Disordered But Rhythmic: the role of intrinsic protein disorder in eukaryotic circadian timing

Emery T. Usher; Jacqueline F. Pelham

REVIEW 2 major objections 3 minor 115 references

Disordered But Rhythmic: the role of intrinsic protein disorder in eukaryotic circadian timing

T0 review · 2 major / 3 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read Two claims share one submission: circadian clock IDRs are dynamic interaction modules; axion cooling feedback lowers supernova-axion detection counts.

desk verdict This submission is a biology abstract glued onto an axion supernova paper; the astro-ph half is a solid, honest simulation study, but the paper as submitted is not reviewable. read the letter →

arxiv 2508.18493 v1 pith:PFQLNABX submitted 2025-08-25 q-bio.BM

Emery T. Usher , Jacqueline F. Pelham This is my paper

classification q-bio.BM

keywords intrinsicallydisorderedproteinscircadianclockaxionsproto-neutronstarcoolingsupernovaaxiondetectionhelioscopecore-collapse

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The submission is two unrelated documents: the title and abstract are a review-style biology claim about intrinsically disordered protein regions (IDRs) in circadian clock proteins, while the attached full text is a supernova-axion physics study. The biology claim is that IDRs act as dynamic interaction modules for activation and repression, supporting robust timekeeping and expanding clock regulation. The astrophysics claim is that coupling axion emission into a 9.6-solar-mass core-collapse simulation cools the proto-neutron star enough to suppress the axion luminosity, so the event number expected in an upgraded axion helioscope pointed at Betelgeuse is 16-64 percent of the post-processing estimate. Neither half cites or uses the other, so the reader cannot attribute one integrated conclusion to the paper. The full text itself concedes that beyond-one-pion-exchange corrections suppress the axion luminosity by an order of magnitude and that other axion production channels are not modeled.

What carries the argument

The astrophysics machinery is the nonlinear cooling feedback: the axion emissivity (eq. 2.4), a one-pion-exchange nucleon-bremsstrahlung rate with degeneracy and many-body suppression (eq. 2.5), is strongly temperature sensitive; subtracting axion energy from the proto-neutron star lowers the temperature, which in turn suppresses the same emissivity. Post-processing keeps the reference temperature profile fixed and therefore overestimates the signal. The biology machinery is the intrinsically disordered region (IDR), a protein segment without stable three-dimensional structure, treated as a dynamic interaction module that expands regulation in the circadian clock.

What would settle it

Redo the 9.6-solar-mass simulation for ma=9 meV with the beyond-one-pion-exchange emissivity of ref. [16] and recompute the Betelgeuse event number at the upgraded IAXO parameters; if it exceeds 1, the paper's central quantitative conclusion fails. Alternatively, if a future galactic supernova is caught by a pointed helioscope and the registered axion burst is at post-processing strength, the claimed feedback suppression is refuted.

Watch

Extended reading notes

Core claim

The central claim of the attached full text is that the axion-emission feedback cannot be ignored when predicting supernova-axion detectability: in self-consistent simulations the proto-neutron-star central temperature drops (for example to roughly 12 MeV at 10 seconds for the 10 meV model versus roughly 30 MeV without axions), the axion emissivity falls by up to two orders of magnitude, and the cumulative event number at an upgraded IAXO helioscope is reduced to a factor of 0.16-0.64 of the post-processing value for axion masses of 3-11 meV. The declared biology paper, by contrast, claims that circadian clock proteins use intrinsic disorder as dynamic interaction modules to achieve robust t

Load-bearing premise

For the astrophysics half the load-bearing premise is that the one-pion-exchange axion emissivity with its many-body suppression factor is accurate enough for quantitative event numbers (the paper itself notes that beyond-OPE corrections suppress it by an order of magnitude and omit other channels); for the declared biology half it is that the surveyed IDR literature is faithfully represented; for the combined submission it is that the two documents are one paper.

