Paper Citation Record · LEDGER

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues

As of 12 August 2026, this Paper Citation Record lists 46 of 46 outbound references and 1 inbound Pith citation observation for arXiv:2412.19709.

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pith.paper-citation-record.v1
2412.19709 v2

Coverage vector

measured 46 of 46 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-11T00:07:44.939545Z

measured 47 of 47 standing notices

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measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-26T07:49:37.004093Z

measured 0 of 1 external citation measurements

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Source: arxiv_reference, observed 2026-07-04T11:39:47.026831Z

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46 of 46 outbound references displayed

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Outbound references

Observation 39b7d586-2619-434d-b22a-cde745b046c6 · outbound

This paper cites Über das Verhalten eines Elektrons im homo- genen elektrischen Feld nach der relativistischen Theorie Diracs,.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Über das Verhalten eines Elektrons im homo- genen elektrischen Feld nach der relativistischen Theorie Diracs,

Reference 1

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Observation 04095367-9139-4dc3-848f-5744b31d12ae · outbound

This paper cites quadratic-approximation.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues quadratic-approximation

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:08:15.894284Z

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Observation 63e72db7-9bd6-43dd-92e5-3bef7463b57b · outbound

This paper cites creation happens.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues creation happens

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:08:15.910635Z

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Observation 04ad68bd-3e7b-4959-8512-e64a9904fbff · outbound

This paper cites grid” lines are obtained by computing instantons at each point on a10 × 10 grid over the rectangle0 < P <1 and −1 < ∆ < 1. The “quadratic.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues grid” lines are obtained by computing instantons at each point on a10 × 10 grid over the rectangle0 < P <1 and −1 < ∆ < 1. The “quadratic

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:08:15.878008Z

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Observation d5f473c2-df76-4319-a403-0bba9355cc4b · outbound

This paper cites On gauge invariance and vacuum po- larization,.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues On gauge invariance and vacuum po- larization,

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-11T00:07:44.731152Z

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Observation 8e2a505e-bb11-4bf2-a403-8829c0fa246c · outbound

This paper cites Pairproductioninvacuumby an alternating field,.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Pairproductioninvacuumby an alternating field,

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:08:15.840559Z

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Observation 779d1164-bdc6-4e22-a608-9df5e2a5c012 · outbound

This paper cites Pair Production in a Variable and Homo- geneous Electric Field as an Oscillator Problem.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Pair Production in a Variable and Homo- geneous Electric Field as an Oscillator Problem

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:08:15.823744Z

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Observation 69ef93ed-9a0f-4e55-9f92-09c421bcb02e · outbound

This paper cites Imaginary-time method in quantum me- chanics and field theory,.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Imaginary-time method in quantum me- chanics and field theory,

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:08:15.805839Z

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Observation 76632e5e-463c-460a-8dd4-e40f11d295d3 · outbound

This paper cites Schwinger Pair Production via Instantons in Strong Electric Fields.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Schwinger Pair Production via Instantons in Strong Electric Fields

Reference 9

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Observation f92b8e66-a583-47c1-b9ec-1da22e36f4ed · outbound

This paper cites Improved Approximations for Fermion Pair Production in Inhomogeneous Electric Fields,.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Improved Approximations for Fermion Pair Production in Inhomogeneous Electric Fields,

Reference 10

Resolution: verified exact; raw_fallback, observed 2026-08-11T00:08:15.609657Z

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Observation 933389f3-a63d-4f8e-9564-b3194732bb37 · outbound

This paper cites The Stokes Phenomenon and Schwinger Vacuum Pair Production in Time-Dependent Laser Pulses.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues The Stokes Phenomenon and Schwinger Vacuum Pair Production in Time-Dependent Laser Pulses

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-11T00:07:44.760205Z

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Observation 227549b6-d4bf-42cc-aa09-cc82eec92a7c · outbound

This paper cites Interference Effects in Schwinger Vacuum Pair Production for Time-Dependent Laser Pulses.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Interference Effects in Schwinger Vacuum Pair Production for Time-Dependent Laser Pulses

Reference 12

Resolution: verified exact; local_arxiv, observed 2026-08-11T00:08:00.491696Z

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Observation 1ebd3e23-b468-4b7a-931b-8b592640975b · outbound

This paper cites Semiclassical pair production rate for time-dependent electrical fields with more than one component: -WKB-approach and world-line instantons.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Semiclassical pair production rate for time-dependent electrical fields with more than one component: -WKB-approach and world-line instantons

Reference 13

Resolution: verified exact; local_arxiv, observed 2026-08-11T00:08:00.468591Z

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Observation 210f9557-8941-4cf0-bad5-e164efb892d3 · outbound

