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Paper Citation Record · LEDGER

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field

As of 21 August 2026, this Paper Citation Record lists 48 of 48 outbound references and 2 inbound Pith citation observations for arXiv:1908.10323.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
1908.10323 v2

Coverage vector

measured 48 of 48 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T10:54:04.583288Z

measured 50 of 50 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-01T04:48:30.563853Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-07-01T11:05:41.391312Z

Reference resolution

48 of 48 outbound references displayed

  • verified exact13
  • verified fuzzy6
  • unresolved29
  • parse uncertain0
  • malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 113f69c0-40e5-46af-9158-81c4e6eb8b4d · outbound

This paper cites an unresolved cited work.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field Unresolved cited work

Reference 1

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Observation 625c4caa-b2f6-4163-81ac-a8550b7df253 · outbound

This paper cites (14) The value of a is given by solving Eq.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field (14) The value of a is given by solving Eq

Reference 2

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Observation e17ba65e-319a-4710-b25b-6a0d15442a2f · outbound

This paper cites (C2) 12 Expanding the matrix structure in Eq.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field (C2) 12 Expanding the matrix structure in Eq

Reference 3

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Observation c4a526a0-b374-477c-838b-f4e2d80a2f78 · outbound

This paper cites It has five tensor structures: /P q, /P⊥, /P qγ1γ2, γ1γ2, and 1.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field It has five tensor structures: /P q, /P⊥, /P qγ1γ2, γ1γ2, and 1

Reference 4

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Observation 328b4de2-f983-49d3-911a-26a44f75b212 · outbound

This paper cites Estimate of the magnetic field strength in heavy-ion collisions.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field Estimate of the magnetic field strength in heavy-ion collisions

Reference 5

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Observation 8d92debf-b02e-4664-9272-ea15bf0ec20a · outbound

This paper cites A systematic study of magnetic field in Relativistic Heavy-ion Collisions in the RHIC and LHC energy regions.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field A systematic study of magnetic field in Relativistic Heavy-ion Collisions in the RHIC and LHC energy regions

Reference 6

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Observation 9b37415b-bc5b-4609-ab6d-6108b3234d7f · outbound

This paper cites Photon decay in strong magnetic field in heavy-ion collisions.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field Photon decay in strong magnetic field in heavy-ion collisions

Reference 7

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Observation ce4a94af-9939-4b88-b565-fc7cce386455 · outbound

This paper cites Electromagnetic field and the chiral magnetic effect in the quark-gluon plasma.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field Electromagnetic field and the chiral magnetic effect in the quark-gluon plasma

Reference 8

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Observation 16378432-79a7-493e-b818-5337ae5708fc · outbound

This paper cites Magnetic contribution to dilepton production in heavy-ion collisions.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field Magnetic contribution to dilepton production in heavy-ion collisions

Reference 9

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Observation 89eb6c5a-2a05-4d7c-8091-e43ccf339a29 · outbound

This paper cites Formation of very strongly magnetized neutron stars - implications for gamma-ray bursts,.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field Formation of very strongly magnetized neutron stars - implications for gamma-ray bursts,

Reference 10

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Observation eeee5aa8-6772-4f7e-8226-bec509d63ddb · outbound

This paper cites Meson masses in electromagnetic fields with Wilson fermions.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field Meson masses in electromagnetic fields with Wilson fermions

Reference 11

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Observation b47cc6b3-33a3-48c3-b084-dee39b3a1964 · outbound

This paper cites Thermal pions in a magnetic background.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field Thermal pions in a magnetic background

Reference 12

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Observation 0d2430ba-635e-4a49-95a0-e8b79cf8560c · outbound

This paper cites Gell-Mann - Oakes - Renner relation in a magnetic field at finite temperature.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field Gell-Mann - Oakes - Renner relation in a magnetic field at finite temperature

Reference 13

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Observation 5ba389ae-d75d-4177-ab50-e0ec2a92975c · outbound

This paper cites Pionic dispersion relations in the presence of a weak magnetic field.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field Pionic dispersion relations in the presence of a weak magnetic field

Reference 14

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Observation a8a8d7fb-93e7-45cf-bec6-d68c48e26a6d · outbound

This paper cites Mass modification of hot pions in magnetized dense medium.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field Mass modification of hot pions in magnetized dense medium

Reference 15

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

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Observation 3072f64b-f7bf-45d8-be4f-c19328b840ba · outbound

