The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-hot-hand-fallacy-state-any-key-e62f

stable pending witness
2026-05-29 07:06:28 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the hot-hand fallacy. State any key formula.
70 chars

Generation

The hot-hand fallacy is the mistaken belief that a person who experiences success in a random event has a greater chance of success in subsequent attempts. For example, basketball fans often believe a player who has made several shots in a row has a "hot hand" and is more likely to make the next shot, when in reality each shot is an independent event. The key insight is that for independent events, **P(success | previous successes) = P(success)**, meaning prior outcomes don't affect future probabilities. This fallacy occurs because people perceive patterns in random sequences that don't actually exist.
28 tokens in · 129 tokens out · 4480 ms · $0.002

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
4486.3 ms
Base LLM
4479.6 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.002

Trail

07:06:28 received prompt_chars=70 verifiers=['scripture_anchors', 'theology_doctrine']
07:06:28 red_gate decision=pass reason=no disqualifying input patterns detected
07:06:32 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=28 tokens_out=129 latency_ms=4479.6 cost_usd=0.002
07:06:32 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:06:32 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:06:32 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:06:32 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:06:32 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:06:32 signed hash_algo=sha256 hash=sha256:ebd26b0a40d47ce4eb9869bcce56d432fd6743b5545fd67563dac68ffb83198e

Content hash

sha256:ebd26b0a40d47ce4eb9869bcce56d432fd6743b5545fd67563dac68ffb83198e

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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