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Paper Citation Record · LEDGER

Uniqueness of null-local modular flow

As of 21 August 2026, this Paper Citation Record lists 100 of 105 outbound references and 0 inbound Pith citation observations for arXiv:2607.20678.

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

pith.paper-citation-record.v1
2607.20678 v1

Coverage vector

measured 100 of 105 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-01T09:52:46.569651Z

measured 100 of 100 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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Reference resolution

100 of 105 outbound references displayed

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Outbound references

Observation 1ef63daa-f411-4a04-9c24-881217a6530f · outbound

This paper cites Notes on Some Entanglement Properties of Quantum Field Theory.

Uniqueness of null-local modular flow Notes on Some Entanglement Properties of Quantum Field Theory

Reference 1

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source=pdf_text observed=2026-08-01T09:52:38.171907Z digest=sha256:5556074f5da1b616aec31f4abf1326f0bcf21a7df3d271433424ef355adedf34

Observation b014c6e4-5360-4a94-af31-35340d6e7263 · outbound

This paper cites An intuitive construction of modular flow.

Uniqueness of null-local modular flow An intuitive construction of modular flow

Reference 2

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source=pdf_text observed=2026-08-01T09:52:38.224782Z digest=sha256:b1295833aa90d247e7ed9a07812d92e8a7c478607e7876b17fb4357a2ebf2754

Observation 101dbca3-c4f9-49b5-9bed-267021886855 · outbound

This paper cites Relative entropy and the Bekenstein bound.

Uniqueness of null-local modular flow Relative entropy and the Bekenstein bound

Reference 3

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source=pdf_text observed=2026-08-01T09:52:38.312174Z digest=sha256:caaaf4eee08bb9d050d6fa22695718ebf77775f1d3818f8a76d9e3420f69bf4e

Observation 46f9c4ef-087a-498f-a489-3aa0f88cccd1 · outbound

This paper cites Proof of a Quantum Bousso Bound.

Uniqueness of null-local modular flow Proof of a Quantum Bousso Bound

Reference 4

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Observation 16a6641a-4c6c-4ee3-8155-a27083be4a93 · outbound

This paper cites Entropy on a null surface for interacting quantum field theories and the Bousso bound.

Uniqueness of null-local modular flow Entropy on a null surface for interacting quantum field theories and the Bousso bound

Reference 5

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source=pdf_text observed=2026-08-01T09:52:38.482914Z digest=sha256:aa6a9607d0520bf54aed0bddb2467e31e4793dc75f38e2a8ed60a6f062e754fc

Observation e733b130-d138-4b9a-864d-c1ca67d2ae1e · outbound

This paper cites Entanglement hamiltonians in two-dimensional conformal field theory.

Uniqueness of null-local modular flow Entanglement hamiltonians in two-dimensional conformal field theory

Reference 6

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source=pdf_text observed=2026-08-01T09:52:38.539633Z digest=sha256:08d0b0ffcc941c342b7acadd5175470f920538db16c6d1827ef73b2d1538e5b0

Observation 25462b9e-ec1f-43e3-aebc-390f7e439489 · outbound

This paper cites Entanglement measures and their properties in quantum field theory.

Uniqueness of null-local modular flow Entanglement measures and their properties in quantum field theory

Reference 7

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source=pdf_text observed=2026-08-01T09:52:38.652621Z digest=sha256:abe70b8637f2878c713ec575b3dcd6a75cba0aedf785c4ac1b561ff8e4c9dafc

Observation 757ed1d6-87f1-413e-bff8-2914724f9b9a · outbound

This paper cites Modular Hamiltonians on the null plane and the Markov property of the vacuum state.

Uniqueness of null-local modular flow Modular Hamiltonians on the null plane and the Markov property of the vacuum state

Reference 8

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Observation 5d8c6bd0-f2ae-41bc-b997-5fbfa15681b5 · outbound

This paper cites Markov property of the CFT vacuum and the a-theorem.

Uniqueness of null-local modular flow Markov property of the CFT vacuum and the a-theorem

Reference 9

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source=pdf_text observed=2026-08-01T09:52:38.827282Z digest=sha256:6d611e886fd4b2438efd448d97921fa3d2a1f47d5ab16c77b67f437bff83d673

Observation a6ee0716-03a8-4508-bdc0-160b3022b93c · outbound

This paper cites Constraining Quantum Fields using Modular Theory.

Uniqueness of null-local modular flow Constraining Quantum Fields using Modular Theory

Reference 10

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source=pdf_text observed=2026-08-01T09:52:38.923471Z digest=sha256:54c9fd6f1a21a3d9e63301802cc0fa35c8787e9f79d6b4ae640929265af426e2

Observation d2fcd84a-9eb4-4d73-8878-ce3749ac906e · outbound

This paper cites Modular zero modes and sewing the states of QFT.

Uniqueness of null-local modular flow Modular zero modes and sewing the states of QFT

Reference 11

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source=pdf_text observed=2026-08-01T09:52:38.966904Z digest=sha256:7bf5d64ad111651f060f6bbebb6ae1e74b8aabdc09db8f211d353c7cc69448ed

Observation 11a0b658-2576-4deb-acdc-1ca954d887a3 · outbound

This paper cites Information loss, mixing and emergent type III$_1$ factors.

Uniqueness of null-local modular flow Information loss, mixing and emergent type III$_1$ factors

Reference 12

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source=pdf_text observed=2026-08-01T09:52:39.054520Z digest=sha256:cdc70d8d7e2ae00c3b5038de20f7602f085959fadbe1252f51a3b4f1f6621081

Observation fea3280a-a9e6-4984-ac48-700c28f27fd5 · outbound

This paper cites van Luijk, A.

