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arxiv: 2605.22329 · v1 · pith:ATJOVRIWnew · submitted 2026-05-21 · 🌀 gr-qc · hep-th· math-ph· math.MP

Vector modes in Type 3 New GR

Alexey Golovnev This is my paper

Pith reviewed 2026-05-22 05:25 UTC · model grok-4.3

classification 🌀 gr-qc hep-thmath-phmath.MP
keywords New GRvector modesdegrees of freedomlinearised gravityweak gravity limitconstraint equationsequations of motionteleparallel gravity
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The pith

Vector modes in Type 3 New GR are not dynamical degrees of freedom

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper establishes that the vector modes in the linearised weak gravity limit of Type 3 New GR are non-dynamical. It reaches this conclusion by examining the linear equations of motion rather than the quadratic Lagrangian. A sympathetic reader would care because an accurate count of physical degrees of freedom determines the theory's perturbative health and whether strong coupling or instabilities appear. The work corrects an error that arose when constraint equations were substituted into the Lagrangian, which falsely suggested independent dynamics.

Core claim

The vector modes in the linearised weak gravity limit of Type 3 New GR are not dynamical. Recent claims to the contrary resulted from substituting constraint equations into the Lagrangian rather than analysing the equations of motion. The linear equations of motion derived in earlier work correctly capture these modes as purely constrained and non-propagating.

What carries the argument

Direct analysis of the linearised equations of motion in the vector sector, which imposes constraints that remove any independent time evolution.

If this is right

  • The total number of degrees of freedom in arbitrary New GR models remains unchanged from the earlier count.
  • Strong coupling issues identified in linear cosmological perturbations continue to apply.
  • Future perturbative analyses of New GR must solve the equations of motion rather than manipulate the Lagrangian after imposing constraints.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same distinction between Lagrangian substitution and equation-of-motion analysis could prevent similar overcounting in other constrained gravitational theories.
  • Numerical integration of the linearised system would provide an independent check that vector perturbations remain non-propagating.
  • Hamiltonian or constraint algebra approaches should be cross-verified against the Euler-Lagrange equations to avoid parallel mistakes.

Load-bearing premise

The linearised equations of motion derived in the author's prior work correctly capture all degrees of freedom without omissions.

What would settle it

A solution to the linearised vector equations that satisfies a wave equation with nontrivial second time derivatives and propagates at finite speed.

read the original abstract

Some time ago, we published the full count of degrees of freedom in the linearised weak gravity limit of arbitrary New GR models. We did it by considering the linear equations of motion and presented a thorough analysis with no ambiguity left. A bit later, we generalised it to linear cosmological perturbations and discussed the strong coupling issues that appear already at this level. Recently, there were claims that some dynamical modes had been missed in our work. However, the authors of the new claims did not look at the equations of motion and analysed the quadratic Lagrangian densities instead. In this paper, I take one of the most elementary cases, namely the vector modes in New GR of Type 3, and show what was their mistake that had led them to claiming that those were dynamical. The main message: Do not substitute constraint equations into a Lagrangian.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The manuscript claims that vector modes in the linearised weak-gravity limit of Type 3 New GR are non-dynamical. Recent contrary claims are attributed to the practice of substituting constraint equations into the quadratic Lagrangian rather than analysing the linear equations of motion directly. The paper uses this elementary vector-sector case to illustrate the general methodological warning against such substitutions for degree-of-freedom counting, building on the author's prior EOM-based analyses.

Significance. If the demonstration holds, the paper provides a targeted methodological correction that reinforces the reliability of prior linearised analyses of New GR models. It explicitly credits the completeness of the earlier EOM derivation for the vector sector and offers a falsifiable, concrete example of how Lagrangian substitution distorts the count. This strengthens the literature on constrained gravity theories by highlighting a standard but easily overlooked pitfall.

minor comments (2)
  1. [Abstract] Abstract: the statement that the prior EOM analysis left 'no ambiguity' would benefit from a one-sentence recap of the key vector-mode constraint that eliminates dynamics, to make the contrast with the Lagrangian substitution fully self-contained.
  2. [Introduction] The manuscript refers to 'the authors of the new claims' without an explicit citation in the introduction; adding the reference would allow readers to directly compare the two approaches.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript, accurate summary of its content, and recommendation for minor revision. We are pleased that the referee recognizes the value of this elementary example in illustrating the methodological issue with substituting constraints into the Lagrangian for degree-of-freedom counting.

read point-by-point responses

  1. Referee: The manuscript claims that vector modes in the linearised weak-gravity limit of Type 3 New GR are non-dynamical. Recent contrary claims are attributed to the practice of substituting constraint equations into the quadratic Lagrangian rather than analysing the linear equations of motion directly. The paper uses this elementary vector-sector case to illustrate the general methodological warning against such substitutions for degree-of-freedom counting, building on the author's prior EOM-based analyses.

    Authors: We appreciate the referee's concise and accurate summary of the paper's purpose and main result. Our analysis of the linear equations of motion indeed shows the vector modes are non-dynamical, and we demonstrate explicitly how substitution of constraints into the quadratic Lagrangian produces the erroneous claim of dynamics. This example is intended to reinforce the reliability of our earlier EOM-based work on New GR models. revision: no

Circularity Check

1 steps flagged

Minor self-citation for prior EOM completeness; methodological correction stands independently

specific steps
  1. self citation load bearing [Abstract]
    "Some time ago, we published the full count of degrees of freedom in the linearised weak gravity limit of arbitrary New GR models. We did it by considering the linear equations of motion and presented a thorough analysis with no ambiguity left."

    The claim that vector modes are non-dynamical uses the prior self-published EOM analysis as the authoritative benchmark that reveals the error in the Lagrangian-based claims; the present paper does not re-derive the full EOM completeness from scratch but invokes the earlier result.

full rationale

The paper's central methodological warning (do not substitute constraints into the Lagrangian) is self-contained and externally verifiable by direct comparison of EOM versus constrained Lagrangian. The reference to the author's prior work supplies the benchmark EOM count but is not load-bearing for the specific vector-mode demonstration in this manuscript, which re-examines the elementary case. No self-definitional loop, fitted prediction, or ansatz smuggling is exhibited.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The analysis rests on the validity of the prior linearised equations of motion and on the standard field-theory rule against substituting constraints into the Lagrangian for degree-of-freedom counting.

axioms (1)
  • domain assumption Linearised weak-gravity equations of motion from prior work accurately determine all propagating degrees of freedom.
    Invoked as the correct benchmark against which the Lagrangian-based claims are judged.

pith-pipeline@v0.9.0 · 5665 in / 1116 out tokens · 56199 ms · 2026-05-22T05:25:29.759449+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

10 extracted references · 10 canonical work pages · 1 internal anchor

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