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Paper Citation Record · LEDGER

Modular Groups of Quantum Fields in Thermal States

As of 19 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 8 inbound Pith citation observations for arXiv:math-ph/9805013.

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

pith.paper-citation-record.v1
math-ph/9805013 v1

Coverage vector

measured 0 of 0 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links

measured 8 of 8 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 8 of 8 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-12T20:34:48.211647Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-10T03:29:22.137310Z

Reference resolution

0 of 0 outbound references displayed

  • verified exact0
  • verified fuzzy0
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  • malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

No outbound reference observations are available for this paper version.

Pith citing papers

Observation d5bac09e-7546-4f4d-9bf6-df90f7facbfa · inbound

Petz-R\'enyi relative entropy in QFT from modular theory cites this paper.

Petz-R\'enyi relative entropy in QFT from modular theory Modular Groups of Quantum Fields in Thermal States

Reference 44

Resolution
unresolved
no resolver link, observed 2026-08-12T20:34:48.211647Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-12T20:34:48.211647Z digest=sha256:71c31c2b2e94888b567d9ac1f59b0f9c198f71ffa49738d0fb0b3b2f8fc3e567

Observation fed3acc7-08c5-4b7e-9138-0dce6a9ea048 · inbound

Relating the modular Hamiltonian to two-point functions cites this paper.

Relating the modular Hamiltonian to two-point functions Modular Groups of Quantum Fields in Thermal States

Reference 27

Resolution
unresolved
no resolver link, observed 2026-08-10T20:00:38.278985Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T20:00:38.278985Z digest=sha256:8f331556c93769b9ed963a1446f2e01f5301f8ac3f26d65fe1e99742732e1734

Observation edb60260-13e8-404b-b9f5-51ea5f6795a6 · inbound

Modular evolutions and causality in two-dimensional conformal field theory cites this paper.

Modular evolutions and causality in two-dimensional conformal field theory Modular Groups of Quantum Fields in Thermal States

Reference 34

Resolution
unresolved
no resolver link, observed 2026-08-10T18:17:53.621689Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T18:17:53.621689Z digest=sha256:c211b52e79b228b0ca9d02d402eb585aeae454ee0ed48677c9b42b8198f27680

Observation 8a6779a2-f4a6-4c23-a903-3465c3344f11 · inbound

Geometric modular flows in 2d CFT and beyond cites this paper.

Geometric modular flows in 2d CFT and beyond Modular Groups of Quantum Fields in Thermal States

Reference 37

Resolution
unresolved
no resolver link, observed 2026-08-09T11:44:45.693786Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-09T11:44:45.693786Z digest=sha256:03128d122a29d6fa33c5e6a831e7d8e77ad2e238e87ee9fb5d87e264c885794e

Observation 5455c2b2-b2ac-4044-bba3-40a6aacc1da2 · inbound

The Crossed Product, Modular (Tomita) Dynamics and its Role in the Transition of Type $III$ to Type $II_{\infty}$ v.Neumann Algebras and Connections to Quantum Gravity cites this paper.

The Crossed Product, Modular (Tomita) Dynamics and its Role in the Transition of Type $III$ to Type $II_{\infty}$ v.Neumann Algebras and Connections to Quantum Gravity Modular Groups of Quantum Fields in Thermal States

Reference 51

Resolution
unresolved
no resolver link, observed 2026-08-06T21:00:00.479971Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T21:00:00.479971Z digest=sha256:1016422bc245fc0797e9dfd8bbc95d6528a5343b3eb82fd849b07dd54863ad8b

Observation a753747d-ba4b-4514-a43e-5d7dbd02f833 · inbound

Modular Theory and the Bell-CHSH inequality in relativistic scalar Quantum Field Theory cites this paper.

Modular Theory and the Bell-CHSH inequality in relativistic scalar Quantum Field Theory Modular Groups of Quantum Fields in Thermal States

Reference 34

Resolution
unresolved
no resolver link, observed 2026-07-13T17:57:04.944386Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-07-13T17:57:04.944386Z digest=sha256:961fc364921dd18b57641ccfe62b56e5c1b614879d2d6e270058423f2e69889a

Observation 817e74b5-e499-4163-8222-6801d80aaace · inbound

Bounding relative entropy for non-unitary excitations in quantum field theory cites this paper.

Bounding relative entropy for non-unitary excitations in quantum field theory Modular Groups of Quantum Fields in Thermal States

Reference 72

Resolution
verified exact
arxiv_id, observed 2026-07-04T16:10:07.962558Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-05-10T03:25:21.603571Z digest=sha256:9bbfc484ae487f9794063f730ec06c80b2548cd60ebec9f550d782184ea67323

Observation 716e72cd-0c29-4992-acff-b1467b04e4ab · inbound

Uniqueness of null-local modular flow cites this paper.

Uniqueness of null-local modular flow Modular Groups of Quantum Fields in Thermal States

Reference 61

Resolution
unresolved
no resolver link, observed 2026-08-01T09:52:42.547475Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-01T09:52:42.547475Z digest=sha256:6b6dfe48928c3d0c99ef19d77e5ee976d7cb7d857cb6133af02657d9b0ccc84b