Uniqueness of null-local modular flow van Luijk, A

Reference 13

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source=pdf_text observed=2026-08-01T09:52:39.141690Z digest=sha256:fff73e826a541d51eb3c7ebcd71eccc871eebcbcc7de48c862fb835ba5aefff0

Observation 21894ea7-a473-4883-83f3-44216ccb5adf · outbound

This paper cites Modular Hamiltonians for Deformed Half-Spaces and the Averaged Null Energy Condition.

Uniqueness of null-local modular flow Modular Hamiltonians for Deformed Half-Spaces and the Averaged Null Energy Condition

Reference 14

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source=pdf_text observed=2026-08-01T09:52:39.224160Z digest=sha256:39627e1c9e626141c1a2c379c42042005c54c007fc15b6d5826d75a3f1c0900a

Observation 08e7a2ef-889a-420a-b3d5-9bcc3b4475c9 · outbound

This paper cites A General Proof of the Quantum Null Energy Condition.

Uniqueness of null-local modular flow A General Proof of the Quantum Null Energy Condition

Reference 15

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source=pdf_text observed=2026-08-01T09:52:39.295314Z digest=sha256:89ebf36c2a402a5f0da0e65f435af7352a4c604d57ec9549945bf01539b107a1

Observation ee57ba58-eef8-4339-8742-53495973ec64 · outbound

This paper cites Recovering the QNEC from the ANEC.

Uniqueness of null-local modular flow Recovering the QNEC from the ANEC

Reference 16

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source=pdf_text observed=2026-08-01T09:52:39.390412Z digest=sha256:82cdb33cf06b153d9a0c864fc01138f734fe5548cb0e922162a678cc7d296e08

Observation e4911996-761a-43f6-a112-226e8d3e1b29 · outbound

This paper cites Hollands and R.

Uniqueness of null-local modular flow Hollands and R

Reference 17

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Observation ee08bb95-f730-4950-8acf-cc016be7a02e · outbound

This paper cites Relative entropy equals bulk relative entropy.

Uniqueness of null-local modular flow Relative entropy equals bulk relative entropy

Reference 18

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source=pdf_text observed=2026-08-01T09:52:39.557940Z digest=sha256:69e8cd7bcd5c3e045e02086232039dba1a584727dbabfb184db463909de79dff

Observation 87eecf5a-d427-4c8c-b4e3-986a8bfc0bf9 · outbound

This paper cites Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality.

Uniqueness of null-local modular flow Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality

Reference 19

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Observation 1056d772-b886-4ef0-8243-aa89c5f3ef29 · outbound

This paper cites Bulk locality from modular flow.

Uniqueness of null-local modular flow Bulk locality from modular flow

Reference 20

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Observation e372b414-b747-4e23-b248-e54aace6c05e · outbound

This paper cites A modular toolkit for bulk reconstruction.

Uniqueness of null-local modular flow A modular toolkit for bulk reconstruction

Reference 21

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Observation db1d46f7-3810-4027-b9b2-8b8b0a8e55f8 · outbound

This paper cites Comments on black hole interiors and modular inclusions.

Uniqueness of null-local modular flow Comments on black hole interiors and modular inclusions

Reference 22

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Observation 3503206e-9858-4e41-8a12-1a123b356692 · outbound

This paper cites Pulling Out the Island with Modular Flow.

Uniqueness of null-local modular flow Pulling Out the Island with Modular Flow

Reference 23

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source=pdf_text observed=2026-08-01T09:52:39.899990Z digest=sha256:c1006ca4c9f2c9ce6dde25bbe7feb1018ec7995547a74235645e8fe08fae7f80

Observation 1b214867-54e9-4f12-987c-db15a1708558 · outbound

This paper cites The holographic map as a conditional expectation.

Uniqueness of null-local modular flow The holographic map as a conditional expectation

Reference 24

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Observation 0417f97b-9a8d-4781-a740-b2cf1f0397c5 · outbound

This paper cites Inside the Hologram: Reconstructing the bulk observer's experience.

Uniqueness of null-local modular flow Inside the Hologram: Reconstructing the bulk observer's experience

Reference 25

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Observation 17aa85f6-5d30-46ca-b1d4-009b017090cf · outbound

This paper cites Seeing the Entanglement Wedge.

Uniqueness of null-local modular flow Seeing the Entanglement Wedge

Reference 26

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Observation 76e3758b-deac-4ccb-85b4-b5375106601d · outbound

This paper cites Causal connectability between quantum systems and the black hole interior in holographic duality.

Uniqueness of null-local modular flow Causal connectability between quantum systems and the black hole interior in holographic duality

Reference 27

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Observation d050e16d-e700-4230-a84c-c22f2c5ee88f · outbound

This paper cites Seeing behind black hole horizons in SYK.

Uniqueness of null-local modular flow Seeing behind black hole horizons in SYK

Reference 28

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Observation 5aa95501-09f6-448c-8c14-c91573d392fa · outbound

This paper cites Emergent times in holographic duality.

Uniqueness of null-local modular flow Emergent times in holographic duality

Reference 29

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source=pdf_text observed=2026-08-01T09:52:40.349306Z digest=sha256:cb7ea10829ab9f72b845ed76ab67ce72135f1b9a4a50b8c6652cabd201e90838

Observation 1762ee58-6a26-415b-bd93-728b874e7643 · outbound

This paper cites On black hole interior reconstruction, singularities and the emergence of time.

