The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-generating-functions-state-any-key-a337

stable pending witness
2026-05-29 03:15:23 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain generating functions. State any key formula.
70 chars

Generation

A generating function is a formal power series where the coefficients encode a sequence of interest. For a sequence (a₀, a₁, a₂, ...), the ordinary generating function is **G(x) = Σ(n≥0) aₙxⁿ = a₀ + a₁x + a₂x² + ...** Generating functions transform problems about sequences into problems about functions, allowing us to use algebraic manipulation and calculus techniques. They're particularly powerful for solving recurrence relations and counting problems in combinatorics.
24 tokens in · 128 tokens out · 4842 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
4849.5 ms
Base LLM
4842.5 ms
Verifiers
0.1 ms
Gates
0.1 ms
Cost
$0.002

Trail

03:15:23 received prompt_chars=70 verifiers=['scripture_anchors', 'theology_doctrine']
03:15:23 red_gate decision=pass reason=no disqualifying input patterns detected
03:15:28 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=24 tokens_out=128 latency_ms=4842.5 cost_usd=0.002
03:15:28 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
03:15:28 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
03:15:28 floor_gate decision=pass reason=output above protective minimum; no mismatches
03:15:28 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
03:15:28 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
03:15:28 signed hash_algo=sha256 hash=sha256:24d734081bccba04a2683520d03b3d60a687f9c827000d8f85e2f5386d177617

Content hash

sha256:24d734081bccba04a2683520d03b3d60a687f9c827000d8f85e2f5386d177617

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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