The Mechanism · Gated-generation receipt

gen-define-the-day-of-the-week-from-a-date-zeller-s-congruence-a-fed9

stable pending witness
2026-05-29 04:40:50 UTC · anthropic/claude-sonnet-4-5

Prompt

Define the day of the week from a date (Zeller's congruence) and give one short worked example.
95 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)* - **K** = year of century (year mod 100) - **J** = century (⌊year/100⌋) *Note: January and February are counted as months 13 and 14 of the previous year ## Worked Example: January 1, 2000 1. **Adjust date:** January 2000 → Month 13 of 1999 - q = 1 - m = 13 - Year = 1999, so K = 99, J = 19 2. **Calculate:** ``` h = (1 + ⌊13(14)/5⌋ + 99 + ⌊99/4⌋ + ⌊19/4⌋ - 2(19)) mod 7 h = (1 + ⌊182/5⌋ + 99 + 24 + 4 - 38) mod 7 h = (1 + 36 + 99 + 24 + 4 - 38) mod 7 h = 126 mod 7 h = 0 ``` 3. **Result:** h = 0 = **Saturday** ✓
32 tokens in · 444 tokens out · 6143 ms · $0.0068

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
6150.1 ms
Base LLM
6142.7 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0068

Trail

04:40:50 received prompt_chars=95 verifiers=['scripture_anchors', 'theology_doctrine']
04:40:50 red_gate decision=pass reason=no disqualifying input patterns detected
04:40:56 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=32 tokens_out=444 latency_ms=6142.7 cost_usd=0.0068
04:40:56 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:40:56 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:40:56 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:40:56 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:40:56 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:40:56 signed hash_algo=sha256 hash=sha256:c6da6ebfcaefc71e50d1afd1ae2834917cdcc136a592f4d1429c6be344612dbb

Content hash

sha256:c6da6ebfcaefc71e50d1afd1ae2834917cdcc136a592f4d1429c6be344612dbb

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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