The Amplitude Law: a candidate two-field completion for a horizon-derived MOND scale, and the solar-system obstruction that blocks it
Year: 2026
Type: article
Abstract: The acceleration scale a0 = κc√(GρΛ) = 9.3619×10-11 m/s2 (with κ = 1/2 fitted, not derived) reproduces the observed MOND scale from the cosmological constant alone. This paper asks what field theory, if any, makes the corresponding halo density ρ = √(GMba0)/(4πGr2) a dynamical consequence rather than an initial condition. Results. (1) The equation-of-state route is not the binding constraint: in the weak field the anisotropy pr-pt is unobservable, an exact flat direction of the two lensing observables, so the constraint is the amplitude. (2) Every static single k-essence scalar obeys pt = -ρ identically for any kinetic function, closing that class as a stress carrier; the framework's own shift-symmetric condensate escapes it. (3) The general khronon fails by a scaling theorem, because a0 cannot be built from c and G alone. (4) Of six candidate mechanisms under adversarial verification, one survives: a two-field lock whose mediator Gauss law plus a pointwise balance yields, for any free function and with no interpolation invoked, GMχ(r)/r2 = gobs - gbar as an identity — the real dark mass equals the phantom mass as a theorem. The resulting profile has coefficient 0.9999975 and d ln(coef)/d ln Mb = 0.500000, with screening keyed structurally on the local total field gradient. This is not a completed field theory. The surviving mechanism's baryon sector is AQUAL as a PDE identity in full generality, so it inherits the modified-gravity solar-system liability: the Cassini quadrupole is 6.7-7.3× the published ceiling, +18σ at face value with an honest floor of >=3σ once the Milky Way mass-model spread is admitted. The cosmological leg is untested, ghost-freedom is uncomputed, clusters remain short by ~2×, and κ = 1/2 remains fitted. Two candidate repairs are identified and neither is computed. Reported as a candidate completion with a live obstruction. All load-bearing claims are backed by committed scripts that exit zero, produced under adversarial verification in which independent agents were instructed to refute each claim, with manufacturing a deficit penalised as heavily as manufacturing a win.
Author: Zimmerman, Carl
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203882461
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