The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-lorentz-transformations-state-any-k-0d38

stable pending witness
2026-05-29 06:38:24 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain Lorentz transformations. State any key formula.
73 chars

Generation

Lorentz transformations are mathematical equations that describe how measurements of space and time change between two observers moving at constant velocity relative to each other, forming the foundation of Einstein's special relativity. They replace the classical Galilean transformations and account for the fact that the speed of light is constant in all inertial reference frames. The key formulas for an observer moving at velocity *v* along the x-axis are: - **x' = γ(x - vt)** - **t' = γ(t - vx/c²)** where **γ = 1/√(1 - v²/c²)** is the Lorentz factor and *c* is the speed of light.
28 tokens in · 162 tokens out · 3302 ms · $0.0025

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
3308.7 ms
Base LLM
3301.6 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0025

Trail

06:38:24 received prompt_chars=73 verifiers=['scripture_anchors', 'theology_doctrine']
06:38:24 red_gate decision=pass reason=no disqualifying input patterns detected
06:38:28 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=28 tokens_out=162 latency_ms=3301.6 cost_usd=0.0025
06:38:28 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:38:28 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:38:28 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:38:28 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:38:28 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:38:28 signed hash_algo=sha256 hash=sha256:a9b3ba661f4ad2726efba0684c7b7e50a5fee8a40bf4b5982ec78eaf35632c9a

Content hash

sha256:a9b3ba661f4ad2726efba0684c7b7e50a5fee8a40bf4b5982ec78eaf35632c9a

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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