The Mechanism · Gated-generation receipt

gen-define-real-versus-virtual-images-and-give-one-short-worked-6ece

stable pending witness
2026-05-29 07:36:23 UTC · anthropic/claude-sonnet-4-5

Prompt

Define real versus virtual images and give one short worked example.
68 chars

Generation

# Real vs Virtual Images ## Definitions **Real Image**: An image formed when light rays actually converge at a point. Real images can be projected onto a screen and are always inverted (upside down) relative to the object. **Virtual Image**: An image formed when light rays appear to diverge from a point but don't actually meet there. Virtual images cannot be projected onto a screen and are typically upright. ## Worked Example: Concave Mirror **Given**: - Concave mirror with focal length f = 10 cm - Object placed 15 cm from mirror **Solution**: Using the mirror equation: 1/f = 1/dₒ + 1/dᵢ 1/10 = 1/15 + 1/dᵢ 1/dᵢ = 1/10 - 1/15 = 3/30 - 2/30 = 1/30 **dᵢ = +30 cm** Since dᵢ is **positive**, this is a **real image** located 30 cm in front of the mirror. Magnification: M = -dᵢ/dₒ = -30/15 = **-2** (inverted, twice the size) --- *Note: If the object were placed at 5 cm (inside the focal point), we'd get dᵢ = -10 cm (negative), indicating a virtual image behind the mirror.*
19 tokens in · 346 tokens out · 7521 ms · $0.0052

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
7530.3 ms
Base LLM
7521.3 ms
Verifiers
0.5 ms
Gates
0.1 ms
Cost
$0.0052

Trail

07:36:23 received prompt_chars=68 verifiers=['scripture_anchors', 'theology_doctrine']
07:36:23 red_gate decision=pass reason=no disqualifying input patterns detected
07:36:31 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=19 tokens_out=346 latency_ms=7521.3 cost_usd=0.0052
07:36:31 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:36:31 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:36:31 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:36:31 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:36:31 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:36:31 signed hash_algo=sha256 hash=sha256:6c602279add449cc2fda541d89d15adfc8f423026ea9fc0e011699ab5b98a286

Content hash

sha256:6c602279add449cc2fda541d89d15adfc8f423026ea9fc0e011699ab5b98a286

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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