Uniqueness of null-local modular flow On black hole interior reconstruction, singularities and the emergence of time

Reference 30

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source=pdf_text observed=2026-08-01T09:52:40.438404Z digest=sha256:e0e86d4c28ffbef4cc71aa4b9ad63f54eb35443df0db61da55a6cb5e18e8385f

Observation 0764e10d-b6d4-4406-8bd0-0528f954823d · outbound

This paper cites Subregion-subalgebra duality: emergence of space and time in holography.

Uniqueness of null-local modular flow Subregion-subalgebra duality: emergence of space and time in holography

Reference 31

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source=pdf_text observed=2026-08-01T09:52:40.523909Z digest=sha256:b3d68eff7112d1a4498ba822b2f4c4c6184909a6615e61a789fd499571343dbc

Observation 7cdebbab-4ea8-4843-8dc8-57c773d284d8 · outbound

This paper cites Algebraic ER=EPR and Complexity Transfer.

Uniqueness of null-local modular flow Algebraic ER=EPR and Complexity Transfer

Reference 32

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Observation 19b04ad0-516d-40e3-8783-eff3120c5c4d · outbound

This paper cites Modular flow in JT gravity and entanglement wedge reconstruction.

Uniqueness of null-local modular flow Modular flow in JT gravity and entanglement wedge reconstruction

Reference 33

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source=pdf_text observed=2026-08-01T09:52:40.663825Z digest=sha256:a8b722cfd221d005a6b66e6147394477900893ed62393c0195b8a5e0b7722f90

Observation f541db9e-e72d-4112-ba3c-06526695ac61 · outbound

This paper cites Relational bulk reconstruction from modular flow.

Uniqueness of null-local modular flow Relational bulk reconstruction from modular flow

Reference 34

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source=pdf_text observed=2026-08-01T09:52:40.758366Z digest=sha256:d2be06b1c4632db5668a50ce3c7ea69a653daaab58b1ea4de7fc833291d0e507

Observation 37f8ebbe-8a43-48a6-b3a9-9f8ce473e559 · outbound

This paper cites Toward stringy horizons.

Uniqueness of null-local modular flow Toward stringy horizons

Reference 35

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source=pdf_text observed=2026-08-01T09:52:40.849942Z digest=sha256:ddd32358bfe3392a95ab3ecfc2824d609c538b18df9d7b2d45c1a4c0ca8cd4cf

Observation 7fa17588-fdaa-495b-bcd1-a1295e6d2bc6 · outbound

This paper cites Gravity and the Crossed Product.

Uniqueness of null-local modular flow Gravity and the Crossed Product

Reference 36

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source=pdf_text observed=2026-08-01T09:52:40.909675Z digest=sha256:a5b22260dbae8039a72386277bbe4a8315ad7f77dcdf8e0585fc11d731d1c93d

Observation 1aa39e6d-982e-470a-a364-27e3058883c8 · outbound

This paper cites An Algebra of Observables for de Sitter Space.

Uniqueness of null-local modular flow An Algebra of Observables for de Sitter Space

Reference 37

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source=pdf_text observed=2026-08-01T09:52:40.987847Z digest=sha256:56305fe1dcc06176b8f638bc2a33d981bce6274ea9138a8720dd41ea47073658

Observation 062951bb-09f3-4435-9635-5d756a498d4a · outbound

This paper cites Large N algebras and generalized entropy.

Uniqueness of null-local modular flow Large N algebras and generalized entropy

Reference 38

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source=pdf_text observed=2026-08-01T09:52:41.072113Z digest=sha256:4edb91c19edb0954bb5c9bc8da8930ae8305b5c9d4b701d63697f561064c2cf6

Observation 7ae98d7c-ea2a-4315-a33d-67cc3938a1e2 · outbound

This paper cites Algebras and States in JT Gravity.

Uniqueness of null-local modular flow Algebras and States in JT Gravity

Reference 39

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source=pdf_text observed=2026-08-01T09:52:41.124669Z digest=sha256:147315e2ef2a568a96b7a4ff81c5f78379fec4e059af07375bf0e49933ba77c5

Observation a0b1056f-b5b0-4294-9f90-bef60de33c16 · outbound

This paper cites Sorce,Notes on the type classification of von Neumann algebras,Rev.

Uniqueness of null-local modular flow Sorce,Notes on the type classification of von Neumann algebras,Rev

Reference 40

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source=pdf_text observed=2026-08-01T09:52:41.175294Z digest=sha256:881531e670989195c14811396aeedfa1f3876d8d1f0de560de13756c22f73ee1

Observation 4fef2655-102f-4862-bce9-031442bc3b6e · outbound

This paper cites von Neumann algebras in JT gravity.

Uniqueness of null-local modular flow von Neumann algebras in JT gravity

Reference 41

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source=pdf_text observed=2026-08-01T09:52:41.263494Z digest=sha256:a9e766fa7a8dbf9f103b9cfe19855338020b35ecb63dfc6c281459efe6737125

Observation 786bf17a-0a27-44fa-b6c0-3208721c64a7 · outbound

This paper cites Generalized entropy for general subregions in quantum gravity.

Uniqueness of null-local modular flow Generalized entropy for general subregions in quantum gravity

Reference 42

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source=pdf_text observed=2026-08-01T09:52:41.339499Z digest=sha256:96ff2031259685d0abda5843bca46346353445bc673c5ca01082ba6896d1608c

Observation b482ee0b-8110-47a9-8737-e9f38a5f53a4 · outbound

This paper cites Crossed product algebras and generalized entropy for subregions.