This paper cites Properties of neutral mesons in a hot and magnetized quark matter.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field Properties of neutral mesons in a hot and magnetized quark matter

Reference 16

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Observation ac8bd59f-d659-4e14-8e77-80a98020203f · outbound

This paper cites Charged pion masses under strong magnetic fields in the NJL model.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field Charged pion masses under strong magnetic fields in the NJL model

Reference 17

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Observation bfa8c9b1-2cb1-4d21-a140-d3ae36b9aa7f · outbound

This paper cites Neutral meson properties under an external magnetic field in nonlocal chiral quark models.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field Neutral meson properties under an external magnetic field in nonlocal chiral quark models

Reference 18

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Observation b5b52c6a-7c8c-4be2-af03-4e2a15d3d10c · outbound

This paper cites Properties of magnetized neutral mesons within a full RPA evaluation.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field Properties of magnetized neutral mesons within a full RPA evaluation

Reference 19

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Observation 83889ed0-9c8b-41ad-8954-2c2674e530f4 · outbound

This paper cites Properties of Mesons in a Strong Magnetic Field.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field Properties of Mesons in a Strong Magnetic Field

Reference 20

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no resolver link, observed 2026-08-14T10:54:04.479949Z

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Observation e312ed41-c4db-40d2-ba44-b4aec5dfd24a · outbound

This paper cites Neutral meson properties in hot and magnetized quark matter: a new magnetic field independent regularization scheme applied to NJL-type model.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field Neutral meson properties in hot and magnetized quark matter: a new magnetic field independent regularization scheme applied to NJL-type model

Reference 21

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Observation 90913537-61dd-4f3a-a242-51b33976f280 · outbound

This paper cites $\pi_0$ pole mass calculation in a strong magnetic field and lattice constraints.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field $\pi_0$ pole mass calculation in a strong magnetic field and lattice constraints

Reference 22

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Observation 9aae26a0-1b1e-405a-9308-f8fed8f3d1d2 · outbound

This paper cites Dressed Polyakov loop and phase diagram of hot quark matter under magnetic field.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field Dressed Polyakov loop and phase diagram of hot quark matter under magnetic field

Reference 23

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no resolver link, observed 2026-08-14T10:54:04.490352Z

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Observation d514e5aa-b789-441d-8d93-c5895d1a9caa · outbound

This paper cites Entanglement between chiral and deconfinement transitions under strong uniform magnetic background field.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field Entanglement between chiral and deconfinement transitions under strong uniform magnetic background field

Reference 24

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verified exact
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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

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Observation 3fe0e0ef-fdf6-447f-876c-14ca9c116292 · outbound

This paper cites Phase diagram of hot QCD in an external magnetic field: possible splitting of deconfinement and chiral transitions.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field Phase diagram of hot QCD in an external magnetic field: possible splitting of deconfinement and chiral transitions

Reference 25

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Observation 52905a8f-ffe4-4658-89a1-6067fb8b4d2b · outbound

This paper cites Phase diagram in an external magnetic field beyond a mean-field approximation.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field Phase diagram in an external magnetic field beyond a mean-field approximation

Reference 26

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no resolver link, observed 2026-08-14T10:54:04.501701Z

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Observation cccaf540-67c7-4515-aa7c-c378f77d3bcb · outbound

This paper cites Quark matter under strong magnetic field in chiral models.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field Quark matter under strong magnetic field in chiral models

Reference 27

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verified exact
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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

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Observation fe5f1b55-79d3-4bdf-a904-ac76f7fe3d5e · outbound

This paper cites The chiral transition in a magnetic background: Finite density effects and the functional renormalization group.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field The chiral transition in a magnetic background: Finite density effects and the functional renormalization group

Reference 28

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verified exact
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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

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Observation 14d910a5-afd8-4dff-b95f-158360760275 · outbound

This paper cites Chiral transition in a strong magnetic background.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field Chiral transition in a strong magnetic background

Reference 29

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Observation 1dfa487e-9687-4ebc-a118-ca1a8940fa32 · outbound

This paper cites Magnetic Susceptibility of the Quark Condensate and Polarization from Chiral Models.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field Magnetic Susceptibility of the Quark Condensate and Polarization from Chiral Models

Reference 30

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no resolver link, observed 2026-08-14T10:54:04.516380Z

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Observation 3f19725b-83fe-4a31-849d-3ccf56914d43 · outbound

This paper cites Chiral transition in a magnetic field and at finite baryon density.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field Chiral transition in a magnetic field and at finite baryon density

