Paper Citation Record · LEDGER

Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence

As of 11 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 0 inbound Pith citation observations for arXiv:2607.28811.

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

pith.paper-citation-record.v1
2607.28811 v1

Coverage vector

measured 24 of 24 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-03T00:25:53.392478Z

measured 24 of 24 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+00:00

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measured 0 of 1 external citation measurements

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Reference resolution

24 of 24 outbound references displayed

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Outbound references

Observation 3d816a5a-f8a4-4fa5-bcf6-15023c6d9fb9 · outbound

This paper cites Reflection positivity and invertible topological phases.Geometry & Topology, 25(3):1165–1330, 2021.

Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence Reflection positivity and invertible topological phases.Geometry & Topology, 25(3):1165–1330, 2021

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-03T00:25:53.325965Z

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Observation 72cf2e84-eb9e-413d-81d6-620f01ecebb6 · outbound

This paper cites Invertible phases of matter with spatial symmetry.

Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence Invertible phases of matter with spatial symmetry

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-03T00:25:53.329544Z

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Observation 4f5b2263-8522-4c21-b517-02557d079239 · outbound

This paper cites Failure of the crystalline equivalence principle for weak free fermions.Phys.

Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence Failure of the crystalline equivalence principle for weak free fermions.Phys

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-03T00:25:53.332989Z

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Observation 6e21add6-5cef-4fb3-b94e-f384e4efcf0d · outbound

This paper cites Periodic table for topological insulators and superconduc- tors.AIP conference proceedings, May 2009.

Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence Periodic table for topological insulators and superconduc- tors.AIP conference proceedings, May 2009

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-03T00:25:53.336012Z

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Observation be089e31-0434-40de-8c0b-3c4f9cb4eba5 · outbound

This paper cites Freed and G.

Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence Freed and G

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-03T00:25:53.339172Z

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Observation 314512ef-45e8-4dfb-a284-e00871250806 · outbound

This paper cites an unresolved cited work.

Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-03T00:25:53.342438Z

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Observation cdca577b-5b61-4827-9267-012bd69d0ac3 · outbound

This paper cites Fermionic symmetry protected topological phases and cobordisms.Journal of High Energy Physics, 2015(12):1–21, 2015.

Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence Fermionic symmetry protected topological phases and cobordisms.Journal of High Energy Physics, 2015(12):1–21, 2015

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-03T00:25:53.345545Z

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Observation 6fb12177-c5ce-4ff9-b30f-49a004e943d3 · outbound

This paper cites Gaiotto and T.

Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence Gaiotto and T

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-03T00:25:53.348199Z

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Observation 174d0c01-91e1-40db-a7ea-dd2171ee6c52 · outbound

This paper cites an unresolved cited work.

Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-03T00:25:53.350926Z

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Observation 0b249ccc-c0d7-443e-b0bc-b58eb0eada4a · outbound

This paper cites Stable homotopy theory of invertible gapped quantum spin systems i: Kitaev’sω-spectrum.arXiv preprint arXiv:2503.12618, 2025.

Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence Stable homotopy theory of invertible gapped quantum spin systems i: Kitaev’sω-spectrum.arXiv preprint arXiv:2503.12618, 2025

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-03T00:25:53.353530Z

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Observation 235ed394-6f7d-451a-a0a7-8678d7519c4e · outbound

This paper cites Weak topological phases in the presence of interactions.

Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence Weak topological phases in the presence of interactions

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-03T00:25:53.356202Z

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Observation 30ec76a7-07f2-4d0e-a0d0-ea8ba1a2ff41 · outbound

This paper cites Gauging spatial symmetries and the classification of topological crystalline phases.Physical Review X, 8(1):011040, 2018.

Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence Gauging spatial symmetries and the classification of topological crystalline phases.Physical Review X, 8(1):011040, 2018

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-03T00:25:53.359267Z

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Observation d4a63126-1ea9-469a-847d-cdb12c62fec6 · outbound

This paper cites Failure of the crys- talline equivalence principle for weak free fermions.Physical Review B, 111(8):L081118, 2025.

Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence Failure of the crys- talline equivalence principle for weak free fermions.Physical Review B, 111(8):L081118, 2025

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-03T00:25:53.362169Z

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Observation 3ddee03b-a5d4-4d63-9322-22eedc8d06cc · outbound

This paper cites Homotopy-theoretic approach to spt phases in action: Z16 classification of three-dimensional superconductors.

Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence Homotopy-theoretic approach to spt phases in action: Z16 classification of three-dimensional superconductors

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-03T00:25:53.364907Z

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Observation 966ee3b0-8272-48d6-83c3-31ecc0638ec9 · outbound

This paper cites Hatcher.Algebraic Topology.

Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence Hatcher.Algebraic Topology

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-03T00:25:53.367582Z

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Observation 5805452e-2dd2-4f18-aefb-0eeb900990c6 · outbound

This paper cites Equivariant stable homotopy theory.

Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence Equivariant stable homotopy theory

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-03T00:25:53.370196Z

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Observation 7d5dd2dd-d6f5-4a43-b7e7-e92eac93b357 · outbound

This paper cites Invertible phases for mixed spatial symmetries and the fermionic crystalline equivalence principle.arXiv preprint arXiv:2102.02941, 2021.

Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence Invertible phases for mixed spatial symmetries and the fermionic crystalline equivalence principle.arXiv preprint arXiv:2102.02941, 2021

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-03T00:25:53.372837Z

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Observation a5511b74-cb3a-478e-b431-581775533870 · outbound

This paper cites A Generalized Crystalline Equivalence Principle.

Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence A Generalized Crystalline Equivalence Principle

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-03T00:25:53.375437Z

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Observation 28cc2b84-e2a9-4191-a931-70d1b9ea7c64 · outbound

This paper cites Unraveling the Bott spiral.

Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence Unraveling the Bott spiral

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-03T00:25:53.378483Z

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Observation 7bec86a5-4256-4e13-ba1f-0248561c89f9 · outbound

This paper cites Crystallographic t-duality.Journal of Geometry and Physics, 139:50–77, 2019.

Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence Crystallographic t-duality.Journal of Geometry and Physics, 139:50–77, 2019

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-03T00:25:53.381685Z

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Observation 2b9f9b89-9697-48eb-818e-03858fb47f20 · outbound

This paper cites The equivariant cobordism category.

Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence The equivariant cobordism category

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-03T00:25:53.384535Z

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Observation 447b78a3-4279-4eb5-bf28-310b931e7700 · outbound

This paper cites Higher coherences for equivariant k-theory.Structured ring spectra, 315:87–114, 2004.

Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence Higher coherences for equivariant k-theory.Structured ring spectra, 315:87–114, 2004

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-03T00:25:53.387155Z

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Observation d1d75d67-2797-4318-9fc9-242c6dfff434 · outbound

This paper cites Topological k–(co) homology of clas- sifying spaces of discrete groups.Algebraic & Geometric Topology, 13(1):1– 34, 2013.

Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence Topological k–(co) homology of clas- sifying spaces of discrete groups.Algebraic & Geometric Topology, 13(1):1– 34, 2013

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-03T00:25:53.389740Z

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Observation 6bf59116-adf1-4cb1-9a6c-4112affb72fd · outbound

This paper cites Twisted crystallo- graphic t-duality via the baum–connes isomorphism.International Journal of Mathematics, 32(10):2150078, 2021.

Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence Twisted crystallo- graphic t-duality via the baum–connes isomorphism.International Journal of Mathematics, 32(10):2150078, 2021

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-03T00:25:53.392478Z

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Pith citing papers

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