Uniqueness of null-local modular flow Crossed product algebras and generalized entropy for subregions

Reference 43

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no resolver link, observed 2026-08-01T09:52:41.378647Z

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source=pdf_text observed=2026-08-01T09:52:41.378647Z digest=sha256:0f9bf923326df7704ac16db1d06e0a983fc41367ad563fad923402fe49d0bb6d

Observation 432f874d-3839-4169-a5fd-c66c46c583e9 · outbound

This paper cites Generalized Black Hole Entropy is von Neumann Entropy.

Uniqueness of null-local modular flow Generalized Black Hole Entropy is von Neumann Entropy

Reference 44

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source=pdf_text observed=2026-08-01T09:52:41.459217Z digest=sha256:dd736f1316f80d18db691ba678946ac0680fa10759ad8155a0cbb8a75a957e43

Observation 0ab14abd-26b3-4195-83fd-4861b86a366d · outbound

This paper cites A covariant regulator for entanglement entropy: proofs of the Bekenstein bound and QNEC.

Uniqueness of null-local modular flow A covariant regulator for entanglement entropy: proofs of the Bekenstein bound and QNEC

Reference 45

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no resolver link, observed 2026-08-01T09:52:41.540585Z

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source=pdf_text observed=2026-08-01T09:52:41.540585Z digest=sha256:c9f22c5fcf7c4da9391610b07dce2ef54937e269ab48b1e4fe4e701b5edd69cf

Observation 38b4a1a9-c8b1-4b75-9f94-bb0dcc807742 · outbound

This paper cites Relative state-counting for semiclassical black holes.

Uniqueness of null-local modular flow Relative state-counting for semiclassical black holes

Reference 46

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no resolver link, observed 2026-08-01T09:52:41.599201Z

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source=pdf_text observed=2026-08-01T09:52:41.599201Z digest=sha256:a74af491112720cf7371e0c316437025972db8b4f27be8a9c40e296828314fcb

Observation cf21f815-11da-41e8-95a8-3382cfda9fbc · outbound

This paper cites Gravitational algebras and the generalized second law.

Uniqueness of null-local modular flow Gravitational algebras and the generalized second law

Reference 47

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source=pdf_text observed=2026-08-01T09:52:41.666502Z digest=sha256:c2de35cd62c4db295c0d11517834656a2332a6451ba0bd8cc18d474b14d4f100

Observation 245858a0-3286-4943-ac1a-e36387d56c84 · outbound

This paper cites Algebraic Observational Cosmology.

Uniqueness of null-local modular flow Algebraic Observational Cosmology

Reference 48

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source=pdf_text observed=2026-08-01T09:52:41.733596Z digest=sha256:bd9082d4022ee75bc5da96f6e7715b928050f54fb64ca08986fed61e8084aff5

Observation 6cd79431-86ba-49a4-8ebb-667cec506ca6 · outbound

This paper cites A clock is just a way to tell the time: gravitational algebras in cosmological spacetimes.

Uniqueness of null-local modular flow A clock is just a way to tell the time: gravitational algebras in cosmological spacetimes

Reference 49

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no resolver link, observed 2026-08-01T09:52:41.802455Z

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source=pdf_text observed=2026-08-01T09:52:41.802455Z digest=sha256:dcf89eb7c1eb3ff21415a4eb063ee0d51416d713d1f40cd44a93e6510b984264

Observation d7f1ff7f-039d-474c-90ac-59b7e22c7678 · outbound

This paper cites Chaos and the Emergence of the Cosmological Horizon.

Uniqueness of null-local modular flow Chaos and the Emergence of the Cosmological Horizon

Reference 50

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no resolver link, observed 2026-08-01T09:52:41.853898Z

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source=pdf_text observed=2026-08-01T09:52:41.853898Z digest=sha256:fff6d9573966f49db7a7dc7aafd2025ce086f41eb04ddeeb319e9c03be0fd3a3

Observation c23a3119-6652-439f-bd80-14a8909f6327 · outbound

This paper cites Algebras and states in super-JT gravity.

Uniqueness of null-local modular flow Algebras and states in super-JT gravity

Reference 51

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no resolver link, observed 2026-08-01T09:52:41.905437Z

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source=pdf_text observed=2026-08-01T09:52:41.905437Z digest=sha256:f28be24c665ff50939893bea998969f9bd5e2f32a62b39f6326f28655902c3bf

Observation 3a7e5f57-34df-4b4e-b0e2-5030cecd0387 · outbound

This paper cites A classical model for semiclassical state-counting.

Uniqueness of null-local modular flow A classical model for semiclassical state-counting

Reference 52

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no resolver link, observed 2026-08-01T09:52:41.957249Z

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source=pdf_text observed=2026-08-01T09:52:41.957249Z digest=sha256:5539689b9eacaa10226c49a20d33e90b6439473a51b5bd3fabf0fc0c1475fe99

Observation b1605706-6369-4d49-a64a-67cadde06eab · outbound

This paper cites an unresolved cited work.

Uniqueness of null-local modular flow Unresolved cited work

Reference 53

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source=pdf_text observed=2026-08-01T09:52:42.008283Z digest=sha256:640e8529f6ea141d606e448014a44d59bc074d8080a31049891eb366db3acf52

Observation 6bbd6fb5-0a13-46e6-a8dd-de73c26501e1 · outbound

This paper cites an unresolved cited work.

Uniqueness of null-local modular flow Unresolved cited work

Reference 54

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source=pdf_text observed=2026-08-01T09:52:42.060721Z digest=sha256:4f39a89704ae345d278b3386b61e678538358bc25df1d323d7cd1f2de511ce09

Observation 16684604-5610-4ba8-8120-a345847d61b7 · outbound

This paper cites an unresolved cited work.

