Paper Citation Record · LEDGER

Bosonic SPT and invertible phases and its relation to Steenrod's problem

As of 22 August 2026, this Paper Citation Record lists 51 of 51 outbound references and 1 inbound Pith citation observation for arXiv:2607.14662.

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pith.paper-citation-record.v1
2607.14662 v1

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measured 51 of 51 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-02T01:41:23.377895Z

measured 52 of 52 standing notices

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

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Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-14T04:36:06.499308Z

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Source: pith, observed 2026-08-14T04:36:08.844976Z

Reference resolution

51 of 51 outbound references displayed

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Outbound references

Observation 24d5e6ac-d14b-4d31-8fec-19a26d64ef87 · outbound

This paper cites A Guide for Computing Stable Homotopy Groups.

Bosonic SPT and invertible phases and its relation to Steenrod's problem A Guide for Computing Stable Homotopy Groups

Reference 1

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Observation 2cca985a-4aed-47af-ac43-b45e453aba75 · outbound

This paper cites an unresolved cited work.

Bosonic SPT and invertible phases and its relation to Steenrod's problem Unresolved cited work

Reference 2

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Observation c1f6d05a-449e-4cc8-97f7-6891f40aa9ac · outbound

This paper cites The Pontrjagin Dual of 3-Dimensional Spin Bordism.

Bosonic SPT and invertible phases and its relation to Steenrod's problem The Pontrjagin Dual of 3-Dimensional Spin Bordism

Reference 3

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Observation e72ad936-ae87-4970-9402-73a29580ebff · outbound

This paper cites The Pontrjagin Dual of 4-Dimensional Spin Bordism.

Bosonic SPT and invertible phases and its relation to Steenrod's problem The Pontrjagin Dual of 4-Dimensional Spin Bordism

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-02T01:41:17.377996Z

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Observation cdec8ef0-3fd0-424d-a6ef-21c6d13d7b68 · outbound

This paper cites Quadratic Functions of Cocycles and Pin Structures.

Bosonic SPT and invertible phases and its relation to Steenrod's problem Quadratic Functions of Cocycles and Pin Structures

Reference 5

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Observation 8a4e0911-abb4-4e82-9e6a-0e767fd0cce7 · outbound

This paper cites Derived functors of the divided power functors.

Bosonic SPT and invertible phases and its relation to Steenrod's problem Derived functors of the divided power functors

Reference 6

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Observation ca766a8a-20f4-40c0-a297-d3a31f72d102 · outbound

This paper cites Global anomalies in $6D$ gauged supergravities.

Bosonic SPT and invertible phases and its relation to Steenrod's problem Global anomalies in $6D$ gauged supergravities

Reference 8

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Observation c9026d11-3d0d-4f64-a845-52f3679d57b1 · outbound

This paper cites Benson and J.

Bosonic SPT and invertible phases and its relation to Steenrod's problem Benson and J

Reference 9

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Observation 82b396d8-05d9-4a9f-86d2-c422e9aa2070 · outbound

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Bosonic SPT and invertible phases and its relation to Steenrod's problem Unresolved cited work

Reference 10

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Observation 4cb1926f-7b89-458f-8764-f26990e6582d · outbound

This paper cites Immersed but not embedded homology classes.

Bosonic SPT and invertible phases and its relation to Steenrod's problem Immersed but not embedded homology classes

Reference 11

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Observation 43d7f5b2-dc63-4c39-9c59-0a31d24ea2fc · outbound

This paper cites Symmetry protected topological orders and the group cohomology of their symmetry group.

Bosonic SPT and invertible phases and its relation to Steenrod's problem Symmetry protected topological orders and the group cohomology of their symmetry group

Reference 12

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Observation af37270a-aaf3-47b6-baa4-04215f7c1018 · outbound

This paper cites Symmetry protected topological orders in interacting bosonic systems.

Bosonic SPT and invertible phases and its relation to Steenrod's problem Symmetry protected topological orders in interacting bosonic systems

Reference 13

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Observation a7b521b8-bbc9-4af4-8bc8-bc0c124a91c2 · outbound

This paper cites An effective proof of the Cartan formula: Odd primes.

