The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-day-of-the-week-from-a-date-zel-4b77

stable pending witness
2026-05-29 05:34:15 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the day of the week from a date (Zeller's congruence). State any key formula.
103 chars

Generation

Zeller's congruence is an algorithm that calculates the day of the week for any given date. The key formula is: **h = (q + ⌊13(m+1)/5⌋ + K + ⌊K/4⌋ + ⌊J/4⌋ - 2J) mod 7**, where h is the day of the week (0=Saturday, 1=Sunday, etc.), q is the day of the month, m is the month (3=March, 4=April, ..., 14=February, with January and February counted as months 13 and 14 of the previous year), K is the year of the century (year mod 100), and J is the zero-based century (⌊year/100⌋). The formula accounts for leap years and the irregularities in the calendar system to produce an accurate day-of-week calculation.
38 tokens in · 213 tokens out · 7094 ms · $0.0033

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
7110.7 ms
Base LLM
7094.5 ms
Verifiers
0.2 ms
Gates
0.1 ms
Cost
$0.0033

Trail

05:34:15 received prompt_chars=103 verifiers=['scripture_anchors', 'theology_doctrine']
05:34:15 red_gate decision=pass reason=no disqualifying input patterns detected
05:34:22 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=38 tokens_out=213 latency_ms=7094.5 cost_usd=0.0033
05:34:22 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:34:22 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:34:22 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:34:22 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:34:22 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:34:22 signed hash_algo=sha256 hash=sha256:44b62f18115dac7b30cd96d77facbb1c63d68f7e3f3b88d4f2eaee5696dd2a7f

Content hash

sha256:44b62f18115dac7b30cd96d77facbb1c63d68f7e3f3b88d4f2eaee5696dd2a7f

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.

Bring another teaching · Run a discernment