Reference 31

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verified exact
local_arxiv, observed 2026-08-14T10:54:04.870260Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

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Observation 2fb01979-57a8-457e-8cae-92bf217bcc7a · outbound

This paper cites The axial vector current in beta decay,.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field The axial vector current in beta decay,

Reference 32

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

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Observation 46befc6e-e7c8-4794-a1ca-7704d553135a · outbound

This paper cites Linear sigma model at finite temperature.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field Linear sigma model at finite temperature

Reference 33

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Observation f5c34c1b-6f7e-4fec-bbcd-a8e185ed0ad0 · outbound

This paper cites Magnetic Corrections to ${\pi}$-${\pi}$ Scattering Lengths in the Linear Sigma Model.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field Magnetic Corrections to ${\pi}$-${\pi}$ Scattering Lengths in the Linear Sigma Model

Reference 34

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

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Observation 10c8e447-f1a7-4fd0-b3af-d4ced907620f · outbound

This paper cites Thermo-magnetic corrections to $\pi$-$\pi$ Scattering Lengths in the Linear Sigma Model.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field Thermo-magnetic corrections to $\pi$-$\pi$ Scattering Lengths in the Linear Sigma Model

Reference 35

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local_arxiv, observed 2026-08-14T10:54:04.831121Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

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Observation dfb96620-0fab-4a49-b402-d9e54740aa09 · outbound

This paper cites The Linear Sigma Model and the formation of a charged pion condensate in the presence of an external magnetic field.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field The Linear Sigma Model and the formation of a charged pion condensate in the presence of an external magnetic field

Reference 36

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verified exact
local_arxiv, observed 2026-08-14T10:54:04.816179Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

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Observation c1751b85-35b8-4ec6-8439-cdf0bcae0bf7 · outbound

This paper cites On the critical end point in a two-flavor linear sigma model coupled to quarks.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field On the critical end point in a two-flavor linear sigma model coupled to quarks

Reference 37

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no resolver link, observed 2026-08-14T10:54:04.542939Z

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source=pdf_text observed=2026-08-14T10:54:04.542939Z digest=sha256:9a4aa15a5e6aaa0ce43bcdb5bf11899adcd38694d8e6a2d1fc981424a4caa843

Observation d2ebda02-1215-475e-ab7f-6913939afede · outbound

This paper cites The effective QCD phase diagram and the critical end point.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field The effective QCD phase diagram and the critical end point

Reference 38

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verified exact
local_arxiv, observed 2026-08-14T10:54:04.793670Z

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Observation 9b1bc31d-089f-441b-b7f8-6c5246b5f525 · outbound

This paper cites QCD phase diagram from chiral symmetry restoration: analytic approach at high and low temperature using the Linear Sigma Model with Quarks.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field QCD phase diagram from chiral symmetry restoration: analytic approach at high and low temperature using the Linear Sigma Model with Quarks

Reference 39

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no resolver link, observed 2026-08-14T10:54:04.550559Z

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source=pdf_text observed=2026-08-14T10:54:04.550559Z digest=sha256:82cbf43210d065b517785bb50d00ff1d8829ba39eccd43ad539a7a107d8bf9f7

Observation 66014ae1-e0ae-4fa0-a292-3631faf921fc · outbound

This paper cites Chiral Phase Transition within Effective Models with Constituent Quarks.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field Chiral Phase Transition within Effective Models with Constituent Quarks

Reference 40

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no resolver link, observed 2026-08-14T10:54:04.554068Z

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source=pdf_text observed=2026-08-14T10:54:04.554068Z digest=sha256:c4eed6a1f4e313f2441af8875611d64c1e2472cfb15c7373e97dbed9184fe673

Observation bee30e82-acfb-4192-9be6-04fdee41e374 · outbound

This paper cites The magnetized effective QCD phase diagram.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field The magnetized effective QCD phase diagram

Reference 41

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no resolver link, observed 2026-08-14T10:54:04.558015Z

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source=pdf_text observed=2026-08-14T10:54:04.558015Z digest=sha256:dca5edcd8fa8d70a8596e44804930083a5f133999111747821a473f851d60ff0

Observation b6583dd0-a4ea-40d2-a679-0aa0fff9263f · outbound

This paper cites Inverse magnetic catalysis in the linear sigma model with quarks.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field Inverse magnetic catalysis in the linear sigma model with quarks

Reference 42

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no resolver link, observed 2026-08-14T10:54:04.561823Z

