What does this research mean for the field?

A proposed constraint-defined Hamiltonian theory of minimally-modified-gravity fails as a relativistic completion for MOND due to fatal theoretical contradictions, including the destruction of gravitational lensing and matter conservation, despite possessing a viable nonrelativistic core. Novelty: ClaimNovelty.CONTRADICTORY. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To assess the relativistic consistency, constraint closure, and observational viability of a constraint-defined Modified Newtonian Dynamics theory formulated within a preferred-foliation Hamiltonian framework.

August 29, 2026Open Access

A Conditionally Closed Constraint-Defined MOND Theory with Two Tensor Degrees of Freedom: Hamiltonian Certification, Kernel-Agnostic Chassis, and Solar-System Viability

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Authors

CZCarl P. ZimmermanAd-Tech (United States)

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Implication

Theoretical analysis demonstrates severe empirical failures in a constraint-defined MOND framework, showing that removing the Hamiltonian constraint destroys lensing and matter conservation.

Key Points

To assess the relativistic consistency, constraint closure, and observational viability of a constraint-defined Modified Newtonian Dynamics theory formulated within a preferred-foliation Hamiltonian framework.
Conducted a 13-gate Dirac–Bergmann constraint audit to establish gauge closure and determine propagating degrees of freedom.
Calculated parametrized post-Newtonian parameters and evaluated theoretical predictions against solar deflection, Cassini Shapiro delay, pulsar timing, and planetary ephemerides.
Tested kernel-agnostic interpolation functions using observational acceleration data from the 175-galaxy SPARC database.
The relativistic completion failed, yielding gamma_PPN = 0 with light experiencing only half the gravitational potential (a ~43,000-sigma tension with Cassini Shapiro delay and a 0.875-arcsecond solar deflection).
The formulation caused catastrophic conservation violations, with momentum parameters alpha_1 = +4 and alpha_3 = -1 (~2.5 x 10^19 times the pulsar limit) and Newtonian matter non-conservation (~10^11 times ephemeris bounds).
The nonrelativistic sector survived intact, preserving the generic-branch two-tensor degrees of freedom, exact AQUAL dynamics, and modularity across interpolation kernels.

Cite This Study

Carl P. Zimmerman (2026) studied this question.

synapsesocial.com/papers/6a9299bb8e5d7d1fc0c11d57 https://doi.org/10.5281/zenodo.22133406

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Implication

Theoretical analysis demonstrates severe empirical failures in a constraint-defined MOND framework, showing that removing the Hamiltonian constraint destroys lensing and matter conservation.

A Conditionally Closed Constraint-Defined MOND Theory with Two Tensor Degrees of Freedom: Hamiltonian Certification, Kernel-Agnostic Chassis, and Solar-System Viability

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Implication

Key Points

Cite This Study

A Conditionally Closed Constraint-Defined MOND Theory with Two Tensor Degrees of Freedom: Hamiltonian Certification, Kernel-Agnostic Chassis, and Solar-System Viability

Discussion

Member takes

Implication

Key Points

Cite This Study

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