Uniqueness of null-local modular flow Unresolved cited work

Reference 55

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source=pdf_text observed=2026-08-01T09:52:42.120444Z digest=sha256:11d3922f782eccd348f6e70fe9763c5affe733e5e62222cec68e30615d086490

Observation c07d9ffe-3849-440b-9ab6-ef1c110c11f9 · outbound

This paper cites an unresolved cited work.

Uniqueness of null-local modular flow Unresolved cited work

Reference 56

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no resolver link, observed 2026-08-01T09:52:42.201285Z

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source=pdf_text observed=2026-08-01T09:52:42.201285Z digest=sha256:4c8c256d162cd6b9686f2b50a6fc6339c49c071362121839dcbfdb78d861d429

Observation fc7e1df5-2d6e-4ac9-a2eb-b3562bca265d · outbound

This paper cites A proof of the generalized second law for rapidly changing fields and arbitrary horizon slices.

Uniqueness of null-local modular flow A proof of the generalized second law for rapidly changing fields and arbitrary horizon slices

Reference 57

Resolution
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source=pdf_text observed=2026-08-01T09:52:42.265653Z digest=sha256:348536acbf975925c71237983cca11e0bc9981b93255d8c504d5c14a991d0ca2

Observation 4b6a7633-ed3e-42f1-8aef-49113bd07f2d · outbound

This paper cites an unresolved cited work.

Uniqueness of null-local modular flow Unresolved cited work

Reference 58

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no resolver link, observed 2026-08-01T09:52:42.324034Z

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source=pdf_text observed=2026-08-01T09:52:42.324034Z digest=sha256:0b95fbf905c85d824e735b900d4c5aeef3d7fb8af1c567f8d1237b38ebf6a3b1

Observation c3e0327d-8921-439d-8546-598c2de66c2b · outbound

This paper cites Towards a derivation of holographic entanglement entropy.

Uniqueness of null-local modular flow Towards a derivation of holographic entanglement entropy

Reference 59

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no resolver link, observed 2026-08-01T09:52:42.399204Z

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source=pdf_text observed=2026-08-01T09:52:42.399204Z digest=sha256:e39472662bc602a3df36f167c3dc3d355aa3678b21d48953834157cbe81f2236

Observation 8628d482-c752-4331-809e-43af469bd5aa · outbound

This paper cites Modular Hamiltonian for de Sitter diamonds.

Uniqueness of null-local modular flow Modular Hamiltonian for de Sitter diamonds

Reference 60

Resolution
unresolved
no resolver link, observed 2026-08-01T09:52:42.465490Z

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source=pdf_text observed=2026-08-01T09:52:42.465490Z digest=sha256:180c0cc7ad433c255cbc2752c8be11761061d4f08b43029e8c30dd1847ddf367

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

This paper cites Modular Groups of Quantum Fields in Thermal States.

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

Reference 61

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

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

Observation 5ca10439-922b-4c78-9bd4-f71e8708168b · outbound

This paper cites Entanglement Temperature and Entanglement Entropy of Excited States.

Uniqueness of null-local modular flow Entanglement Temperature and Entanglement Entropy of Excited States

Reference 62

Resolution
unresolved
no resolver link, observed 2026-08-01T09:52:42.597851Z

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Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-01T09:52:42.597851Z digest=sha256:f2e5577006312fab15ee64581acdda644ffce30fcf709c05a6b00741c49df716

Observation 0cf1a715-37e2-4ed8-a31c-e3137b57b855 · outbound

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

Uniqueness of null-local modular flow Geometric modular flows in 2d CFT and beyond

Reference 63

Resolution
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no resolver link, observed 2026-08-01T09:52:42.687954Z

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source=pdf_text observed=2026-08-01T09:52:42.687954Z digest=sha256:03bd5ab25c4b84cdbf99e2e203c27dfdc3bf0f1ce00f90e0d257f2c42a1efae5

Observation 3bf0533a-35c2-4a35-93ae-37be0d8217f2 · outbound

This paper cites Reduced density matrix and internal dynamics for multicomponent regions.

Uniqueness of null-local modular flow Reduced density matrix and internal dynamics for multicomponent regions

Reference 64

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no resolver link, observed 2026-08-01T09:52:42.761749Z

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source=pdf_text observed=2026-08-01T09:52:42.761749Z digest=sha256:a967054e5560b964c0df4985ea863856bed7f65f146c92925f4054d599c36518

Observation 3996a553-531f-489b-bad9-a4d21d48c3d1 · outbound

This paper cites Geometric modular action for disjoint intervals and boundary conformal field theory.

Uniqueness of null-local modular flow Geometric modular action for disjoint intervals and boundary conformal field theory

Reference 65

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no resolver link, observed 2026-08-01T09:52:42.864059Z

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source=pdf_text observed=2026-08-01T09:52:42.864059Z digest=sha256:2b48d4b7b56e45e744db7adb0807b492102db155b75d657cc8716d9ef4f6460a

Observation c5fd96e0-5437-42ff-94e1-b4a2a722f53a · outbound

This paper cites Entanglement Hamiltonians for chiral fermions with zero modes.

Uniqueness of null-local modular flow Entanglement Hamiltonians for chiral fermions with zero modes

Reference 66

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no resolver link, observed 2026-08-01T09:52:42.935431Z

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source=pdf_text observed=2026-08-01T09:52:42.935431Z digest=sha256:80f4e618365ee04b822ffa78d7095ec3d1f24c10b462a625a7affe38f054012c

Observation 61af7fc6-4819-4715-8b09-583c26f7ee14 · outbound

This paper cites On the modular operator of mutli-component regions in chiral CFT.