Editorial extensions

If this is right

Detectability forecasts for supernova axions must use self-consistent simulations; post-processing overestimates event counts when axion luminosity approaches neutrino luminosity.
For the 9.6-solar-mass KSVZ model satisfying the SN 1987A luminosity constraint, an upgraded IAXO helioscope sees fewer than one axion from Betelgeuse, and the distance for a detectable signal shrinks from about 150 pc to about 100 pc.
The same cooling feedback shortens the neutrino-luminosity decay, which would affect axion bounds drawn from SN 1987A neutrino burst durations.
The total axion energy grows with axion mass more slowly than the mass-squared scaling because cooling suppresses production; simple coupling-based extrapolations overpredict energy loss.
If IDRs in clock proteins are dynamic interaction modules as claimed, clock regulation is distributed over disordered interaction surfaces, making post-translational modification and partner-switching central control points.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Beyond the paper: if the cooling feedback is generic, any exotic cooling channel with a steep temperature dependence, such as dark photons or new neutrino interactions, should be simulated self-consistently before claiming detectability, not just axions.
Beyond the paper: rerunning the same 9.6-solar-mass calculation with the beyond-one-pion-exchange emissivity could narrow or invert the gap between post-processing and self-consistent event numbers, because the lower emissivity would produce a much smaller temperature drop.
Beyond the paper: the biology abstract implies a testable prediction of its own: clock proteins with engineered removal or addition of IDRs should show altered period robustness, temperature compensation, or partner-binding dynamics relative to the wild-type oscillator.
Beyond the paper: whichever half is intended as the actual contribution, the two documents need to be separated before the submission can be read as a single paper.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague—

You should know upfront that this submission is two different papers stapled together. The title and abstract describe a biology review on intrinsically disordered regions in circadian clocks (Usher & Pelham). The attached full text is an unrelated axion-supernova simulation paper (Mori & Mori, arXiv:2508.18491v2) with different authors and a different subject. There is no single object here whose central claim can be checked.

That said, the astro-ph half is worth taking seriously on its own. The authors couple axion emission to the GR1D code for a 9.6 solar-mass progenitor and run to 20 seconds post-bounce, which is a legitimate step beyond the usual post-processing estimates. They show that the axion cooling feedback lowers the PNS temperature and, for masses 3–11 meV, cuts the expected helioscope event numbers to between 0.16 and 0.64 of the post-processed values. The qualitative point—that feedback matters for a SN1987A-consistent detectability estimate—is well made and likely robust. They are also honest about the cracks: the OPE emissivity may be off by an order of magnitude once beyond-OPE corrections, pion-induced channels, and strangeness channels are included (they cite ref. [16] for the suppression), and the progenitor is a single 9.6 solar-mass model. They mention these limitations in the text, so the paper reads as a careful first pass rather than an overclaim.

The biology abstract is a review claim about IDR prevalence and function in clock proteins; it is plausible but there is no biology full text to evaluate, so it is literally unverifiable in this submission.

The soft spot is the structural mismatch. It is not a minor error; it breaks the coherence of the submission. The right disposition is to return it to the authors for correction: either the metadata/abstract must match the full text, or the biology review must be submitted with its own full text. Sending this to peer review as-is would waste referees' time.

If the axion paper is the intended content, it deserves a serious referee after the mismatch is fixed; I would read it for a journal. The biology review, if properly paired, might be a useful subfield synthesis.

Recommendation: desk-reject or return for correction, not send to review. Flag the astro-ph half as a promising standalone manuscript.

Referee Report

2 major / 3 minor

Summary. The submission under review is not a single coherent paper. The title, category, and abstract describe a review of intrinsically disordered protein regions (IDRs) in eukaryotic circadian clock proteins: IDRs are said to act as dynamic interaction modules for activation/repression, supporting robust timekeeping and expanded regulation. The attached full text, however, is a JCAP astro-ph.HE paper titled 'Impacts of axion cooling on the direct detection of supernova axions', with different authors and references. That text reports 1D general-relativistic neutrino-radiation-hydrodynamics simulations of a 9.6 solar-mass progenitor coupled to axion emission, and finds that axion cooling reduces the proto-neutron-star temperature, axion luminosity, and helioscope event numbers compared with post-processing. No section of the full text addresses IDRs or circadian clocks, and nothing in the abstract concerns axions or supernovae. As submitted, therefore, the manuscript has no single central claim that can be checked against its body.

Significance. If the axion text were the intended paper, it would have a genuine methodological strength: the axion emission is coupled into long-term 1D supernova hydrodynamics rather than applied as a post-processing step, and the self-consistent versus post-process event-number comparison (Table 1, Fig. 4) is a useful contribution to direct-detection forecasts. The text also candidly enumerates its own limitations: the OPE emissivity may miss order-of-magnitude corrections (Sec. 2), pion-induced and strangeness channels are omitted, and the calculations use a single progenitor in spherical symmetry. If the biology abstract were the intended paper, the full text provides zero supporting evidence. Because the two documents are unrelated, the significance of either cannot be evaluated in this submission.

major comments (2)

