The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-time-dilation-state-any-key-formula-f6ae

stable pending witness
2026-05-29 06:53:17 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain time dilation. State any key formula.
63 chars

Generation

Time dilation is the phenomenon where time passes at different rates for observers in different reference frames, either due to relative motion (special relativity) or gravitational fields (general relativity). An observer moving at high speed or in a strong gravitational field will experience time passing more slowly compared to an observer in a different frame. The key formula for time dilation due to relative motion is: **Δt = γΔt₀** where **γ = 1/√(1 - v²/c²)** Here, Δt₀ is the proper time (time measured by a clock at rest), Δt is the dilated time measured by a moving observer, v is relative velocity, and c is the speed of light.
25 tokens in · 165 tokens out · 3862 ms · $0.0026

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
3869.1 ms
Base LLM
3862.0 ms
Verifiers
0.3 ms
Gates
0.0 ms
Cost
$0.0026

Trail

06:53:17 received prompt_chars=63 verifiers=['scripture_anchors', 'theology_doctrine']
06:53:17 red_gate decision=pass reason=no disqualifying input patterns detected
06:53:21 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=25 tokens_out=165 latency_ms=3862.0 cost_usd=0.0026
06:53:21 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:53:21 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:53:21 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:53:21 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:53:21 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:53:21 signed hash_algo=sha256 hash=sha256:4026b4021c47944a478234f584128dbb766c8c47cd61491a9eba501cd319cc2c

Content hash

sha256:4026b4021c47944a478234f584128dbb766c8c47cd61491a9eba501cd319cc2c

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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