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source=pdf_text observed=2026-08-14T10:54:04.561823Z digest=sha256:02e53d8ecfb0a53f532e52bff95a3172201f99598bcb8d6eaf721199d7b811cd

Observation 73c735da-0c41-49f1-837b-676088b3e65e · outbound

This paper cites Magnetic field-dependence of the neutral pion mass in the linear sigma model coupled to quarks: The weak field case.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field Magnetic field-dependence of the neutral pion mass in the linear sigma model coupled to quarks: The weak field case

Reference 43

Resolution
unresolved
no resolver link, observed 2026-08-14T10:54:04.565242Z

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source=pdf_text observed=2026-08-14T10:54:04.565242Z digest=sha256:41159c93df30eba9978ef59a64b6866ed8740cbf2ca73181c8c7c94f9a0f8817

Observation 420abeb1-b2db-48b0-8346-9b2da2d5b1ed · outbound

This paper cites Vacuum polarization in thermal QED with an external magnetic field.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field Vacuum polarization in thermal QED with an external magnetic field

Reference 44

Resolution
verified exact
local_arxiv, observed 2026-08-14T10:54:04.734167Z

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source=pdf_text observed=2026-08-14T10:54:04.568886Z digest=sha256:dd478a333f9208a7e4bf4147cb20b952868c0182ce4f56a0ff4f9f87827856a5

Observation 68ad0395-44c6-4f2a-906f-991a1285f141 · outbound

This paper cites Vacuum Polarization in Homogeneous Mag- netic Fields,.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field Vacuum Polarization in Homogeneous Mag- netic Fields,

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T10:54:05.269118Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-14T10:54:04.572480Z digest=sha256:c833b84fc1967a9d2a0baefd91e654837993b20a51b8eb08c0ee39061c94abb5

Observation 113b54d0-3ea6-411c-a51d-851ee63d3312 · outbound

This paper cites Chiral Symmetry transition in the Linear Sigma Model with quarks: Counting effective QCD degrees of freedom from low to high temperature.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field Chiral Symmetry transition in the Linear Sigma Model with quarks: Counting effective QCD degrees of freedom from low to high temperature

Reference 46

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no resolver link, observed 2026-08-14T10:54:04.576133Z

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source=pdf_text observed=2026-08-14T10:54:04.576133Z digest=sha256:e638288f9d16ee53502fba0afd8292bc96fba00f1f963f74413c1b19e7c48031

Observation 9ad8d74f-e26b-4f8c-b00d-06a98a02451a · outbound

This paper cites Aspects of Chiral Symmetry.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field Aspects of Chiral Symmetry

Reference 47

Resolution
verified exact
local_arxiv, observed 2026-08-14T10:54:04.710018Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-14T10:54:04.579614Z digest=sha256:d7e3125b83bd90f34ebd8b9b36f47ce210c1f40c7bf79a4d47934986a48ef867

Observation b7925c45-e6f5-43e9-bc7c-0e9662b33be9 · outbound

This paper cites Introduction to chiral symmetry ,.

Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field Introduction to chiral symmetry ,

Reference 48

Resolution
verified exact
raw_fallback, observed 2026-08-14T10:54:04.696127Z

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source=pdf_text observed=2026-08-14T10:54:04.583288Z digest=sha256:77acae3ffb2116746040b2ad2709eaa66d10ff24db2d16aeeee14f2383a8f184

Pith citing papers

Observation 6569c461-c505-405b-9aa6-6e90838dc68a · inbound

Complete one-loop self-energies of the linear sigma model coupled to quarks at finite temperature and in a magnetic field cites this paper.

Complete one-loop self-energies of the linear sigma model coupled to quarks at finite temperature and in a magnetic field Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field

Reference 73

Resolution
verified exact
arxiv_id, observed 2026-06-30T20:55:04.701940Z

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source=pdf_text observed=2026-06-30T20:46:17.090053Z digest=sha256:4e676451ae8a2f54747f0d4ac92d4887fd2c147754dd43f85e9e3281a085a889

Observation b6674857-d3f6-4333-8f06-3de5aeae1cfb · inbound

Hadronic exceptional points cites this paper.

Hadronic exceptional points Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field

Reference 155

Resolution
verified exact
arxiv_id, observed 2026-07-01T11:05:41.392836Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-07-01T04:48:30.563853Z digest=sha256:5b091f34f2821c684341dc64ba5997bc31827e0090219ed50120a10220cd2b9b