Uniqueness of null-local modular flow On the modular operator of mutli-component regions in chiral CFT

Reference 67

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no resolver link, observed 2026-08-01T09:52:43.033708Z

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source=pdf_text observed=2026-08-01T09:52:43.033708Z digest=sha256:120281db35dc47d05de314877cdc463f7bb829ff75d3e5a2fc3719d914560d07

Observation a3d6ab2c-6786-4b3d-a0a5-04a5d9975ba2 · outbound

This paper cites Modular Hamiltonian of a chiral fermion on the torus.

Uniqueness of null-local modular flow Modular Hamiltonian of a chiral fermion on the torus

Reference 68

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no resolver link, observed 2026-08-01T09:52:43.137786Z

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source=pdf_text observed=2026-08-01T09:52:43.137786Z digest=sha256:f95e22c12be3a7f8838970c44238fa8ac75592c47d659b70a03ed1b44a309372

Observation cab0f3f7-970e-4ec2-ba5c-b64ae10e5acb · outbound

This paper cites The entanglement spectrum of chiral fermions on the torus.

Uniqueness of null-local modular flow The entanglement spectrum of chiral fermions on the torus

Reference 69

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no resolver link, observed 2026-08-01T09:52:43.243719Z

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source=pdf_text observed=2026-08-01T09:52:43.243719Z digest=sha256:47cbfeba4cf9a507d5b2870b088227e0f99bb62d57d026153cb113f09dc6e1e8

Observation 5f11034e-e52a-4f7c-a222-d0d6459474fe · outbound

This paper cites Resolving modular flow: a toolkit for free fermions.

Uniqueness of null-local modular flow Resolving modular flow: a toolkit for free fermions

Reference 70

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no resolver link, observed 2026-08-01T09:52:43.381717Z

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source=pdf_text observed=2026-08-01T09:52:43.381717Z digest=sha256:56e77dbd0ff1d356f16d71b1eda8751b25d3905c20058023f80bd0663eb15daa

Observation a3dc4812-72bd-42c4-8459-0f4020b862b9 · outbound

This paper cites Modular Hamiltonian and modular flow of massless fermions on a cylinder.

Uniqueness of null-local modular flow Modular Hamiltonian and modular flow of massless fermions on a cylinder

Reference 71

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no resolver link, observed 2026-08-01T09:52:43.478555Z

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source=pdf_text observed=2026-08-01T09:52:43.478555Z digest=sha256:a0a8190195c7bf831848944fd029eed30fe2ac39635ee0ca2adc3801b26fbc79

Observation 7c6a6e82-9fbc-439b-9ff9-196b9a3400a9 · outbound

This paper cites Keyl,Remarks on the relation between causality and quantum fields,Class.

Uniqueness of null-local modular flow Keyl,Remarks on the relation between causality and quantum fields,Class

Reference 72

Resolution
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no resolver link, observed 2026-08-01T09:52:43.546666Z

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source=pdf_text observed=2026-08-01T09:52:43.546666Z digest=sha256:863d998c8a202c42424ced2453f162b974132208e29b339e60b03a97bb679161

Observation 4203d9ee-7f87-45ab-a83c-848eebc2641d · outbound

This paper cites Analyticity and the Unruh effect: a study of local modular flow.

Uniqueness of null-local modular flow Analyticity and the Unruh effect: a study of local modular flow

Reference 73

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source=pdf_text observed=2026-08-01T09:52:43.670655Z digest=sha256:0659228239314fada0b2311995ef2291c9dc26c31fdd0d60034508b7aeb0ea0e

Observation 3437cf2f-961f-4b15-a3ad-8955c2851d37 · outbound

This paper cites an unresolved cited work.

Uniqueness of null-local modular flow Unresolved cited work

Reference 74

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no resolver link, observed 2026-08-01T09:52:43.737297Z

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source=pdf_text observed=2026-08-01T09:52:43.737297Z digest=sha256:e38d624ee3e1fa89bf0aa0ee84f13c70d52626696c98133cc4b5814a3ec72c5c

Observation 62bdd117-5646-4825-b9ed-da76a10a514d · outbound

This paper cites Dimock and B.

Uniqueness of null-local modular flow Dimock and B

Reference 75

Resolution
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no resolver link, observed 2026-08-01T09:52:43.818668Z

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source=pdf_text observed=2026-08-01T09:52:43.818668Z digest=sha256:1171d5596ffcc0049618ba29638ad3f857601201e3e8c3f3cd75caec70b32868

Observation 8be90deb-0365-4be5-bd76-4c915216c405 · outbound

This paper cites Rigorous construction and Hadamard property of the Unruh state in Schwarzschild spacetime.

Uniqueness of null-local modular flow Rigorous construction and Hadamard property of the Unruh state in Schwarzschild spacetime

Reference 76

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no resolver link, observed 2026-08-01T09:52:43.922131Z

Source-reported events for the cited work

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source=pdf_text observed=2026-08-01T09:52:43.922131Z digest=sha256:438da179eb6e9f4ddd2540a5b5a222c1a6fd332c402fa03c2d40a2f828fd97d8

Observation f34a5291-8e78-4215-afc5-2603d820727c · outbound

This paper cites The Unruh state for massless fermions on Kerr spacetime and its Hadamard property.

