The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-annuities-and-perpetuities-state-an-68d0

stable pending witness
2026-05-29 05:04:27 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain annuities and perpetuities. State any key formula.
76 chars

Generation

**Annuities** are series of equal payments made at regular intervals for a fixed period of time (e.g., car loans, mortgages). **Perpetuities** are annuities that continue forever, with no end date (e.g., preferred stock dividends, endowments). **Key formulas:** - Present Value of Annuity: PV = PMT × [(1 - (1 + r)^-n) / r] - Present Value of Perpetuity: PV = PMT / r where PMT = payment amount, r = interest rate per period, n = number of periods
29 tokens in · 144 tokens out · 3872 ms · $0.0022

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
3880.9 ms
Base LLM
3871.6 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0022

Trail

05:04:27 received prompt_chars=76 verifiers=['scripture_anchors', 'theology_doctrine']
05:04:27 red_gate decision=pass reason=no disqualifying input patterns detected
05:04:30 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=144 latency_ms=3871.6 cost_usd=0.0022
05:04:30 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:04:30 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:04:30 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:04:30 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:04:30 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:04:30 signed hash_algo=sha256 hash=sha256:ee9b3f7a93c8f9e15195fb670a6a8b9bcea215cf3e24f0ffdd80126154509c0e

Content hash

sha256:ee9b3f7a93c8f9e15195fb670a6a8b9bcea215cf3e24f0ffdd80126154509c0e

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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