Bosonic SPT and invertible phases and its relation to Steenrod's problem An effective proof of the Cartan formula: Odd primes

Reference 14

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Observation 4a4b9334-557e-48a5-adf2-2c6df9cf1508 · outbound

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Bosonic SPT and invertible phases and its relation to Steenrod's problem Unresolved cited work

Reference 15

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Observation 09d8e4fe-df1d-45c4-84c1-fd98b2d0c7a0 · outbound

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Bosonic SPT and invertible phases and its relation to Steenrod's problem Unresolved cited work

Reference 16

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Observation b144d4b2-3871-4ac4-baa7-e86a68069706 · outbound

This paper cites Dijkgraaf and E.

Bosonic SPT and invertible phases and its relation to Steenrod's problem Dijkgraaf and E

Reference 17

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Observation ab15bb7b-de4b-41af-9e44-69ba1887c229 · outbound

This paper cites Eilenberg, On the problems of topology, Annals of Mathematics 50 (1949) 247--260 http://www.jstor.org/stable/1969448.

Bosonic SPT and invertible phases and its relation to Steenrod's problem Eilenberg, On the problems of topology, Annals of Mathematics 50 (1949) 247--260 http://www.jstor.org/stable/1969448

Reference 18

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Observation bce972eb-3d0d-442e-bf56-337df392af21 · outbound

This paper cites Fomenko and D.

Bosonic SPT and invertible phases and its relation to Steenrod's problem Fomenko and D

Reference 19

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Observation 0725443f-581c-4443-8770-02a3cb1c7a4f · outbound

This paper cites Reflection positivity and invertible topological phases.

Bosonic SPT and invertible phases and its relation to Steenrod's problem Reflection positivity and invertible topological phases

Reference 20

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Observation 52928c72-3972-4e7d-b64f-3fc56d997758 · outbound

This paper cites An Exactly Solvable Model for a $4+1D$ Beyond-Cohomology Symmetry Protected Topological Phase.

Bosonic SPT and invertible phases and its relation to Steenrod's problem An Exactly Solvable Model for a $4+1D$ Beyond-Cohomology Symmetry Protected Topological Phase

Reference 21

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Observation 9334bbd5-eacc-4e23-8401-3f54f1d17da2 · outbound

This paper cites Setting the quantum integrand of M-theory.

Bosonic SPT and invertible phases and its relation to Steenrod's problem Setting the quantum integrand of M-theory

Reference 22

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Observation 0306836c-acb5-4872-b0a7-22242f7a1279 · outbound

This paper cites Anomalies and Invertible Field Theories.

Bosonic SPT and invertible phases and its relation to Steenrod's problem Anomalies and Invertible Field Theories

Reference 23

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Observation 0c196f33-5c1f-4680-a5e3-7cfdef52d682 · outbound

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Bosonic SPT and invertible phases and its relation to Steenrod's problem Unresolved cited work

Reference 24

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Observation ed3bf1a3-200c-40e2-a1fd-3fcffa85852a · outbound

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Bosonic SPT and invertible phases and its relation to Steenrod's problem Unresolved cited work

Reference 25

Resolution: verified exact; doi, observed 2026-08-02T01:43:32.639291Z

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Observation 15b2c255-164a-4a96-87f8-db0d49e0417c · outbound

This paper cites an unresolved cited work.

Bosonic SPT and invertible phases and its relation to Steenrod's problem Unresolved cited work

Reference 26

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Observation 09ca0167-ea26-4894-8a1e-71e0589f98ab · outbound

This paper cites Symmetry Protected Topological phases and Generalized Cohomology.

Bosonic SPT and invertible phases and its relation to Steenrod's problem Symmetry Protected Topological phases and Generalized Cohomology

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-02T01:41:20.405746Z

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Observation 9a2b27eb-c298-40cf-a0eb-456df05686fd · outbound

This paper cites Spin TQFTs and fermionic phases of matter.

Bosonic SPT and invertible phases and its relation to Steenrod's problem Spin TQFTs and fermionic phases of matter

Reference 28

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Observation 72cae48a-e0b3-41e1-b46c-64a8911db431 · outbound

This paper cites Symmetry-protected topological orders for interacting fermions -- Fermionic topological nonlinear $\sigma$ models and a special group supercohomology theory.

Bosonic SPT and invertible phases and its relation to Steenrod's problem Symmetry-protected topological orders for interacting fermions -- Fermionic topological nonlinear $\sigma$ models and a special group supercohomology theory

Reference 29

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Observation d5b5fe99-10d2-44bb-b92a-069385a7cc31 · outbound

This paper cites Hanke, Bordism of elementary abelian groups via inessential brown–peterson homology, Journal of Topology 9 (2016) 725–746 http://dx.doi.org/10.1112/jtopol/jtw009.