Uniqueness of null-local modular flow The Unruh state for massless fermions on Kerr spacetime and its Hadamard property

Reference 77

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no resolver link, observed 2026-08-01T09:52:44.046770Z

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source=pdf_text observed=2026-08-01T09:52:44.046770Z digest=sha256:0c2255b39dc2b2dfb3ce18a74ae704a15ec92012229f39d41ee32abc44f86daa

Observation 52f6f92b-5527-4360-b5e0-1869aab4e2eb · outbound

This paper cites Hadamard state in Schwarzschild-de Sitter spacetime.

Uniqueness of null-local modular flow Hadamard state in Schwarzschild-de Sitter spacetime

Reference 78

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no resolver link, observed 2026-08-01T09:52:44.171627Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-01T09:52:44.171627Z digest=sha256:4eaf12ac5a0290331b4ac0f5f5cc85a3b3a9636b8772491a1eb438c2349cab37

Observation 7932528c-83b7-4684-b181-fcb89163845d · outbound

This paper cites Quantum Instability of the Cauchy Horizon in Reissner-Nordstr\"om-deSitter Spacetime.

Uniqueness of null-local modular flow Quantum Instability of the Cauchy Horizon in Reissner-Nordstr\"om-deSitter Spacetime

Reference 79

Resolution
unresolved
no resolver link, observed 2026-08-01T09:52:44.291936Z

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source=pdf_text observed=2026-08-01T09:52:44.291936Z digest=sha256:768d1304557d0c1472717425a6e3468881b78aae4920a664ef803656b1767833

Observation a2527bab-1117-4226-a35a-aea8f343c597 · outbound

This paper cites Construction of the Unruh State for a Real Scalar Field on the Kerr-de Sitter Spacetime.

Uniqueness of null-local modular flow Construction of the Unruh State for a Real Scalar Field on the Kerr-de Sitter Spacetime

Reference 80

Resolution
unresolved
no resolver link, observed 2026-08-01T09:52:44.399096Z

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source=pdf_text observed=2026-08-01T09:52:44.399096Z digest=sha256:d12d8253442077d7a7877bd9812d1721ab60b3f9433825d8dc6d3f0ebc699ad0

Observation 7c7b1562-e002-4e9b-9a34-022cb6b30e9c · outbound

This paper cites Excitability in quantum field theory.

Uniqueness of null-local modular flow Excitability in quantum field theory

Reference 81

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no resolver link, observed 2026-08-01T09:52:44.478778Z

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source=pdf_text observed=2026-08-01T09:52:44.478778Z digest=sha256:61eaa68247bdd9118e8245e438119e15df27412b7e91f4cf903fd5a6983c3dbe

Observation 541dbc6a-5023-4a52-9176-18bc3396ef8f · outbound

This paper cites an unresolved cited work.

Uniqueness of null-local modular flow Unresolved cited work

Reference 82

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no resolver link, observed 2026-08-01T09:52:44.589518Z

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source=pdf_text observed=2026-08-01T09:52:44.589518Z digest=sha256:f6264a64b1429f8c6e55ef3d269250ac50c95ffe786024ef912f1165180f00ae

Observation b92abb50-5087-4caa-8631-03cb6319ad06 · outbound

This paper cites Van Daele,Quasi-equivalence of quasi-free states on the weyl algebra,Commun.

Uniqueness of null-local modular flow Van Daele,Quasi-equivalence of quasi-free states on the weyl algebra,Commun

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source=pdf_text observed=2026-08-01T09:52:44.674077Z digest=sha256:80035e23ad081b17e8e2d3ff6a3af3feacb5ea81a122f7f737b873d17afb955a

Observation 29a1e16a-0abc-4988-a9f4-30543ac01289 · outbound

This paper cites Araki,On quasifree states of the canonical commutation relations: II.,.

Uniqueness of null-local modular flow Araki,On quasifree states of the canonical commutation relations: II.,

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source=pdf_text observed=2026-08-01T09:52:44.813607Z digest=sha256:3dd571b8d0929a7eefe507393eb8198b64f11025432b380e22c1f2e3e13c811f

Observation b5fc7c0f-47a9-4e59-8de4-973ebdd72816 · outbound

This paper cites Araki and S.

Uniqueness of null-local modular flow Araki and S

Reference 85

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source=pdf_text observed=2026-08-01T09:52:44.920400Z digest=sha256:d788ab07d15c39a4afa944eb29c1527233c0232a09f4aec6304c1c67349063f6

Observation 7f352f13-651a-4b64-9121-69cf961361c4 · outbound

This paper cites an unresolved cited work.

Uniqueness of null-local modular flow Unresolved cited work

Reference 86

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source=pdf_text observed=2026-08-01T09:52:45.002895Z digest=sha256:429fa7ca1d8ba75882dd0f247d536a7bf121b93db7e2cb618e3d6c262208534e

Observation de7aaa71-71f4-442d-a4a8-b68ddad25e1c · outbound

This paper cites Quantum fields in curved spacetime.

Uniqueness of null-local modular flow Quantum fields in curved spacetime

Reference 87

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source=pdf_text observed=2026-08-01T09:52:45.069630Z digest=sha256:b0b1a9592770ea1260ef38a5aec4f47dfffd9fc1086b47b149f5b6007b46e2c7

Observation 4c525d71-abd0-43cc-8d47-af1159ad397e · outbound

This paper cites American Mathematical Soc., 2000.

Uniqueness of null-local modular flow American Mathematical Soc., 2000

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source=pdf_text observed=2026-08-01T09:52:45.186035Z digest=sha256:149149fc1bf7f5ea4449b2b54950eafcdfea15a24c5d16d3c93b615e8e01c4bc

Observation 4ea4e495-8f0c-4cf2-97e5-9ef4212fba23 · outbound

This paper cites Sorce,Continuum canonical purifications,arXiv:2512.17014.

