UDCT v7.06 - sign audit of a Hessian term absent from the standard MOND equation: action-consistent virial work and conditional Jeans tests in three ultra-faint dwarfs
- 1Independent Researcher, Auckland, New Zealand
Abstract
This note recasts the UDCT v7.01–v7.06 calculations as a verification paper. Standard MOND-family field theories (AQUAL, QUMOND) employ a positive interpolating function μ or ν. Their weak-field equations do not contain the extra Hessian-sourced tensor Pij tested in this UDCT candidate. The object under audit is therefore not standard AQUAL or QUMOND. Where the density-weighted virial integral is negative, that sign is not produced by a negative interpolating function. It is produced because the action-derived Hessian contribution exceeds the positive leading term. A previously preregistered ultra-faint-dwarf velocity proxy (O8d / D8b) matched 0/22 objects within a factor of two; that historical gate is not reopened. This file is a wording revision of the 29 September 2026 verification draft; no new calculations were performed. Simulations, code and drafting in this series were carried out with substantial assistance from large language models (Anthropic Claude; OpenAI ChatGPT; Google Gemini; xAI Grok) under the author's direction. The author defined the research questions and released code for independent reproduction. The historical O8d/D8b result remains a prior registered gate (0/22). This v7.06 note is a post-outcome wording revision and does not reopen that gate.
Related
- An Analytical Toy Equation of State for Neutron Stars Consistent with Current Observations
- An Analytical Toy Equation of State for Neutron Stars Consistent with Current Observations
- Thermodynamically consistent equation of state tables for use in giant planet and brown dwarf interior modeling
- Population III Host Candidates at z∼2: Strong He II λ1640 and Absent UV Metal Lines in HETDEX Lyα Emitters
- Population III Host Candidates at z ∼ 2: Strong He II λ 1640 and Absent Ultraviolet Metal Lines in HETDEX Ly α Emitters
BibTeX
@misc{paik2026udct,
title = {{UDCT v7.06 - sign audit of a Hessian term absent from the standard MOND equation: action-consistent virial work and conditional Jeans tests in three ultra-faint dwarfs}},
author = {Won Shik Paik},
howpublished = {Zenodo (CERN European Organization for Nuclear Research)},
year = {2026},
month = sep,
doi = {10.5281/zenodo.23039753},
url = {https://doi.org/10.5281/zenodo.23039753},
note = {CC BY},
}
RIS
TY - UNPB
TI - UDCT v7.06 - sign audit of a Hessian term absent from the standard MOND equation: action-consistent virial work and conditional Jeans tests in three ultra-faint dwarfs
AU - Won Shik Paik
PY - 2026
DA - 2026/09/29
PB - Zenodo (CERN European Organization for Nuclear Research)
DO - 10.5281/zenodo.23039753
UR - https://doi.org/10.5281/zenodo.23039753
AB - This note recasts the UDCT v7.01–v7.06 calculations as a verification paper. Standard MOND-family field theories (AQUAL, QUMOND) employ a positive interpolating function μ or ν. Their weak-field equations do not contain the extra Hessian-sourced tensor Pij tested in this UDCT candidate. The object under audit is therefore not standard AQUAL or QUMOND. Where the density-weighted virial integral is negative, that sign is not produced by a negative interpolating function. It is produced because the action-derived Hessian contribution exceeds the positive leading term. A previously preregistered ultra-faint-dwarf velocity proxy (O8d / D8b) matched 0/22 objects within a factor of two; that historical gate is not reopened. This file is a wording revision of the 29 September 2026 verification draft; no new calculations were performed. Simulations, code and drafting in this series were carried out with substantial assistance from large language models (Anthropic Claude; OpenAI ChatGPT; Google Gemini; xAI Grok) under the author's direction. The author defined the research questions and released code for independent reproduction. The historical O8d/D8b result remains a prior registered gate (0/22). This v7.06 note is a post-outcome wording revision and does not reopen that gate.
ER -