# ISS-CAL-2026-001: Technical Audit & Errata Dossier for QP-CAL-001 v1.0.0 ## 1 Executive Summary This dossier records the formal Round 1 peer-review and technical audit findings for the standard specification paper **QP-CAL-001 v1.0.0** (*Architecture and Astronomical Reference Model of the Quizzman Lunisolar Calendar System*). The audit strictly adheres to the verifiable epistemological framework: **Claim → Cross-Reference → Empirical Counter-Evidence**. The audit identified **10 technical defects** spanning manuscript formulation, mathematical formula precision, citation provenance, and methodological claims. Notably, these discrepancies reside primarily in the theoretical expository layer of the paper; the executable code provided in Annex A frequently exhibits higher fidelity than the manuscript text itself. All 10 findings have been **fully accepted** by the Quizzman Paper Standard Editorial Board, and the corrective errata release **QP-CAL-001 v1.0.1** has been scheduled. --- ## 2 Defect Severity Matrix | Issue Code | Severity | Section | Claim in Paper v1.0.0 | Scientific Counter-Evidence | Audit Finding | |---|---|---|---|---|---| | **ISS-01** | **Critical** | §7.1 | JDN formula includes constant $1,721,013.5$ and lacks Gregorian century leap correction terms. | Evaluates to half-integer real ($2451544.5$ at 2000-01-01), contradicting integer JDN definition and Annex A code. | **ACCEPTED** (Theoretical formula defect; Annex A is correct) | | **ISS-02** | **Critical** | §9.1 | *"The 60 Sexagenary cycle is an algebraic structure isomorphic to the ring $\mathbb{Z}_{10} \times \mathbb{Z}_{12}$."* | The direct product ring $\mathbb{Z}_{10} \times \mathbb{Z}_{12}$ has 120 elements ($\gcd(10,12)=2$). The cycle is isomorphic only to a 60-element subring under parity constraint ($c \equiv d \pmod 2$). | **ACCEPTED** (Abstract algebra formulation error) | | **ISS-03** | **High** | §7.4 | New Moon calculation cited as *"Meeus 1998, Chapter 49"*. | Constant uses epoch 1900.0 ($2415020.75933$), whereas Meeus (1998, 2nd ed, Ch. 49) published epoch J2000.0 ($2451550.09765$). Epoch 1900 originates from Meeus 1979/1988 or Ho Ngoc Duc. | **ACCEPTED** (Citation edition discrepancy) | | **ISS-04** | **High** | §3.1, §7.3 | Confounding dynamical and civil time scales ($\text{TT}, \text{UT}, \text{UT1}, \text{UTC}$). | Identifies $\text{TT} = \text{UT} + \Delta T$ and $\Delta T = \text{TT} - \text{UT1}$ without accounting for $\text{UT1} - \text{UTC}$ drift in civil UTC. Erroneous translation of Terrestrial Time. | **ACCEPTED** (Time scale conceptual rigor defect) | | **ISS-05** | **High** | §7.3 | Hardcoded $\Delta T = 70.000\text{ s}$ at epoch 2025.0. | IERS Bulletin B and finals2000A at 2025-01-01 report $\Delta T \approx 69.138\text{ s}$. 70.000 s is an undocumented coarse internal rounding. | **ACCEPTED** (Empirical rounding must be disclosed) | | **ISS-06** | **High** | §6.2, §10.1 | Claimed *"complete digital historical reproduction according to IANA Asia/Ho_Chi_Minh"*. | IANA tzdb mandates $+07:06:30$ PLMT (Phu Lien Mean Time, 1906-07-01 to 1911-05-01). The paper simplified 1906–1942 directly to UTC+07:00. | **ACCEPTED** (Overclaim vs underlying tzdb ground truth) | | **ISS-07** | **High** | §8.2 | Claimed New Moon residual of *"0.07 min ≈ 4 seconds"* against NASA. | NASA catalog is published to 1-minute integer resolution ($11:57\text{ UTC}$). Evaluating 4-second precision against a 1-minute datum is False Precision; NASA also relies on Meeus. | **ACCEPTED** (False Precision & lack of algorithmic independence) | | **ISS-08** | **High** | §10.3, §12 | Claimed *"absolute mathematical certitude"* based on 146,462-day bidirectional roundtrip. | `solarToLunar` $\leftrightarrow$ `lunarToSolar` roundtrip only proves internal bijective invertibility/consistency, not external astronomical validity. | **ACCEPTED** (Epistemological method overclaim) | | **ISS-09** | **Medium** | §8.2 | Cardinal solar term validation table recorded Autumnal Equinox 2024 at 12:43:00Z. | Official USNO and NASA Astronomical Almanac specify Autumnal Equinox 2024 as 12:44 UT. 1-minute typo in reference datum. | **ACCEPTED** (1-minute reference datum typo) | | **ISS-10** | **Low** | §3.1, §7.2 | Defined time parameter $\tau$ as *"Julian millennium (10,000 years)"*. | Formula uses denominator $365,250\text{ days} = 1,000\text{ Julian years}$ (1 millennium), not 10,000 years (myriad). | **ACCEPTED** (Typesetting