[Abstract (unlabeled) vs. full text (Secs. 2-4)] The manuscript contains two incompatible documents. The abstract announces a q-bio review of IDRs in circadian clock proteins, with claims about IDRs as dynamic interaction modules and a survey 'from fungi to mammals.' The attached full text is a JCAP astro-ph.HE paper, 'Impacts of axion cooling on the direct detection of supernova axions,' by Kanji Mori and Masamitsu Mori, with an abstract, keywords, and reference list entirely about axions and core-collapse supernovae. No passage of the full text discusses IDRs, circadian clocks, or clock proteins, and no passage of the abstract discusses axions, supernovae, or helioscopes. There is therefore no single coherent object whose central claim can be evaluated. If the intended submission is the biology review, the full text is wholly extraneous; if the intended submission is the axion study, the abstract and category are wholly extraneous. N
[Sec. 2, Eqs. (2.4)-(2.5); Sec. 3, Table 1] Even reading the full text as the intended paper, the quantitative prediction is not robust to the acknowledged model uncertainty. The emissivity is computed in the one-pion-exchange approximation with a many-body suppression factor (Eqs. 2.4-2.5), but the text immediately states that beyond-OPE corrections from ref. [16] suppress the axion luminosity by an order of magnitude, and that pion-induced reactions and strangeness channels are omitted (Sec. 2). The central quantitative result is the ratio of self-consistent to post-process event numbers in Table 1, which ranges from 0.64 to 0.16. An order-of-magnitude shift in the input emissivity can change the magnitude or even the sign of this feedback effect, yet the event-number estimates in Sec. 3.2 are presented without propagating these systematic uncertainties. The authors flag the issue, but the model dependence is a load-bearing part

minor comments (3)

[Throughout the full text] Many equations, tables, and references are garbled or have placeholder glyphs (e.g., Eqs. (2.4)-(2.5), Table 1, and several reference entries). This may be a rendering artifact, but as submitted it makes verification of the formulas and simulation details difficult.
[Metadata / front matter] The arXiv category (q-bio.BM), title, and abstract do not match the full text's stated journal ('Prepared for submission to JCAP') and author list. The front matter should be reconciled with the actual manuscript content.
[Abstract] The circadian biology abstract contains no references and no indication of the review's scope, criteria, or use of the literature. If this abstract is to be attached to the correct review, those elements are needed; however, this point is secondary to the structural mismatch.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity in the axion simulation; the submission's biology/astrophysics mismatch is an incoherence, not a circular step.

full rationale

The astrophysics body that actually contains a derivation chain is a forward simulation, not a fit or a self-referential prediction. The internal energy update (Sec. 2, "The internal energy epsilon per volume at the (n+1)-th step is then estimated as epsilon^{n+1} = epsilon^n - Q_a Delta t") uses a published OPE bremsstrahlung emissivity plus a many-body suppression factor (eqs. 2.4-2.5). The simulation then integrates this to obtain L_a (eq. 3.1) and the helioscope event number N (eq. 3.3) with fixed IAXO-upgraded detector parameters. No parameter appearing in the predicted event number is fitted to that event number, and the SN1987A luminosity limit is applied after the simulations as a selection criterion, not as an input. The acknowledged simplifications (beyond-OPE corrections from ref. [16] suppressing luminosity by an order of magnitude, and omitted pion-induced and strangeness channels) are limitations of the imported microphysics, not circular replacements for the result. The self-citations (e.g., refs. [50], [95]) support code setup and prior simulation context, but the central claim that axion cooling suppresses the PNS temperature and thereby reduces the axion signal follows from the coupled evolution itself. The submitted manuscript is, however, internally incoherent: the abstract is a biology review of intrinsically disordered regions in circadian clock proteins, while the attached full text is the axion-supernova paper. That is a severe coherence/metadata defect, but it is not a circular derivation. No step in either half reduces to the quantity it is claimed to predict, so the honest circularity finding is 0.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central claim of the submission is ambiguous due to the two-document mismatch. The full text's quantitative predictions rest on a small set of adopted astrophysical inputs listed above; none are fitted to the target detection rate, but all are imported from prior literature without in-paper derivation. The biology abstract introduces no new entities or parameters.

free parameters (2)

many-body suppression normalization Gamma_sigma = 10 MeV (rho/1e14 g/cm^3)^(1/4) (T/1 MeV)^2
This phenomenological spin-fluctuation rate from refs. [14,15] attenuates the vacuum OPE emissivity via min(Gamma_sigma_lowest/Gamma_sigma,1) (eq. 2.5). It is an adopted model input, not measured in this paper.
mean axion energy scaling = <omega> = 2.3 T
Used to convert axion luminosity to number rate in eq. (3.3). A phenomenological thermal average, not derived in this paper.

