What a Complete Mechanism for a Lambda-Tied MOND Law Would Have to Do: A Closure Map of Scoped No-Gos and a Reading of the Requirements
Year: 2026
Type: article
Abstract: Version 1.1: wording corrections after an independent referee (CFG265: 1 CRITICAL, 3 MAJOR, 19 MINOR, 7 NIT); no result changes. The programme ties the MOND acceleration scale to the vacuum, a0 = kappa c sqrt(G rho_Lambda), with kappa = 1/2 fitted, never derived. Its best current effective law, candidate B, is the MOND kernel plus hierarchical ownership (only the outermost bound system carries the phantom) plus a cold component with the cosmic amount Omega_c h^2 ~ 0.12: the mass is still required, and no dark-matter particle is added. No committed action produces B. This note is a map of failed routes and a reading of what they suggest, not a result. The gaps. Three gaps separate B from a mechanism: a legal owned switch (Gap 1), the cold fluid that is the law's dark density (Gap 2), and the a0-Lambda tie with its coefficient (Gap 3). What Lean certifies. A Lean library of 331 theorems (standard axioms only) certifies, from stated premises, that the postulated ownership rule is not a function of the internal and external field at a point, that a continuous law with no external-field effect is linear, that among monomials a length proportional to M^(1/2) needs an acceleration scale, and that an AQUAL action gives the kernel in spherical symmetry; it certifies no empirical fact. The routes. We tabulate 25 committed routes: 22 are scoped no-gos on their frozen classes, two owner-directed lanes find no mechanism (11D's hand-check, and CFG253's background calculation, which asks where the cold amount comes from; without it the count is 24), and one shows realisability only. None is a mechanism. Every route's criteria were written before its scripts; for 20 of the 25 they were committed first, and for five they were committed together with the scripts, as the lanes disclose. A reading of the requirements. The failures suggest a specification. It is a reading of the scored classes, not a theorem: only the acceleration-scale item rests on a theorem (for monomials) and the cosmic amount on the inherited CMB gate; the rest rests on the failure of one to three scored classes per item. The reading asks for an early cold fluid present before structure forms (a dust created at turnaround supplies Omega h^2 = 0.1200 x 10^-1376.8 at z = 1100); ownership that remembers boundness (a causal latch keeps n = 0.791 at one free-fall time against the required 0.99); a distribution that carries the M^(1/2) scale itself (passive bound infall scales as M^(0.33-0.34), and relaxation at a vacuum-set rate reaches Gamma tau <= 0.79 against the ~4.1-4.2 needed); a target that is field-local in the Newtonian field but needs bound-domain labels; and no created rest mass. Satellites and the coefficient. B's ultra-faint failure (3.5-3.9 sigma) does not move under the 2026 binary-corrected and DEIMOS dispersions, and Gate H leans toward the bound-core (LambdaCDM-comparator) reading at satellites by small margins (planted-sample power 0.28, carried entirely by the ultra-faints): a lean, not a detection. kappa = 1/2 is fitted (0.465 +- 0.076 from the baryonic Tully-Fisher relation), and Milgrom's cH0/2pi footing fits SPARC at least as well as either framework footing. What decides. Gaia DR4 (2 December 2026) is a survival test of B against the merged (no-ownership) law: decisive against Arm A's nu_RAR kernel (floor 1.161, alt 1.192; the preregistration falsifies Arm A below 1.056), but only 2.3-3.7 sigma against the P2 kernel (merge 1.063-1.102 canonical, N = 30,000), and no separation from the derivation chain's ceiling; B, LambdaCDM and Newton all predict gamma-hat = 1.000, and 1.084 <= gamma-hat <= 1.23 falsifies B if the frozen stability requirements pass. For the flat a0(z) law against a0 proportional to H(z), the limit that survives an unlimited sample is the absolute baryon calibration; at present sizes several lanes are also limited by statistical power or by the Newtonian regime (PAPER38 version 1.2, doi:10.5281/zenodo.23085582). Every number carried by an audit row is re-read from committed files by PAPER39_audit.py (201 of 201); the tex is checked at block level, not sentence level, and numbers quoted only in running text are not checked by the script. The menu of routes was written knowing the target, and the referees were not blind. AI-assisted research programme; not peer reviewed; nothing here is claimed closed.
Author: Zimmerman, Carl P.
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7219633117
FWCI:
Cites:
Cited by:
Related to: