The Mechanism · Gated-generation receipt

gen-define-area-and-perimeter-relationships-and-give-one-short-w-27a7

stable pending witness
2026-05-29 05:00:32 UTC · anthropic/claude-sonnet-4-5

Prompt

Define area and perimeter relationships and give one short worked example.
74 chars

Generation

# Area and Perimeter Relationships ## Definitions **Perimeter**: The total distance around the outside of a 2D shape (measured in linear units: cm, m, etc.) **Area**: The amount of space enclosed within a 2D shape (measured in square units: cm², m², etc.) ## Key Relationship **Perimeter and area are independent** — shapes can have the same perimeter but different areas, or the same area but different perimeters. --- ## Worked Example **A rectangle has length 8 cm and width 3 cm. Find its perimeter and area.** **Perimeter:** - P = 2(length + width) - P = 2(8 + 3) - P = 2(11) - **P = 22 cm** **Area:** - A = length × width - A = 8 × 3 - **A = 24 cm²** Notice: Perimeter is measured in cm (linear), area in cm² (square units).
20 tokens in · 242 tokens out · 5035 ms · $0.0037

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
5042.7 ms
Base LLM
5035.2 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0037

Trail

05:00:32 received prompt_chars=74 verifiers=['scripture_anchors', 'theology_doctrine']
05:00:32 red_gate decision=pass reason=no disqualifying input patterns detected
05:00:37 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=20 tokens_out=242 latency_ms=5035.2 cost_usd=0.0037
05:00:37 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:00:37 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:00:37 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:00:37 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:00:37 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:00:37 signed hash_algo=sha256 hash=sha256:0a4eab7a2512d2f6631bce09a84d2fbda88036bd920d8ae38eb2a02ada38f4d5

Content hash

sha256:0a4eab7a2512d2f6631bce09a84d2fbda88036bd920d8ae38eb2a02ada38f4d5

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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