assumptions (4)

domain assumption The OPE approximation with the many-body suppression factor (eqs. 2.4-2.5) adequately describes axion emission in the proto-neutron star environment.
The paper adopts this emissivity and notes in Section 2 that beyond-OPE corrections can change the result by an order of magnitude, making this a fragile premise.
domain assumption The SN1987A neutrino burst imposes the bound L_a < 3e52 erg/s at 1 second, and this bound is applicable to the present models.
Used in Section 3.2 to select viable axion masses (ma <= 9 meV). This is a standard external constraint, not derived here.
domain assumption The IAXO upgraded configuration (B=35 kG, L=22 m, A=3.9 m^2) is a valid benchmark for the helioscope sensitivity.
Adopted from ref. [35] in Section 3.2 for event-number estimates.
domain assumption The 9.6 solar mass zero-metallicity progenitor is representative enough for the conclusions about detectability.
The paper acknowledges in the conclusion that axion luminosity is progenitor-dependent; the choice is made because this star explodes in 1D without artificial shocks.

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Cite this review

Pith. "Pith review of Disordered But Rhythmic: the role of intrinsic protein disorder in eukaryotic circadian timing." pith.science (2026). https://pith.science/paper/PFQLNABX

@misc{pith2026250818493,
  author       = {Pith},
  title        = {Pith review of: Disordered But Rhythmic: the role of intrinsic protein disorder in eukaryotic circadian timing},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PFQLNABX}},
  note         = {Machine review of arXiv:2508.18493}
}

read the original abstract

Intrinsically disordered protein regions (IDRs) are found across all domains of life and are characterized by a lack of stable 3D structure. Nevertheless, IDRs play critical roles in the most tightly regulated cellular processes, including in the core circadian clock. The molecular oscillator at the heart of circadian regulation leverages IDRs as dynamic interaction modules for activation and repression to support robust timekeeping and expand clock output and regulation. Here, we cover the biophysical mechanisms conferred by IDRs and their modulators. We survey the intrinsically disordered regions in clock proteins that are widely prevalent from fungi to mammals and discuss the importance of IDRs to the core clock and beyond.

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Works this paper leans on

115 extracted references · 74 canonical work pages

[16]

Carenza, T

P. Carenza, T. Fischer, M. Giannotti, G. Guo, G. Mart ´ ınez-Pinedo and A. Mirizzi, �� , �� (2019) 016 [�� ]

2019
[1]

Weinberg, � �� , �� (1978) 223

S. Weinberg, � �� , �� (1978) 223

1978
[2]

Wilczek, �� , �� (1978) 279

F. Wilczek, �� , �� (1978) 279

1978
[3]

Abbott and P

L.F. Abbott and P. Sikivie, � �� , �� (1983) 133

1983
[4]

Preskill, M.B

J. Preskill, M.B. Wise and F. Wilczek, �� , �� (1983) 127

1983
[5]

Dine and W

M. Dine and W. Fischler, �� , �� (1983) 137

1983
[6]

Vysotsskii, Y.B

M.I. Vysotsskii, Y.B. Zel’dovich, M.Y. Khlopov and V.M. Chechetkin, �� , �� (1978) 502

1978
[7]

Choi, S.H

K. Choi, S.H. Im and C.S. Shin, �� , �� (2021) 225 [�� ]

2021

Show all 115 references

[8]

Caputo and G

A. Caputo and G. Raffelt, �� , �� (2024) arXiv:2401.13728 [�� ]

2024 arXiv
[9]

Carenza, M

P. Carenza, M. Giannotti, J. Isern, A. Mirizzi and O. Straniero, �� , �� (2025) 1 [�� ]

2025
[10]

Turner, �� , �� (1988) 1797

M.S. Turner, �� , �� (1988) 1797

1988
[11]

Burrows, M.S

A. Burrows, M.S. Turner and R.P. Brinkmann, �� , �� (1989) 1020

1989
[12]

Raffelt and D

G. Raffelt and D. Seckel, �� , �� (1988) 1793

1988
[13]

Engel, D

J. Engel, D. Seckel and A.C. Hayes, �� , �� (1990) 960. – 11 –

1990
[14]

Keil, H.-T

W. Keil, H.-T. Janka, D.N. Schramm, G. Sigl, M.S. Turner and J. Ellis, �� , �� (1997) 2419 [�� ]

1997
[15]

