
02:43:23 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=25 tokens_out=124 latency_ms=3966.7 cost_usd=0.0019
02:43:23 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
02:43:23 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
02:43:23 floor_gate decision=pass reason=output above protective minimum; no mismatches
02:43:23 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
02:43:23 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
02:43:23 signed hash_algo=sha256 hash=sha256:e20f8e18046677b0d470d3ddb53e4c55ef05aa9dffc1017a5df53f0c895abc57

Content hash

sha256:e20f8e18046677b0d470d3ddb53e4c55ef05aa9dffc1017a5df53f0c895abc57

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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