The Mechanism · Gated-generation receipt

gen-state-amortized-analysis-precisely-and-explain-why-it-matter-35c0

stable pending witness
2026-05-29 06:19:26 UTC · anthropic/claude-sonnet-4-5

Prompt

State amortized analysis precisely and explain why it matters in 2-3 sentences.
79 chars

Generation

# Amortized Analysis **Precise Definition:** Amortized analysis determines the average cost per operation over a worst-case sequence of n operations, even when individual operations may have varying costs. It guarantees that for any sequence of n operations, the total cost is at most n times the amortized cost. **Why It Matters:** Amortized analysis reveals the true practical efficiency of data structures like dynamic arrays or splay trees, where occasional expensive operations (like resizing) are offset by many cheap operations. This provides tighter, more realistic bounds than worst-case-per-operation analysis, which can be overly pessimistic and misrepresent actual performance.
26 tokens in · 148 tokens out · 4950 ms · $0.0023

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
4957.4 ms
Base LLM
4950.3 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0023

Trail

06:19:26 received prompt_chars=79 verifiers=['scripture_anchors', 'theology_doctrine']
06:19:26 red_gate decision=pass reason=no disqualifying input patterns detected
06:19:31 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=26 tokens_out=148 latency_ms=4950.3 cost_usd=0.0023
06:19:31 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:19:31 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:19:31 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:19:31 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:19:31 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:19:31 signed hash_algo=sha256 hash=sha256:efe3ac58ff7773a32964bae865b996eba84a9d2febeb9e48714b03f9ba1838d1

Content hash

sha256:efe3ac58ff7773a32964bae865b996eba84a9d2febeb9e48714b03f9ba1838d1

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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