The Mechanism · Gated-generation receipt

gen-briefly-explain-similar-triangles-and-one-common-misconcepti-ee05

stable pending witness
2026-05-29 05:31:01 UTC · anthropic/claude-sonnet-4-5

Prompt

Briefly explain similar triangles and one common misconception about it.
72 chars

Generation

# Similar Triangles **Similar triangles** are triangles that have the same shape but not necessarily the same size. They have: - **All corresponding angles equal** - **All corresponding sides in the same ratio** (called the scale factor) For example, if triangle ABC is similar to triangle DEF with a scale factor of 2, then AB/DE = BC/EF = AC/DF = 2. ## Common Misconception **"If two triangles have the same angles, their sides must be equal."** Many students confuse *similar* with *congruent*. While similar triangles have equal corresponding angles, their sides are only **proportional**, not necessarily equal. The sides are only equal when the scale factor is 1—which means the triangles are congruent (both similar AND the same size). In short: All congruent triangles are similar, but not all similar triangles are congruent.
21 tokens in · 211 tokens out · 4872 ms · $0.0032

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
4880.2 ms
Base LLM
4872.4 ms
Verifiers
0.4 ms
Gates
0.1 ms
Cost
$0.0032

Trail

05:31:01 received prompt_chars=72 verifiers=['scripture_anchors', 'theology_doctrine']
05:31:01 red_gate decision=pass reason=no disqualifying input patterns detected
05:31:06 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=21 tokens_out=211 latency_ms=4872.4 cost_usd=0.0032
05:31:06 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:31:06 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:31:06 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:31:06 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:31:06 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:31:06 signed hash_algo=sha256 hash=sha256:933e092b23c71d115fff5fcce3b440e87d7495cca4736bb3288b01ed55716f99

Content hash

sha256:933e092b23c71d115fff5fcce3b440e87d7495cca4736bb3288b01ed55716f99

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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