Fischer, S

T. Fischer, S. Chakraborty, M. Giannotti, A. Mirizzi, A. Payez and A. Ringwald, �� , �� (2016) 085012 [�� ]

2016
[17]

Fischer, P

T. Fischer, P. Carenza, B. Fore, M. Giannotti, A. Mirizzi and S. Reddy, �� , �� (2021) 103012 [�� ]

2021
[18]

Betranhandy and E

A. Betranhandy and E. O’Connor, �� , �� (2022) 063019

2022
[19]

Foguel and E.S

A.L. Foguel and E.S. Fraga, �� , �� (2023) 102855 [�� ]

2023
[20]

Lella, P

A. Lella, P. Carenza, G. Co’, G. Lucente, M. Giannotti, A. Mirizzi et al., �� , �� (2024) 023001 [�� ]

2024
[21]

Grifols, E

J.A. Grifols, E. Mass´ o and R. Toldr` a,�� , �� (1996) 2372 [�� ]

1996
[22]

Brockway, E.D

J.W. Brockway, E.D. Carlson and G.G. Raffelt, �� , �� (1996) 439 [�� ]

1996
[23]

Payez, C

A. Payez, C. Evoli, T. Fischer, M. Giannotti, A. Mirizzi and A. Ringwald, �� , �� (2015) 006 [�� ]

2015
[24]

Kohri and H

K. Kohri and H. Kodama, �� , �� (2017) 051701 [�� ]

2017
[25]

Manzari, Y

C.A. Manzari, Y. Park, B.R. Safdi and I. Savoray, �� , �� (2024) 211002 [�� ]

2024
[26]

Raffelt, J

G.G. Raffelt, J. Redondo and N.V. Maira, �� , �� (2011) 103008 [�� ]

2011
[27]

Calore, P

F. Calore, P. Carenza, M. Giannotti, J. Jaeckel and A. Mirizzi, �� , �� (2020) 123005 [�� ]

2020
[28]

Calore, P

F. Calore, P. Carenza, C. Eckner, T. Fischer, M. Giannotti, J. Jaeckel et al., �� , �� (2022) 063028 [�� ]

2022
[29]

Carlson, �� , �� (1995) 245

E.D. Carlson, �� , �� (1995) 245

1995
[30]

Xiao, K.M

M. Xiao, K.M. Perez, M. Giannotti, O. Straniero, A. Mirizzi, B.W. Grefenstette et al., �� , �� (2021) 031101 [�� ]

2021
[31]

M. Xiao, P. Carenza, M. Giannotti, A. Mirizzi, K.M. Perez, O. Straniero et al., �� , �� (2022) 123019 [�� ]

2022
[32]

K. Mori, T. Takiwaki and K. Kotake, �� , �� (2022) 023020 [�� ]. – 12 –

2022
[33]

Anastassopoulos, S

V. Anastassopoulos, S. Aune, K. Barth, A. Belov, H. Br¨ auninger, G. Cantatore et al., �� , �� (2017) 584 [�� ]

2017
[34]

Inoue, Y

Y. Inoue, Y. Akimoto, R. Ohta, T. Mizumoto, A. Yamamoto and M. Minowa, �� , �� (2008) 93 [�� ]

2008
[35]

Armengaud, D

E. Armengaud, D. Atti´ e, S. Basso, P. Brun, N. Bykovskiy, J.M. Carmona et al., �� , �� (2019) 047 [�� ]

2019
[36]

Anastassopoulos, F

V. Anastassopoulos, F. Avignone, A. Bykov, G. Cantatore, S.A. Cetin, A. Derbin et al., �� , �� (2017) P11019 [�� ]

2017
[37]

S.-F. Ge, K. Hamaguchi, K. Ichimura, K. Ishidoshiro, Y. Kanazawa, Y. Kishimoto et al., �� , �� (2020) 059 [�� ]

2020
[38]

S. Asai, Y. Kanazawa, T. Moroi and T. Sichanugrist, �� , �� (2022) 137137 [�� ]

2022
[39]

Carenza, J.A

P. Carenza, J.A. Garc ´ ıa Pascual, M. Giannotti, I.G. Irastorza, M. Kaltschmidt, A. Lella et al., �� , �� (2025) arXiv:2502.19476 [�� ]

2025 arXiv
[40]

Odrzywolek, M

A. Odrzywolek, M. Misiaszek and M. Kutschera, �� , �� (2004) 303 [�� ]

2004
[41]