Uniqueness of null-local modular flow Sorce,Continuum canonical purifications,arXiv:2512.17014

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source=pdf_text observed=2026-08-01T09:52:45.352189Z digest=sha256:d493a2777222339463263aad871b465dc76866e27596e149ac050f65d3eb509f

Observation 488d490a-3c7c-4890-8ecd-42b86126da93 · outbound

This paper cites Haag,Local Quantum Physics.

Uniqueness of null-local modular flow Haag,Local Quantum Physics

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source=pdf_text observed=2026-08-01T09:52:45.464519Z digest=sha256:25acc5f86466ade70469f108d40ef3056558ccf471dd89d34bdbcd0d6cd1c1a6

Observation 431cb9fb-5b2d-4f2a-962c-24b5c9721c0a · outbound

This paper cites Takesaki,Theory of operator algebras II, vol.

Uniqueness of null-local modular flow Takesaki,Theory of operator algebras II, vol

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source=pdf_text observed=2026-08-01T09:52:45.578708Z digest=sha256:8baf98f07a2600adb6fa1a24a632d990fd295add30ef426f42a6ac6df1e78959

Observation 7661838f-ef46-4b31-ba42-713791dea1e2 · outbound

This paper cites Hollands,Aspects of quantum field theory in curved spacetime,University of York Ph.D.

Uniqueness of null-local modular flow Hollands,Aspects of quantum field theory in curved spacetime,University of York Ph.D

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source=pdf_text observed=2026-08-01T09:52:45.659386Z digest=sha256:680313b8c664866e7c24d672a7f8dd671f0021e394caa679a3911d378a8bd85d

Observation 04a3720b-af8c-4756-b199-30675ecf20e9 · outbound

This paper cites Reeh and S.

Uniqueness of null-local modular flow Reeh and S

Reference 93

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source=pdf_text observed=2026-08-01T09:52:45.782361Z digest=sha256:b635707e778b5b06a8c61205c103a0a807e6dcec18453fa2a08c0a37d196c789

Observation a0275e67-d5ae-438d-9914-22b0be7924f5 · outbound

This paper cites Excitability of Gaussian states with VEVs.

Uniqueness of null-local modular flow Excitability of Gaussian states with VEVs

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source=pdf_text observed=2026-08-01T09:52:45.873944Z digest=sha256:63e9bbddbaf4c0d86356e3e6f7823e1c534ebabab23144695ece0712dbf96a2a

Observation 0af90964-a245-45c5-a902-0b1276c7a729 · outbound

This paper cites Hadamard states on spherically symmetric characteristic surfaces, the semi-classical Einstein equations and the Hawking effect.

Uniqueness of null-local modular flow Hadamard states on spherically symmetric characteristic surfaces, the semi-classical Einstein equations and the Hawking effect

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source=pdf_text observed=2026-08-01T09:52:45.974372Z digest=sha256:9897ac1c9262f72fa07b35d9a8f9273a33831d5b8f5c6ae935b552464e90c8a6

Observation c7119c17-1171-4c27-9b2d-84bb78e98732 · outbound

This paper cites Verch,Local definiteness, primarity and quasiequivalence of quasifree Hadamard quantum states in curved space-time,Commun.

Uniqueness of null-local modular flow Verch,Local definiteness, primarity and quasiequivalence of quasifree Hadamard quantum states in curved space-time,Commun

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source=pdf_text observed=2026-08-01T09:52:46.051218Z digest=sha256:0dd4fad8c1c75dbeca0066478b3d93996bf9c0943366dfe389510395691db342

Observation 4489cca4-da63-41ee-9556-55802bf857ff · outbound

This paper cites an unresolved cited work.

Uniqueness of null-local modular flow Unresolved cited work

Reference 97

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source=pdf_text observed=2026-08-01T09:52:46.194969Z digest=sha256:a3b6b15c2e8d0d229b20df359bf1cc7c4b42ffb9f92568dcfab9f64c7c3cafb2

Observation b9262e47-c5eb-4505-a32f-af4b67e8e383 · outbound

This paper cites Quasi-free isomorphisms of second quantisation algebras and modular theory.

Uniqueness of null-local modular flow Quasi-free isomorphisms of second quantisation algebras and modular theory

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source=pdf_text observed=2026-08-01T09:52:46.319175Z digest=sha256:05d271d5564254b1e02a2f7b37d882533abde5bf5f51b7ce4cac7d6eb6b89101

Observation af4b0a7f-9f9d-4d4b-a26a-7c56c1088d41 · outbound

This paper cites Scaling Algebras and Renormalization Group in Algebraic Quantum Field Theory. II. Instructive Examples.

Uniqueness of null-local modular flow Scaling Algebras and Renormalization Group in Algebraic Quantum Field Theory. II. Instructive Examples

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source=pdf_text observed=2026-08-01T09:52:46.417315Z digest=sha256:7baf9cf08642e2ae13ccf5fa93a7e38c3401deb8b49901f4bafc81d09e95f4d1

Observation 7b5a77e8-6d25-485b-bbdd-089daff51daf · outbound

This paper cites Local causal structures, Hadamard states and the principle of local covariance in quantum field theory.

Uniqueness of null-local modular flow Local causal structures, Hadamard states and the principle of local covariance in quantum field theory

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source=pdf_text observed=2026-08-01T09:52:46.569651Z digest=sha256:4dfc1cda2d15dba5db2ff2844ffdbd5018c0092b47ff498a558fb54b4677dac8

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