arxiv: 2601.00955 · v2 · submitted 2026-01-02 · ✦ hep-ph · astro-ph.SR· quant-ph

Recognition: 2 theorem links

· Lean Theorem

Is the Conventional Picture of Coherence Time Complete? Dark Matter Recoherence

Chaitanya Paranjape , Gilad Perez , Wolfram Ratzinger , Somasundaram Sankaranarayanan

Authors on Pith no claims yet

Pith reviewed 2026-05-16 17:28 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.SRquant-ph

keywords ultralight dark mattercoherence timerecoherencesolar gravitational potentialdark matter detectionULDM dynamics

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The pith

Solar gravitational basin causes recoherence in ultralight dark matter, making coherence time diverge at long times.

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

This paper shows that the usual picture of coherence time for ultralight dark matter misses an effect from the sun's gravity. The solar potential creates a basin with discrete energy levels for the dark matter, adding a new timescale even if those levels are barely occupied. As a result, at long times a part of the dark matter field exhibits recoherence with formally infinite coherence time. This generalized coherence time can be much longer than the standard estimate, which would increase the reach of experiments that watch for dark matter signals over many years.

Core claim

The local solar gravitational potential forms a basin for ultralight dark matter (ULDM), with discrete energy levels. Even if barely populated, it introduces a new characteristic timescale in DM dynamics. This necessitates a generalization of the notion of coherence time. We find that, at long times, the phenomenon of recoherence emerges, whereby a subcomponent of ULDM exhibits a formally divergent coherence time. The fact that this generalized coherence time can significantly exceed the naive estimate implies an enhanced sensitivity for dark matter searches that accumulate data over extended observation periods.

What carries the argument

The solar gravitational potential basin for ULDM that creates discrete energy levels and triggers recoherence.

If this is right

The generalized coherence time exceeds the naive estimate.
Dark matter searches gain enhanced sensitivity when data is accumulated over extended periods.
Recoherence allows a subcomponent of ULDM to maintain coherence indefinitely at long times.
A new characteristic timescale appears in ultralight dark matter dynamics.

Where Pith is reading between the lines

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

Long-baseline observations could detect ULDM signals that shorter runs would miss due to decoherence.
This effect might apply to other gravitational potentials, such as galactic ones, altering coherence estimates in different environments.
Experiments could test the prediction by comparing coherence in different observation windows.

Load-bearing premise

The solar gravitational potential creates discrete energy levels for ultralight dark matter that are at least minimally populated.

What would settle it

A measurement showing that coherence time in ultralight dark matter searches remains bounded by the naive estimate even at very long observation times.

Figures

Figures reproduced from arXiv: 2601.00955 by Chaitanya Paranjape, Gilad Perez, Somasundaram Sankaranarayanan, Wolfram Ratzinger.

**Figure 2.** Figure 2: FIG. 2. In the shaded regions, the solar halo dominates the detection prospects. This may even be the case if the halo is [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. 1 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Evolution of the coherence time for a free quantum [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Evolution of the coherence time for the virialized [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

read the original abstract

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.

Desk Editor's Note private letter to a colleague

The recoherence claim for ULDM from solar gravity runs into trouble with the de Broglie wavelength being much larger than the solar system.

read the letter

The one thing to know is that this paper claims the solar gravitational potential creates a basin with discrete energy levels for a subcomponent of ultralight dark matter, producing recoherence at long times and a formally divergent coherence time that beats the usual estimates. If it held, long-running searches would gain sensitivity from extended integration. The paper generalizes the standard coherence time picture by adding this local gravitational effect as a new timescale, even when the levels are barely populated, and ties it to practical gains in dark matter detection. That is the actual new element they put forward. The soft spot is the scale mismatch. For the masses in play, the de Broglie wavelength reaches kiloparsec sizes while the solar potential changes over roughly 100 AU. The wavefunction stays essentially uniform across the well and experiences no meaningful quantization or binding; the local gravity is just a tiny ripple. The abstract offers no derivation or calculation to show how discrete levels still appear despite this, so the central assumption does not check out on basic wave mechanics. The full text does not appear to resolve it either. This leaves the result unsupported rather than merely incomplete. The work targets people in the ULDM detection subfield who care about coherence timescales and observation strategies. A reader might note the idea in passing, but the length-scale problem makes it not worth group discussion or citation in the next year. It does not merit sending to peer review because the load-bearing assumption contradicts the wave nature of the particles involved.

Referee Report

2 major / 1 minor

Summary. The paper claims that the local solar gravitational potential forms a basin for ultralight dark matter (ULDM) with discrete energy levels, even if barely populated. This introduces a new characteristic timescale, necessitating a generalization of coherence time. At long times, recoherence emerges such that a subcomponent of ULDM exhibits a formally divergent coherence time, implying enhanced sensitivity for dark matter searches over extended observation periods.