Patton, C

K.M. Patton, C. Lunardini, R.J. Farmer and F.X. Timmes, �� , �� (2017) 6 [�� ]

2017
[42]

C. Kato, K. Ishidoshiro and T. Yoshida, �� , �� (2020) 121 [�� ]

2020
[43]

Al Kharusi, S.Y

S. Al Kharusi, S.Y. BenZvi, J.S. Bobowski, W. Bonivento, V. Brdar, T. Brunner et al., �� , �� (2021) 031201 [�� ]

2021
[44]

Mukhopadhyay, C

M. Mukhopadhyay, C. Lunardini, F.X. Timmes and K. Zuber, �� , �� (2020) 153 [�� ]

2020
[45]

Li, Y.-F

H.-L. Li, Y.-F. Li, L.-J. Wen and S. Zhou, �� , �� (2020) 049 [�� ]

2020
[46]

O’Connor and C.D

E. O’Connor and C.D. Ott, � �� , �� (2010) 114103 [�� ]

2010
[47]

O’Connor, �� , �� (2015) 24 [�� ]

E. O’Connor, �� , �� (2015) 24 [�� ]

2015
[48]

Shibata, K

M. Shibata, K. Kiuchi, Y. Sekiguchi and Y. Suwa, �� , �� (2011) 1255 [�� ]

2011
[49]

Cardall, E

C.Y. Cardall, E. Endeve and A. Mezzacappa, �� , �� (2013) 103004 [�� ]. – 13 –

2013
[50]

M. Mori, Y. Suwa, K. Nakazato, K. Sumiyoshi, M. Harada, A. Harada et al., �� , �� (2021) 023E01 [�� ]

2021
[51]

M. Mori, R. Sawada, Y. Suwa, A. Tanikawa, K. Kashiyama and K. Murase, �� , �� (2025) 127 [�� ]

2025
[52]

Typel, �� , �� (2005) 064301 [�� ]

S. Typel, �� , �� (2005) 064301 [�� ]

2005
[53]

Hempel and J

M. Hempel and J. Schaffner-Bielich, � �� , �� (2010) 210 [�� ]

2010
[54]

Melson, H.-T

T. Melson, H.-T. Janka and A. Marek, �� , �� (2015) L24 [�� ]

2015
[55]

Kim, �� , �� (1979) 103

J.E. Kim, �� , �� (1979) 103

1979
[56]

Shifman, A.I

M.A. Shifman, A.I. Vainshtein and V.I. Zakharov, �� , �� (1980) 493

1980
[57]

Carena and R.D

M. Carena and R.D. Peccei, �� , �� (1989) 652

1989
[58]

di Cortona, E

G.G. di Cortona, E. Hardy, J.P. Vega and G. Villadoro, �� , �� (2016) 34 [�� ]

2016
[59]

Brinkmann and M.S

R.P. Brinkmann and M.S. Turner, �� , �� (1988) 2338

1988
[60]

Raffelt and D

G. Raffelt and D. Seckel, �� , �� (1995) 1780 [�� ]

1995
[61]

Hannestad and G

S. Hannestad and G. Raffelt, �� , �� (1998) 339 [�� ]

1998
[62]

Chang, R

J.H. Chang, R. Essig and S.D. McDermott, �� , �� (2018) 51 [�� ]

2018
[63]

Stoica, B

S. Stoica, B. Pastrav, J.E. Horvath and M.P. Allen, �� , �� (2009) 439 [�� ]

2009
[64]

Ericson and J.F

T.E.O. Ericson and J.F. Mathiot, �� , �� (1989) 507

1989
[65]

Raffelt and D

G. Raffelt and D. Seckel, �� , �� (1991) 2605

1991
[66]

Janka, W

H.-T. Janka, W. Keil, G. Raffelt and D. Seckel, �� , �� (1996) 2621 [�� ]

1996
[67]

Carenza, B

P. Carenza, B. Fore, M. Giannotti, A. Mirizzi and S. Reddy, �� , �� (2021) 071102 [�� ]

2021
[68]

Cavan-Piton, D

M. Cavan-Piton, D. Guadagnoli, M. Oertel, H. Seong and L. Vittorio, �� , �� (2024) 121002 [�� ]

2024
[69]

Sikivie, �� , �� (1983) 1415

P. Sikivie, �� , �� (1983) 1415. – 14 –

1983
[70]

T. Adam, F. An, G. An, Q. An, N. Anfimov, V. Antonelli et al., �� , �� (2015) arXiv:1508.07166 [�� ]

2015 arXiv
[71]