Bosonic SPT and invertible phases and its relation to Steenrod's problem Hanke, Bordism of elementary abelian groups via inessential brown–peterson homology, Journal of Topology 9 (2016) 725–746 http://dx.doi.org/10.1112/jtopol/jtw009

Reference 30

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Observation 0d843ae3-ebc8-4e92-9a2b-1515625cd5c0 · outbound

This paper cites Hirzebruch, On Steenrod reduced powers in oriented manifolds.

Bosonic SPT and invertible phases and its relation to Steenrod's problem Hirzebruch, On Steenrod reduced powers in oriented manifolds

Reference 31

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Observation 0235c9d7-e35c-466d-9632-81e0662ac7bf · outbound

This paper cites Hsieh, Y.

Bosonic SPT and invertible phases and its relation to Steenrod's problem Hsieh, Y

Reference 32

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Observation 1171f884-097e-47f2-bf46-50243fd5e224 · outbound

This paper cites Bordism categories and orientations of moduli spaces.

Bosonic SPT and invertible phases and its relation to Steenrod's problem Bordism categories and orientations of moduli spaces

Reference 33

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Observation dca4b823-da82-478d-a836-222455581f5f · outbound

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Bosonic SPT and invertible phases and its relation to Steenrod's problem Unresolved cited work

Reference 34

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Observation 2aa7bc00-dfde-42c4-a725-74001db71314 · outbound

This paper cites On Quantum Aspects of 1-Form Symmetries II: Bordism, Invertible Phases, and Anomalies.

Bosonic SPT and invertible phases and its relation to Steenrod's problem On Quantum Aspects of 1-Form Symmetries II: Bordism, Invertible Phases, and Anomalies

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-02T01:41:21.668838Z

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Observation 48036141-0669-4f26-95c2-d003491c0bb0 · outbound

This paper cites Symmetry Protected Topological Phases, Anomalies, and Cobordisms: Beyond Group Cohomology.

Bosonic SPT and invertible phases and its relation to Steenrod's problem Symmetry Protected Topological Phases, Anomalies, and Cobordisms: Beyond Group Cohomology

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-02T01:41:21.850470Z

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Observation 60c26fe2-548e-4ffa-8f4a-78c836971006 · outbound

This paper cites Cochain level May-Steenrod operations.

Bosonic SPT and invertible phases and its relation to Steenrod's problem Cochain level May-Steenrod operations

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-02T01:41:22.036303Z

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Observation fb5f0d36-eba3-436f-9562-a0fdd96d5203 · outbound

This paper cites Fermionic Symmetry Protected Topological Phases and Cobordisms.

Bosonic SPT and invertible phases and its relation to Steenrod's problem Fermionic Symmetry Protected Topological Phases and Cobordisms

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-02T01:41:22.167710Z

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Observation 39cb1572-1e44-418a-949e-c1dfcd6e0629 · outbound

This paper cites Milnor, The S teenrod algebra and its dual , http://dx.doi.org/10.2307/1969932 Ann.

Bosonic SPT and invertible phases and its relation to Steenrod's problem Milnor, The S teenrod algebra and its dual , http://dx.doi.org/10.2307/1969932 Ann

Reference 39

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Observation c10cfa63-6ab8-400e-8379-89cf4d5e4bfa · outbound

This paper cites Miller, http://dx.doi.org/10.1142/12132 Lectures on algebraic topology , Hackensack, NJ: World Scientific, 2022 (English).

Bosonic SPT and invertible phases and its relation to Steenrod's problem Miller, http://dx.doi.org/10.1142/12132 Lectures on algebraic topology , Hackensack, NJ: World Scientific, 2022 (English)

Reference 40

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Observation 38e50843-8dc9-489d-ae32-42d3d8c82f11 · outbound

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Bosonic SPT and invertible phases and its relation to Steenrod's problem Unresolved cited work

Reference 41

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Observation b836e0ac-0085-416c-9843-bdf0f197e10c · outbound

This paper cites Categorical Symmetry of the Standard Model from Gravitational Anomaly.

Bosonic SPT and invertible phases and its relation to Steenrod's problem Categorical Symmetry of the Standard Model from Gravitational Anomaly

Reference 42

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Observation b418b84e-6f3d-4ae1-a9dd-b924eab7b73c · outbound

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Bosonic SPT and invertible phases and its relation to Steenrod's problem Unresolved cited work

Reference 43

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Observation abcc007d-8234-4e54-89ed-c1700e9444fb · outbound

This paper cites Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect.