arithmetic typo) | --- ## 3 Detailed Audit Findings ### ISS-01 (Critical): JDN Formula Contradiction and Missing Gregorian Century Correction - **Location:** QP-CAL-001, Section 7.1, Equation 136. - **Evidence:** Substituting $Y=2000, M=1, D=1$ yields $2,451,544.5$ (half-integer JD at 00:00, not integer JDN at 12:00 UTC). Annex A.1 uses Fliegel & Van Flandern (1968) which correctly outputs integer $2,451,545$. - **Resolution:** Synchronize theoretical formula §7.1 with the correct Fliegel–Van Flandern / Meeus algorithm in v1.0.1. ### ISS-02 (Critical): Mathematical Error in 60 Sexagenary Cycle Isomorphism Claim - **Location:** QP-CAL-001, Section 9.1, Line 251. - **Evidence:** Ring $\mathbb{Z}_{10} \times \mathbb{Z}_{12}$ contains 120 elements. Since $\gcd(10,12)=2$, $\mathbb{Z}_{10} \times \mathbb{Z}_{12} \not\cong \mathbb{Z}_{60}$. The 60 Sexagenary pairs form an isomorphic cyclic group $\mathbb{Z}_{60}$ embedded via parity matching ($I_{\text{can}} \equiv I_{\text{chi}} \pmod 2$). - **Resolution:** Correct abstract algebra formulation in v1.0.1. ### ISS-03 (High): Meeus Chapter 49 Citation Provenance and Epoch 1900 - **Location:** QP-CAL-001, Section 7.4. - **Evidence:** Meeus (1998, 2nd ed, Ch. 49) defines lunar conjunctions anchored at J2000.0 ($2451550.09765$). The formula anchored at $2415020.75933$ is from epoch 1900.0. - **Resolution:** Clarify historical adoption of epoch 1900 in Vietnamese computational history, with migration roadmap to canonical J2000. ### ISS-04 (High): Confounding Dynamical and Civil Time Scales (TT, UT, UT1, UTC) - **Location:** QP-CAL-001, Section 3.1 & 7.3. - **Evidence:** Confounds $\text{TT} = \text{UT} + \Delta T$ with $\text{TT} = \text{UT1} + \Delta T$, omitting $\text{UT1} - \text{UTC}$ offset. - **Resolution:** Clarify explicit definitions of TT, TAI, UT1, and UTC with formal reduction pathways. ### ISS-05 (High): Coarse Rounding of Delta T at Epoch 2025.0 - **Location:** QP-CAL-001, Section 7.3. - **Evidence:** IERS Bulletin B 443 establishes $\Delta T_{2025.0} = 69.1378\text{ s} \approx 69.14\text{ s}$. Hardcoding $70\text{ s}$ introduces $0.86\text{ s}$ unnecessary deviation. - **Resolution:** Fixed in codebase v1.2.1 to $69.14\text{ s}$ (IERS Bulletin B 443). ### ISS-06 (High): Missing Phu Lien Mean Time (PLMT) 1906–1911 in Historical Civil Timeline - **Location:** QP-CAL-001, Section 6.2 & 10.1. - **Evidence:** IANA tzdb `Zone Asia/Ho_Chi_Minh` designates $+07:06:30$ PLMT from 1906-07-01 to 1911-05-01. - **Resolution:** Implemented PLMT era in codebase v1.2.1. ### ISS-07 (High): False Precision in NASA New Moon Residual Claim - **Location:** QP-CAL-001, Section 8.2. - **Evidence:** NASA catalog publishes integer-minute data ($11:57\text{ UTC}$). Claiming 4-second residual against 1-minute data represents false precision. - **Resolution:** Re-word validation section to declare conformity within $\pm 1\text{ minute}$ boundary. ### ISS-08 (High): Epistemological Overclaim of Roundtrip Testing - **Location:** QP-CAL-001, Section 10.3 & 12. - **Evidence:** Roundtrip testing proves internal algebraic invertibility, not external astronomical ground truth. - **Resolution:** Refactor methodology wording to distinguish internal consistency from external ephemeris benchmarks. ### ISS-09 (Medium): Autumnal Equinox 2024 Reference Datum Typo - **Location:** QP-CAL-001, Section 8.2. - **Evidence:** USNO & NASA Astronomical Almanac specify 12:44 UT. Benchmark route had 12:43:00Z. - **Resolution:** Corrected datum in codebase v1.2.1 to `12:44:00Z`. ### ISS-10 (Low): Typesetting Error in Julian Millennium Unit Definition - **Location:** QP-CAL-001, Section 3.1 & 7.2. - **Evidence:** $\tau$ is defined with denominator 365,250 days = 1,000 years, not 10,000 years. - **Resolution:** Fix typo in v1.0.1. --- ## 4 Patch Release Plan for QP-CAL-001 v1.0.1 The Quizzman Paper Standard Editorial Board has formally approved: 1. **Theoretical Errata:** Synchronize §7.1 JDN formula with Annex A.1; update algebra of 60 Sexagenary cycle; clarify time scales; anchor $\Delta T = 69.14\text{ s}$; correct Autumnal Equinox datum to 12:44 UT; fix $\tau$ definition. 2. **Epistemology & Methodology:** Remove false precision claims and clarify internal invertibility scope. 3. **Artifacts Directory:** Maintain open downloadable test vectors at `/papers/QP-CAL-001/artifacts/test-vectors.json` and fix report at `/papers/QP-CAL-001/artifacts/ISSUE_FIX_REPORT_ISS_05_06_07.en.md`.