Carl P. Zimmerman

A Conserved Clock Rate, and the Board Run End to End

The solar system demands a clock running about 1.5e7 times proper time, a number nothing explained. We show it does not need explaining. The closure's two kinetic coefficients descend from a SINGLE logarithmic function P(X) = -(U/2) log(U - 2 d X) whose pole is a SPEED LIMIT, wit...

A Clock That Cannot Be Dragged: Why the Preferred-Frame Test Does Not Bite a Cuscuton-Clock MOND Sector

A clock field defining a preferred foliation is normally in danger from the post-Newtonian preferred-frame parameters: a body moving at velocity w through the clock's rest frame sees a clock with a spatial gradient, and an order-unity coefficient in front of that tilt is excluded...

The Coldness Is Dynamical: How Cold a Self-Critical MOND Sector Ends Up, and Why Nothing Has To Be Tuned

A cuscuton-clock MOND sector whose clock runs faster than proper time is gradient-unstable at zero field gradient, but its own MOND nonlinearity turns the sound speed positive at a finite gradient Y*, whose marginal state has cs2 = 0 and isotropic stress (doi:10.5281/zenodo.22727...

The Decoupling Locus: a MOND Scale Derived from a Clock, and the Solar System Reduced to One Number

A cuscuton-clock sector with a projected-gradient scalar produces a cold clustering component and passes nine gates as a dark component, but produces no force law, because matter in that action is minimally coupled. Adding a coupling is what would give MOND, and the obstruction w...

The Clock Stability Theorem: the Sub-Horizon Sound Speed of a Cuscuton-Clock MOND Sector Is Set by the Clock Rate

A relativistic MOND candidate built from a cuscuton clock, a dynamical scalar with a projected-gradient (MOND) sector and a cubic coupling has a homogeneous cosmological branch on which the clock sector gravitates like dust. We derive, in the uniform-clock gauge and the sub-horiz...

The Dark-Fraction Ledger Is Geometry: One Universal Concentration Reproduces the Host-Mass Dependence, and the Lyman-alpha Forest Closes the Late-and-Puffy Component

A MOND kernel on the de Sitter-locked acceleration scale passes galaxies, clusters and the CMB together only if a real cold component is present with a fraction of its LambdaCDM halo mass that rises with host mass: below 0.105 inside three disc scale lengths of a 1.2e10 solar-mas...

Gradient-Driven Criticality: a MOND Sector That Cures Its Own Gradient Instability, and a Marginal State That Is Exactly Cold

A relativistic MOND candidate built from a cuscuton clock, a dynamical scalar with a projected-gradient sector and a cubic coupling has a sub-horizon sound speed cs2 = (1 - s0) mrel/(2 - mrel), negative whenever the clock rate exceeds unity (doi:10.5281/zenodo.22717950). That res...

Gradient-Driven Criticality: a MOND Sector That Cures Its Own Gradient Instability, and a Marginal State That Is Exactly Cold

A relativistic MOND candidate built from a cuscuton clock, a dynamical scalar with a projected-gradient sector and a cubic coupling has a sub-horizon sound speed cs2 = (1 - s0) mrel/(2 - mrel), negative whenever the clock rate exceeds unity (doi:10.5281/zenodo.22717950). That res...

The Clock Rate Is the Dark Matter Pressure: a Closed-Form Coefficient History for a Self-Critical MOND Sector, and a Prediction of Positive w_dm

A cuscuton-clock MOND sector is driven by its own gradient instability onto a critical surface where its stress is isotropic and its sound speed vanishes, making it a clustering cold component without tuning (doi:10.5281/zenodo.22727111, doi:10.5281/zenodo.22727860). That constru...

The Coldness Is Dynamical: How Cold a Self-Critical MOND Sector Ends Up, and Why Nothing Has To Be Tuned

A cuscuton-clock MOND sector whose clock runs faster than proper time is gradient-unstable at zero field gradient, but its own MOND nonlinearity turns the sound speed positive at a finite gradient Y*, whose marginal state has cs2 = 0 and isotropic stress (doi:10.5281/zenodo.22727...