Fukuda, Y

S. Fukuda, Y. Fukuda, T. Hayakawa, E. Ichihara, M. Ishitsuka, Y. Itow et al., �� , �� (2003) 418

2003
[72]

Machado, K

L.N. Machado, K. Abe, Y. Hayato, K. Hiraide, K. Ieki, M. Ikeda et al., �� , �� (2022) 40 [�� ]

2022
[73]

S. Abe, M. Eizuka, S. Futagi, A. Gando, Y. Gando, S. Goto et al., �� , �� (2024) 140 [�� ]

2024
[74]

Hyper-Kamiokande Proto-Collaboration, :, K. Abe, K. Abe, H. Aihara, A. Aimi et al., �� , �� (2018) arXiv:1805.04163 [�� ]

2018 arXiv
[75]

Suzuki, �� , �� (2014) 3094 [�� ]

A. Suzuki, �� , �� (2014) 3094 [�� ]

2014
[76]

Asakura, A

K. Asakura, A. Gando, Y. Gando, T. Hachiya, S. Hayashida, H. Ikeda et al., �� , �� (2016) 91 [�� ]

2016
[77]

B. Abi, R. Acciarri, M.A. Acero, G. Adamov, D. Adams, M. Adinolfi et al., �� , �� (2020) T08008 [�� ]

2020
[78]

Albanese, R

SNO+ Collaboration, :, V. Albanese, R. Alves, M.R. Anderson, S. Andringa et al., �� , �� (2021) arXiv:2104.11687 [�� ]

2021 arXiv
[79]

Raffelt and L

G. Raffelt and L. Stodolsky, �� , �� (1988) 1237

1988
[80]

Raffelt, �� , �� (1990) 1

G.G. Raffelt, �� , �� (1990) 1

1990
[81]

Joyce, S.-C

M. Joyce, S.-C. Leung, L. Moln´ ar, M. Ireland, C. Kobayashi and K. Nomoto, �� , �� (2020) 63 [��...

2020
[82]

van Leeuwen, �� , �� (2007) 653 [�� ]

F. van Leeuwen, �� , �� (2007) 653 [�� ]

2007
[83]

Tkachenko, J.M

A. Tkachenko, J.M. Matthews, C. Aerts, K. Pavlovski, P.I. P´ apics, K. Zwintz et al., �� β �� , �� (2016) 1964 [�� ]

2016
[84]

Howarth and K.C

I.D. Howarth and K.C. Smith, �� , �� (2001) 353

2001
[85]

Tetzlaff, R

N. Tetzlaff, R. Neuh¨ auser and M.M. Hohle,� �� , �� (2011) 190 [�� ]

2011
[86]

Ohnaka, K.H

K. Ohnaka, K.H. Hofmann, D. Schertl, G. Weigelt, C. Baffa, A. Chelli et al., �� , �� (2013) A24 [�� ]

2013
[87]

Giannotti, L.D

M. Giannotti, L.D. Duffy and R. Nita, �� , �� (2011) 015 [�� ]

2011
[88]

Lucente, P

G. Lucente, P. Carenza, T. Fischer, M. Giannotti and A. Mirizzi, �� , �� (2020) 008 [�� ]. – 15 –

2020
[89]

Nakamura, S

K. Nakamura, S. Horiuchi, M. Tanaka, K. Hayama, T. Takiwaki and K. Kotake, �� , �� (2016) 3296 [�� ]

2016
[90]

Neuh¨ auser, G

R. Neuh¨ auser, G. Torres, M. Mugrauer, D.L. Neuh¨ auser, J. Chapman, D. Luge et al.,�� , �� (2022) 693 [�� ]

2022
[91]

T. Luo, H. Umeda, T. Yoshida and K. Takahashi, �� , �� (2022) 115 [�� ]

2022
[92]

H. Saio, D. Nandal, G. Meynet and S. Ekstr¨ om, �� , �� (2023) 2765 [�� ]

2023
[93]

Renzo and Y

M. Renzo and Y. G¨ otberg,�� ζ ��, �� (2021) 277 [�� ]

2021
[94]

Takata, K

T. Takata, K. Mori, K. Nakamura and K. Kotake, �� , �� (2025) arXiv:2503.09005 [�� ]

2025
[95]

K. Mori, T. Takiwaki, K. Kotake and S. Horiuchi, �� , �� (2023) 063027 [�� ]

2023
[96]

Kotake, K

K. Kotake, K. Sato and K. Takahashi, �� , �� (2006) 971 [�� ]

2006
[97]