This paper cites Perturbative Quantum Field Theory in the String-Inspired Formalism.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Perturbative Quantum Field Theory in the String-Inspired Formalism

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-11T00:07:44.776534Z

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Observation 447272c9-f685-4aa3-9b52-4aee103b0c72 · outbound

This paper cites Quantum mechanical path integrals in the first quantised approach to quantum field theory,.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Quantum mechanical path integrals in the first quantised approach to quantum field theory,

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-11T00:07:44.781901Z

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Observation 797b4aab-d637-4bbf-a1c5-28d13dba86ff · outbound

This paper cites Pair Produc- tion at Strong Coupling in Weak External Fields,.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Pair Produc- tion at Strong Coupling in Weak External Fields,

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-11T00:07:44.786530Z

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Observation 0d257020-ea68-4230-aa50-70a50bd7ce78 · outbound

This paper cites Worldline Instantons and Pair Production in Inhomogeneous Fields.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Worldline Instantons and Pair Production in Inhomogeneous Fields

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-11T00:07:44.791086Z

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Observation e8fe80a1-f4c6-4f9d-b8db-785060e796b0 · outbound

This paper cites Worldline Instantons II: The Fluctuation Prefactor.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Worldline Instantons II: The Fluctuation Prefactor

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-11T00:07:44.796292Z

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Observation 91291e8b-9769-4686-b385-11f8f1c52b59 · outbound

This paper cites Complex Worldline Instantons and Quantum Interference in Vacuum Pair Production.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Complex Worldline Instantons and Quantum Interference in Vacuum Pair Production

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-11T00:07:44.801400Z

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Observation 1c15acf5-0535-4309-bdb3-273e697afd84 · outbound

This paper cites Electron- Positron Pair Production in an Elliptic Polarized Time Varying Field.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Electron- Positron Pair Production in an Elliptic Polarized Time Varying Field

Reference 20

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Observation dc967299-a0ae-453b-a1d6-935c288823f4 · outbound

This paper cites Nonperturbative pair production in interpolating fields.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Nonperturbative pair production in interpolating fields

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-11T00:07:44.811061Z

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Observation 8e297460-41b5-4999-a91a-f0d4f5a5d385 · outbound

This paper cites Sauter-Schwinger effect for colliding laser pulses.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Sauter-Schwinger effect for colliding laser pulses

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-11T00:07:44.816782Z

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Observation 69106a73-5232-4ae4-9a68-69b9be0ec3b6 · outbound

This paper cites Multidimensional Worldline Instantons.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Multidimensional Worldline Instantons

Reference 23

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Observation f505b5d4-d2c7-4357-844a-f9d29ad7db61 · outbound

This paper cites Discrete worldline instantons.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Discrete worldline instantons

Reference 24

Resolution: verified exact; local_arxiv, observed 2026-08-11T00:07:45.248834Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation bd1f3d54-596c-4aff-80c2-816d63f6b455 · outbound

This paper cites Thermal Schwinger pair production at arbitrary coupling.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Thermal Schwinger pair production at arbitrary coupling

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-11T00:07:44.830839Z

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Observation 5d8cf444-6682-4bbf-b083-9bb29b738d5e · outbound

This paper cites Worldline instantons for nonlinear Breit-Wheeler pair production and Compton scattering.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Worldline instantons for nonlinear Breit-Wheeler pair production and Compton scattering

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-11T00:07:44.835245Z

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Observation ee84f6ea-cdb7-4ed0-9ae8-a889e4b2fd32 · outbound

This paper cites Worldline instantons for the momentum spectrum of Schwinger pair production in space-time dependent fields.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Worldline instantons for the momentum spectrum of Schwinger pair production in space-time dependent fields

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-11T00:07:44.840014Z

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Observation 8228173f-33ef-4c1e-94b6-9f3bb08eaa15 · outbound

This paper cites Momentum spectrum of Schwinger pair production in four-dimensional e-dipole fields.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Momentum spectrum of Schwinger pair production in four-dimensional e-dipole fields

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-11T00:07:44.844478Z

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Observation b1f2d615-5e18-4a0d-8ee8-613918db66a5 · outbound

This paper cites Momentum signatures for Schwinger pair production in short laser pulses with a sub-cycle structure.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Momentum signatures for Schwinger pair production in short laser pulses with a sub-cycle structure

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-11T00:07:44.849300Z

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Observation c7dd1b23-6361-4ee9-821d-682ed6c28a1d · outbound

This paper cites Schwinger Vacuum Pair Production in Chirped Laser Pulses.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Schwinger Vacuum Pair Production in Chirped Laser Pulses

Reference 30

Resolution: verified exact; local_arxiv, observed 2026-08-11T00:07:45.140500Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 734cbb9e-b372-400e-ba3b-cf654566dce1 · outbound

