The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-a-metric-space-state-any-key-formul-44f1

stable pending witness
2026-05-29 06:36:00 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain a metric space. State any key formula.
64 chars

Generation

A metric space is a set equipped with a distance function (called a metric) that measures how far apart any two elements are. The metric must satisfy four properties: non-negativity, identity of indiscernibles, symmetry, and the triangle inequality. **Key formula:** For a metric space (X, d), the metric d: X × X → ℝ must satisfy: - d(x, y) ≥ 0 with d(x, y) = 0 iff x = y - d(x, y) = d(y, x) - d(x, z) ≤ d(x, y) + d(y, z) (triangle inequality)
25 tokens in · 161 tokens out · 4110 ms · $0.0025

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
4117.3 ms
Base LLM
4110.4 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0025

Trail

06:36:00 received prompt_chars=64 verifiers=['scripture_anchors', 'theology_doctrine']
06:36:00 red_gate decision=pass reason=no disqualifying input patterns detected
06:36:04 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=25 tokens_out=161 latency_ms=4110.4 cost_usd=0.0025
06:36:04 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:36:04 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:36:04 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:36:04 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:36:04 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:36:04 signed hash_algo=sha256 hash=sha256:29c408df52a9a58feb8ab0c02ffbb04769ad6a29597036b6c6ae5a4c68365fc3

Content hash

sha256:29c408df52a9a58feb8ab0c02ffbb04769ad6a29597036b6c6ae5a4c68365fc3

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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