The Mechanism · Gated-generation receipt

gen-define-hyperfocal-distance-and-give-one-short-worked-example-cb9a

stable pending witness
2026-05-29 07:14:06 UTC · anthropic/claude-sonnet-4-5

Prompt

Define hyperfocal distance and give one short worked example.
61 chars

Generation

# Hyperfocal Distance **Hyperfocal distance** is the closest focusing distance at which a lens can be focused while keeping objects at infinity acceptably sharp. When focused at this distance, everything from half the hyperfocal distance to infinity appears in acceptable focus. ## Formula **H = f²/(N × c) + f** Where: - H = hyperfocal distance - f = focal length - N = f-number (aperture) - c = circle of confusion (acceptable blur) For practical purposes, when f is small compared to H, this simplifies to: **H ≈ f²/(N × c)** ## Worked Example **Given:** - Focal length: f = 50mm - Aperture: f/16 (N = 16) - Circle of confusion: c = 0.03mm (typical for full-frame) **Calculate:** H = (50)²/(16 × 0.03) = 2500/0.48 ≈ **5,208mm ≈ 5.2m** **Result:** Focus the lens at 5.2m, and everything from 2.6m (half of 5.2m) to infinity will be acceptably sharp. This maximizes depth of field, making it useful for landscape photography.
20 tokens in · 307 tokens out · 8422 ms · $0.0047

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
8429.1 ms
Base LLM
8421.5 ms
Verifiers
0.3 ms
Gates
0.0 ms
Cost
$0.0047

Trail

07:14:06 received prompt_chars=61 verifiers=['scripture_anchors', 'theology_doctrine']
07:14:06 red_gate decision=pass reason=no disqualifying input patterns detected
07:14:15 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=20 tokens_out=307 latency_ms=8421.5 cost_usd=0.0047
07:14:15 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:14:15 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:14:15 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:14:15 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:14:15 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:14:15 signed hash_algo=sha256 hash=sha256:bd7a5d7c01e0dc85435a0f416c85cfc6dfca3ed3f653e6ca6eb3ea3e22a02aff

Content hash

sha256:bd7a5d7c01e0dc85435a0f416c85cfc6dfca3ed3f653e6ca6eb3ea3e22a02aff

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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