This paper cites Ramsey Fringes and Time-domain Multiple-Slit Interference from Vacuum.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Ramsey Fringes and Time-domain Multiple-Slit Interference from Vacuum

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-11T00:07:44.859490Z

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Observation c9319db0-6ea5-42b8-9d20-d9379b59e56c · outbound

This paper cites Particle self-bunching in the Schwinger effect in spacetime-dependent electric fields.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Particle self-bunching in the Schwinger effect in spacetime-dependent electric fields

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-11T00:07:44.864597Z

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Observation 9ed3b744-0069-4cf7-8562-8151d1a3d816 · outbound

This paper cites Electron-positron pair production in inhomogeneous electromagnetic fields.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Electron-positron pair production in inhomogeneous electromagnetic fields

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-11T00:07:44.869721Z

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Observation 967ca013-0b21-42b5-90d7-294d4af1c45e · outbound

This paper cites Effects of finite spatial extent on Schwinger pair production.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Effects of finite spatial extent on Schwinger pair production

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-11T00:07:44.875631Z

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Observation 18c4ac5c-301a-4e9f-8087-bdb78a956e7f · outbound

This paper cites Pair production in temporally and spatially oscillating fields.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Pair production in temporally and spatially oscillating fields

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-11T00:07:44.881280Z

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Observation 15115900-573f-4d17-8019-9c518f42462d · outbound

This paper cites Quantum field theory.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Quantum field theory

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:08:15.762120Z

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Observation 0fd1426b-7e35-49bf-9503-24375894d331 · outbound

This paper cites Pair Production In An Electric Field In A Time Dependent Gauge,.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Pair Production In An Electric Field In A Time Dependent Gauge,

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:08:15.746252Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 4394789f-e22e-4794-92b3-5043169d263e · outbound

This paper cites Momentum spectrum of nonlinear Breit-Wheeler pair production in space-time fields.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Momentum spectrum of nonlinear Breit-Wheeler pair production in space-time fields

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-11T00:07:44.897217Z

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Observation 31d05c96-58c7-4c99-9b72-37a508a0b19e · outbound

This paper cites Significance of electromag- netic potentials in the quantum theory,.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Significance of electromag- netic potentials in the quantum theory,

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:08:15.728953Z

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Observation 95953986-caf7-49c8-ac43-a34d49a3cafb · outbound

This paper cites The Refractive Index in Electron Optics and the Principles of Dynamics.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues The Refractive Index in Electron Optics and the Principles of Dynamics

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:08:15.710712Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 870246c1-421a-4734-a37d-505a920038af · outbound

This paper cites Coherent quantum enhancement of pair production in the null domain.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Coherent quantum enhancement of pair production in the null domain

Reference 41

Resolution: verified exact; local_arxiv, observed 2026-08-11T00:07:45.006965Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 9ae00cd9-8027-41c3-ada0-22e2b861b812 · outbound

This paper cites A Primer on Resurgent Transseries and Their Asymptotics.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues A Primer on Resurgent Transseries and Their Asymptotics

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-11T00:07:44.919093Z

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Observation 925e8057-66e1-45b4-ba24-1f7cc6529337 · outbound

This paper cites Methods of mathematical physics.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Methods of mathematical physics

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:08:15.693331Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 1a137764-390f-4941-ace1-315ebd539c56 · outbound

This paper cites Large Eigenvalues and Trace Formulas for Matrix Sturm-Liouville Problems.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues Large Eigenvalues and Trace Formulas for Matrix Sturm-Liouville Problems

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:08:15.676844Z

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Observation 8cc32710-54d7-48b3-a93a-cdf10b9a0cca · outbound

This paper cites The Calculus of Variations In the Large.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues The Calculus of Variations In the Large

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:08:15.661554Z

Source-reported events for the cited work

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Observation 23559b90-0dfb-4189-8856-33ae5f178850 · outbound

This paper cites A New Approach to Gaussian Path Integrals and the Evaluation of the Semiclassical Propagator,.

Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues A New Approach to Gaussian Path Integrals and the Evaluation of the Semiclassical Propagator,

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:08:15.644450Z

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Pith citing papers

Observation e06d30fa-d6c7-4c92-97ae-2a5efeb52fa7 · inbound

Scattered wave functions and worldline instantons for particle production in curved spacetime cites this paper.

Scattered wave functions and worldline instantons for particle production in curved spacetime Schwinger pair production in spacetime fields: Moir\'e patterns, Aharonov-Bohm phases and Sturm-Liouville eigenvalues

Reference 43

Resolution: verified exact; arxiv_id, observed 2026-07-04T11:39:47.029322Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.