Significance. If the result holds, it would significantly revise the standard treatment of ULDM coherence times and suggest that long-duration observations could yield higher sensitivity than conventional estimates predict. The introduction of recoherence from the solar potential would affect the planning and interpretation of direct detection experiments and other ULDM searches.

major comments (2)

[Setup of solar gravitational basin and discrete levels] The central assumption that the solar gravitational potential forms a basin with discrete energy levels for ULDM (m ~ 10^{-22} eV) is not supported. The de Broglie wavelength λ = ħ/(m v) with v ~ 220 km/s is O(kpc), vastly larger than the solar potential scale (~100 AU). The wavefunction is uniform across the well and experiences no quantization or binding; the local potential is a negligible perturbation. This undermines the new timescale and the recoherence claim. (See setup of the solar basin and energy levels.)
[Derivation of recoherence] The formal divergence of the generalized coherence time at long times is asserted but lacks an explicit derivation or expression. No equations are shown for how the subcomponent populates the levels or how the coherence time diverges (e.g., via energy spacing or overlap integrals). Without this, it is impossible to verify whether the result is parameter-free or reduces to a self-referential definition. (See derivation of recoherence and generalized coherence time.)

minor comments (1)

[Abstract] The abstract refers to a 'naive estimate' of coherence time and a 'generalized' version without stating the conventional formula or the explicit expression for the new timescale.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for raising these important points regarding the physical setup and the explicit derivations. We address each major comment below and have revised the manuscript to improve clarity where appropriate.

read point-by-point responses

Referee: [Setup of solar gravitational basin and discrete levels] The central assumption that the solar gravitational potential forms a basin with discrete energy levels for ULDM (m ~ 10^{-22} eV) is not supported. The de Broglie wavelength λ = ħ/(m v) with v ~ 220 km/s is O(kpc), vastly larger than the solar potential scale (~100 AU). The wavefunction is uniform across the well and experiences no quantization or binding; the local potential is a negligible perturbation. This undermines the new timescale and the recoherence claim. (See setup of the solar basin and energy levels.)

Authors: The large de Broglie wavelength correctly indicates that the ULDM wavefunction is delocalized on solar-system scales. Nevertheless, the position-dependent gravitational potential Φ(r) still induces a spatially varying phase evolution δϕ(r,t) = -m Φ(r) t / ħ in the local frame. When the wavefunction is expanded in the basis of states that diagonalize the local Hamiltonian including this potential, the resulting energy eigenvalues exhibit an effective spacing set by the depth and radial extent of the solar well. This spacing, although small, defines a new timescale for phase revival. The manuscript already contains the perturbative treatment showing that the effect is not negligible for coherence properties at long times; we have added a clarifying paragraph in Section 2 to emphasize that the discretization is with respect to the phase dynamics rather than classical binding. revision: partial
Referee: [Derivation of recoherence] The formal divergence of the generalized coherence time at long times is asserted but lacks an explicit derivation or expression. No equations are shown for how the subcomponent populates the levels or how the coherence time diverges (e.g., via energy spacing or overlap integrals). Without this, it is impossible to verify whether the result is parameter-free or reduces to a self-referential definition. (See derivation of recoherence and generalized coherence time.)

Authors: We agree that an explicit derivation improves the presentation. The generalized coherence function is obtained by projecting the ULDM field onto the energy eigenstates of the solar-potential Hamiltonian: C(t) = ∑_n |⟨ψ_n|ψ⟩|^2 exp(-i E_n t / ħ), where the sum is restricted to the subcomponent whose energy spread is set by the level spacing ΔE of the solar basin. For observation times t ≫ ħ/ΔE the phases of the lowest-lying components periodically realign, causing the time-averaged |C(t)|^2 to approach a non-zero constant rather than decaying to zero. This yields a formally divergent coherence time for that subcomponent. The overlap integrals |⟨ψ_n|ψ⟩|^2 are determined by the local DM velocity distribution and are parameter-free once the solar potential is fixed. We have inserted the full derivation, including the expression for C(t) and the resulting coherence-time formula, into a new appendix and referenced it in the main text. revision: yes

Circularity Check

0 steps flagged

No significant circularity; recoherence follows from external gravitational basin model

full rationale

The paper posits that the solar gravitational potential creates a basin with discrete energy levels for a subcomponent of ULDM, introducing a new timescale that leads to recoherence (formally divergent coherence time at long times). This is a modeling assumption about the potential, not a self-definition or fitted input renamed as prediction. No self-citations, uniqueness theorems, or ansatzes from prior author work are invoked in the abstract or description to bear the central claim. The derivation chain is self-contained: the recoherence is a derived dynamical consequence of the assumed discrete levels rather than reducing to the input by construction. The skeptic concern addresses physical validity of the basin assumption, which is outside the scope of circularity analysis.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim rests on the domain assumption that the solar gravitational potential supports discrete energy levels for ULDM particles even when sparsely populated.

axioms (1)

domain assumption The local solar gravitational potential forms a basin for ULDM with discrete energy levels
This premise is stated directly in the abstract as the source of the new characteristic timescale.

pith-pipeline@v0.9.0 · 5399 in / 1107 out tokens · 45388 ms · 2026-05-16T17:28:06.053690+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

τ_coh(T_obs) = ∫_{-T_obs}^{T_obs} dτ [Γ(τ)/Γ(0)]² with Γ(τ) = Σ |ψ_i|² N_i /m cos(ω_i τ); recoherence when T_obs ≳ δE^{-1} yields τ ~ T_obs / N_nd
IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

solar gravitational atom bound states E_nlml = -m α² / 2n²; virialized halo N_nd ~ n_max² after rotation lifts m_l degeneracy

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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