The Mechanism · Gated-generation receipt

gen-state-the-day-of-the-week-from-a-date-zeller-s-congruence-pr-fdff

stable pending witness
2026-05-29 04:10:34 UTC · anthropic/claude-sonnet-4-5

Prompt

State the day of the week from a date (Zeller's congruence) precisely and explain why it matters in 2-3 sentences.
114 chars

Generation

# Zeller's Congruence **Formula:** h = (q + ⌊13(m+1)/5⌋ + K + ⌊K/4⌋ + ⌊J/4⌋ - 2J) mod 7 Where: - h = day of week (0=Saturday, 1=Sunday, 2=Monday, ..., 6=Friday) - q = day of month - m = month (3=March, 4=April, ..., 14=February, with Jan/Feb counted as months 13/14 of previous year) - K = year mod 100 - J = ⌊year/100⌋ **Example:** For January 1, 2025 → treat as month 13 of 2024 - h = (1 + ⌊14×14/5⌋ + 24 + 6 + 5 - 40) mod 7 = 3 → **Wednesday** ## Why It Matters Zeller's congruence matters because it provides a mathematical algorithm to calculate the day of the week for any date in history or future without needing lookup tables or calendars. This is essential for computer systems, scheduling algorithms, and historical research where determining weekdays programmatically is more efficient than storing vast amounts of calendar data.
39 tokens in · 317 tokens out · 6880 ms · $0.0049

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
6892.6 ms
Base LLM
6880.1 ms
Verifiers
0.3 ms
Gates
0.1 ms
Cost
$0.0049

Trail

04:10:34 received prompt_chars=114 verifiers=['scripture_anchors', 'theology_doctrine']
04:10:34 red_gate decision=pass reason=no disqualifying input patterns detected
04:10:41 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=39 tokens_out=317 latency_ms=6880.1 cost_usd=0.0049
04:10:41 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:10:41 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:10:41 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:10:41 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:10:41 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:10:41 signed hash_algo=sha256 hash=sha256:499ff06343b6ad0ba6ad18098b3a7eb3ba64c0fffa87206e0d4c869c4c606f89

Content hash

sha256:499ff06343b6ad0ba6ad18098b3a7eb3ba64c0fffa87206e0d4c869c4c606f89

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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