Bosonic SPT and invertible phases and its relation to Steenrod's problem Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect

Reference 44

Resolution: unresolved; no resolver link, observed 2026-08-02T01:41:22.592828Z

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Observation b71f3a34-4acb-49c5-bd28-18bdd8c4c5ce · outbound

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Bosonic SPT and invertible phases and its relation to Steenrod's problem Unresolved cited work

Reference 45

Resolution: unresolved; no resolver link, observed 2026-08-02T01:41:22.670292Z

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Observation cddc2c35-e357-417e-bb5d-88fd4181a573 · outbound

This paper cites Thom, Quelques propri \'e t \'e s globales des vari \'e t \'e s diff \'e rentiables , http://dx.doi.org/10.1007/BF02566923 Commentarii Mathematici Helvetici 28 (1954) 17--86.

Bosonic SPT and invertible phases and its relation to Steenrod's problem Thom, Quelques propri \'e t \'e s globales des vari \'e t \'e s diff \'e rentiables , http://dx.doi.org/10.1007/BF02566923 Commentarii Mathematici Helvetici 28 (1954) 17--86

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-02T01:41:22.753184Z

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Observation 179c5265-d8f5-4dff-a24d-7d618bec628f · outbound

This paper cites Trou\'e, The orders of the P ostnikov invariants of the T hom spectrum MSO , Illinois J.

Bosonic SPT and invertible phases and its relation to Steenrod's problem Trou\'e, The orders of the P ostnikov invariants of the T hom spectrum MSO , Illinois J

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-02T01:41:22.838325Z

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Observation 6ed52560-93d2-4590-a13e-0960fb88ffcd · outbound

This paper cites Higher Anomalies, Higher Symmetries, and Cobordisms I: Classification of Higher-Symmetry-Protected Topological States and Their Boundary Fermionic/Bosonic Anomalies via a Generalized Cobordism Theory.

Bosonic SPT and invertible phases and its relation to Steenrod's problem Higher Anomalies, Higher Symmetries, and Cobordisms I: Classification of Higher-Symmetry-Protected Topological States and Their Boundary Fermionic/Bosonic Anomalies via a Generalized Cobordism Theory

Reference 48

Resolution: unresolved; no resolver link, observed 2026-08-02T01:41:22.845968Z

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Observation bb2ab6c9-f102-48fd-be1c-095d4390fd87 · outbound

This paper cites Fermion Families and Pontryagin Class: Topological Field Theory via Colour Symmetry Extension.

Bosonic SPT and invertible phases and its relation to Steenrod's problem Fermion Families and Pontryagin Class: Topological Field Theory via Colour Symmetry Extension

Reference 49

Resolution: unresolved; no resolver link, observed 2026-08-02T01:41:22.933981Z

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Observation a37b65e3-ee89-47ba-84a7-42f31fbb3e45 · outbound

This paper cites Minimalist approach to the classification of symmetry protected topological phases.

Bosonic SPT and invertible phases and its relation to Steenrod's problem Minimalist approach to the classification of symmetry protected topological phases

Reference 50

Resolution: unresolved; no resolver link, observed 2026-08-02T01:41:23.094627Z

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Observation 25b2afe8-d79c-43c0-80d3-5318bf118903 · outbound

This paper cites Gapped boundary of (4+1)d beyond-cohomology bosonic SPT phase.

Bosonic SPT and invertible phases and its relation to Steenrod's problem Gapped boundary of (4+1)d beyond-cohomology bosonic SPT phase

Reference 51

Resolution: unresolved; no resolver link, observed 2026-08-02T01:41:23.256656Z

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Observation a682f5b7-c25f-488b-b3fb-5844eb282d7c · outbound

This paper cites On the cobordism classification of symmetry protected topological phases.

Bosonic SPT and invertible phases and its relation to Steenrod's problem On the cobordism classification of symmetry protected topological phases

Reference 52

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Pith citing papers

Observation 2ce11710-a262-4f48-a833-11f385da905e · inbound

Understanding Non-Split 2-Group Symmetry: (3+1)D SymTFT, Anomaly and Bordism cites this paper.

Understanding Non-Split 2-Group Symmetry: (3+1)D SymTFT, Anomaly and Bordism Bosonic SPT and invertible phases and its relation to Steenrod's problem

Reference 179

Resolution: verified exact; local_arxiv, observed 2026-08-14T04:36:08.866795Z

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