Janka, �� , �� (2012) 407 [�� ]

H.-T. Janka, �� , �� (2012) 407 [�� ]

2012
[98]

Burrows and D

A. Burrows and D. Vartanyan, �� , �� (2021) 29 [�� ]

2021
[99]

Yamada, H

S. Yamada, H. Nagakura, R. Akaho, A. Harada, S. Furusawa, W. Iwakami et al., �� , �� (2024) 190

2024
[100]

Abbar, H

S. Abbar, H. Duan, K. Sumiyoshi, T. Takiwaki and M.C. Volpe, �� , �� (2019) 043004 [�� ]

2019
[101]

Nagakura, T

H. Nagakura, T. Morinaga, C. Kato and S. Yamada, �� , �� (2019) 139 [�� ]

2019
[102]

Abbar, F

S. Abbar, F. Capozzi, R. Glas, H.T. Janka and I. Tamborra, �� , �� (2021) 063033 [�� ]

2021
[103]

Nagakura, A

H. Nagakura, A. Burrows, L. Johns and G.M. Fuller, �� , �� (2021) 083025 [�� ]

2021
[104]

J. Liu, R. Akaho, A. Ito, H. Nagakura, M. Zaizen and S. Yamada, �� , �� (2023) 123024 [�� ]

2023
[105]

Xiong, M.-R

Z. Xiong, M.-R. Wu, G. Mart ´ ınez-Pinedo, T. Fischer, M. George, C.-Y. Lin et al., �� , �� (2023) 083016 [�� ]. – 16 –

2023
[106]

Nagakura, �� , �� (2023) 211401 [�� ]

H. Nagakura, �� , �� (2023) 211401 [�� ]

2023
[107]

Ehring, S

J. Ehring, S. Abbar, H.-T. Janka, G. Raffelt and I. Tamborra, �� , �� (2023) 103034 [�� ]

2023
[108]

Ehring, S

J. Ehring, S. Abbar, H.-T. Janka, G. Raffelt and I. Tamborra, �� , �� (2023) 061401 [�� ]

2023
[109]

Akaho, J

R. Akaho, J. Liu, H. Nagakura, M. Zaizen and S. Yamada, �� , �� (2024) 023012 [�� ]

2024
[110]

K. Mori, T. Takiwaki, K. Kotake and S. Horiuchi, �� , �� (2025) L9 [�� ]

2025
[111]

Fiorillo, H.-T

D.F.G. Fiorillo, H.-T. Janka and G.G. Raffelt, �� , �� (2025) arXiv:2507.22985 [�� ]

2025
[112]

Sumiyoshi, T

K. Sumiyoshi, T. Kojo and S. Furusawa, �� , in �� , I. Tanihata, H. Toki and T. Kajino, eds., (Singapore), pp. 1–51, Springer Nature Singapore (2020), DOI

2020
[113]

Burgio, H.J

G.F. Burgio, H.J. Schulze, I. Vida˜ na and J.B. Wei, �� , �� (2021) 103879 [�� ]

2021
[114]

Liebend¨ orfer, S.C

M. Liebend¨ orfer, S.C. Whitehouse and T. Fischer, �� , �� (2009) 1174 [�� ]

2009
[115]

Sumiyoshi and S

K. Sumiyoshi and S. Yamada, �� , �� (2012) 17 [�� ]. – 17 –

2012

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.

[1] [16]

Carenza, T

P. Carenza, T. Fischer, M. Giannotti, G. Guo, G. Mart ´ ınez-Pinedo and A. Mirizzi, �� , �� (2019) 016 [�� ]

2019

[2] [1]

Weinberg, � �� , �� (1978) 223

S. Weinberg, � �� , �� (1978) 223

1978

[3] [2]

Wilczek, �� , �� (1978) 279

F. Wilczek, �� , �� (1978) 279

1978

[4] [3]

Abbott and P

L.F. Abbott and P. Sikivie, � �� , �� (1983) 133

1983

[5] [4]

Preskill, M.B

J. Preskill, M.B. Wise and F. Wilczek, �� , �� (1983) 127

1983

[6] [5]

Dine and W

M. Dine and W. Fischler, �� , �� (1983) 137

1983

[7] [6]

Vysotsskii, Y.B

M.I. Vysotsskii, Y.B. Zel’dovich, M.Y. Khlopov and V.M. Chechetkin, �� , �� (1978) 502

1978

[8] [7]

Choi, S.H

K. Choi, S.H. Im and C.S. Shin, �� , �� (2021) 225 [�� ]

2021