What a Clock Can and Cannot Do: a Cold Dark Sector Derived, a Force Law Excluded, and the Rate of Cosmic Time Certified

A cuscuton-clock sector with a projected-gradient scalar produces a cold clustering component by driving itself onto a critical surface, and passes nine successive cosmological and solar-system gates. Every one of those derivations set the cubic coupling to zero. We restore it an...

A Preferred Frame Is Forced: Static Weak-Field MOND with One Metric and Two Propagating Modes, and the Lensing Lock That Discharges the Locality Hypothesis

A theorem: if a relativistic theory of gravity (i) reduces to Milgrom's modified Newtonian dynamics in the static weak field, (ii) carries a single physical metric to which matter couples minimally, and (iii) propagates exactly two gravitational degrees of freedom, then it contai...

A Ceiling Dark Matter Cannot Impose: the Bounded-Boost Theorem for MOND-Class Kernels, and What It Says About Galaxies and Clusters

Version 4: the kernel swap the theorem selects is carried through the framework's whole constraint ladder, not just the Solar System. The carried kernel enters every gate through one function, J_Y(s) = s/Δ(s), whose saturated slope is e for the exponential carrier and 1.544 for ν...

A Ceiling Dark Matter Cannot Impose: the Bounded-Boost Theorem for MOND-Class Kernels, and What It Says About Galaxies and Clusters

Version 4: the kernel swap the theorem selects is carried through the framework's whole constraint ladder, not just the Solar System. The carried kernel enters every gate through one function, J_Y(s) = s/Δ(s), whose saturated slope is e for the exponential carrier and 1.544 for ν...

A Ceiling Dark Matter Cannot Impose: the Bounded-Boost Theorem for MOND-Class Kernels, and What It Says About Galaxies and Clusters

Version 2: references added, and three results folded in — the carrier theorem is shown to BE the bounded-boost theorem (a matter-sourced scalar can carry a kernel only up to the maximum of Δ, so the saturation is universal and every kernel leaves a constant residual force C a0);...

The Filtered MOND Action: a Central Tidal Identity, Comparable-Mass Forces, a First Covariant Clock Action, and the Operator That Screens the Solar System

Preprint; AI-assisted research draft; not peer reviewed. This deposit timestamps results and their reproducibility scripts. It claims no completed relativistic MOND theory, no derivation of the coherence length or of a0, and no empirical detection. For the spatially filtered two-...

The Filtered MOND Action: a Central Tidal Identity, Comparable-Mass Forces, a First Covariant Clock Action, and the Operator That Screens the Solar System

Preprint; AI-assisted research draft; not peer reviewed. This deposit timestamps results and their reproducibility scripts. It claims no completed relativistic MOND theory, no derivation of the coherence length or of a0, and no empirical detection. For the spatially filtered two-...

A local, generally covariant field theory of modified inertia

VERSION 5: the paper now states its own FALSIFICATION TEST, with the power computed BEFORE the data -- and the honest headline is that the test is ASYMMETRIC. SAID FIRST, because it bounds everything that follows: the wide-binary prediction is NOT derived from this paper's steps...

A local, generally covariant field theory of modified inertia

v7 (2026-08-09): the modified-gravity arm is COMPLETED as AeST and this kernel embeds in it, turning v6's 21.2-sigma lensing exclusion into 0.601 sigma with gamma_PPN = 1. A bounded (DBI-type) K(Q) dissolves Blanchet & Skordis 2024's published 455x no-go, with a theorem: for any...

The modified-gravity arm: a Bekenstein-Milgrom field theory for a_0 = kappa c sqrt(G rho_Lambda)

This paper switches the framework's operative arm from modified INERTIA to modified GRAVITY, and says why in its first section rather than its last. WHY THE SWITCH. In modified inertia the metric is unmodified and baryon-sourced -- not incidentally but by requirement, since the w...