{"as_of":"2026-08-08T02:22:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:99c754ef300737ce671c68a533ffccf648a636382f30203bd22b87b9474cf6bf","coverage":[{"denominator":24,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":24,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-03T00:25:53.392478Z","state":"measured"},{"denominator":24,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":24,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-07T06:34:17.273281+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2607.28811/citation-record","integrity":"/paper/2607.28811/integrity","json":"/paper/2607.28811/citation-record.json","paper":"/paper/2607.28811"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T00:25:53.325965Z","title":"Reflection positivity and invertible topological phases.Geometry & Topology, 25(3):1165–1330, 2021","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.28811","last_updated":"2026-07-30T20:13:40Z","snapshot_observed_at":"2026-08-06T08:18:56.211874Z","submitted_at":"2026-07-30T20:13:40Z","title":"Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-03T00:25:53.325965Z"},"links":{"citing_paper":"/paper/2607.28811"},"observation_digest":"sha256:1c4ecd5c855644f04a92bc05e9110921a39818692fe258d44b532cd6cb770d0b","observation_id":"3d816a5a-f8a4-4fa5-bcf6-15023c6d9fb9","resolution":{"observed_at":"2026-08-03T00:25:53.325965Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1901.06419","last_updated":"2019-01-16T22:06:43Z","snapshot_observed_at":"2026-08-04T04:35:22.520097Z","submitted_at":"2019-01-16T22:06:43Z","title":"Invertible phases of matter with spatial symmetry","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1901.06419","snapshot_observed_at":"2026-08-03T00:25:53.329544Z","title":"Invertible phases of matter with spatial symmetry.arXiv preprint arXiv:1901.06419, 2019","venue":null,"work_id":null,"year":1901},"citing_paper":{"arxiv_id":"2607.28811","last_updated":"2026-07-30T20:13:40Z","snapshot_observed_at":"2026-08-06T08:18:56.211874Z","submitted_at":"2026-07-30T20:13:40Z","title":"Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-03T00:25:53.329544Z"},"links":{"cited_paper":"/paper/1901.06419","citing_paper":"/paper/2607.28811"},"observation_digest":"sha256:f618ee67dae5991880307c0cfbdfdf10570d7184e58ff95c6641adf619ca14ba","observation_id":"72cf2e84-eb9e-413d-81d6-620f01ecebb6","resolution":{"observed_at":"2026-08-03T00:25:53.329544Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T00:25:53.332989Z","title":"Failure of the crystalline equivalence principle for weak free fermions.Phys","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.28811","last_updated":"2026-07-30T20:13:40Z","snapshot_observed_at":"2026-08-06T08:18:56.211874Z","submitted_at":"2026-07-30T20:13:40Z","title":"Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-03T00:25:53.332989Z"},"links":{"citing_paper":"/paper/2607.28811"},"observation_digest":"sha256:9649d33cf7314610b9fb0526d7e207f2ac9aee6ac22c3dbd6887577689dade55","observation_id":"4f5b2263-8522-4c21-b517-02557d079239","resolution":{"observed_at":"2026-08-03T00:25:53.332989Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T00:25:53.336012Z","title":"Periodic table for topological insulators and superconduc- tors.AIP conference proceedings, May 2009","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2607.28811","last_updated":"2026-07-30T20:13:40Z","snapshot_observed_at":"2026-08-06T08:18:56.211874Z","submitted_at":"2026-07-30T20:13:40Z","title":"Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-03T00:25:53.336012Z"},"links":{"citing_paper":"/paper/2607.28811"},"observation_digest":"sha256:09602f5cd9d057f2256b72a0c0a56366847fc8c04cd0f7d7313cabaf8e600676","observation_id":"6e21add6-5cef-4fb3-b94e-f384e4efcf0d","resolution":{"observed_at":"2026-08-03T00:25:53.336012Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T00:25:53.339172Z","title":"Freed and G","venue":null,"work_id":null,"year":1927},"citing_paper":{"arxiv_id":"2607.28811","last_updated":"2026-07-30T20:13:40Z","snapshot_observed_at":"2026-08-06T08:18:56.211874Z","submitted_at":"2026-07-30T20:13:40Z","title":"Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-03T00:25:53.339172Z"},"links":{"citing_paper":"/paper/2607.28811"},"observation_digest":"sha256:0ccf9cfbba216049c97c1f67f08b2ec496e52d4c50158c31384b7b8c7d134a17","observation_id":"be089e31-0434-40de-8c0b-3c4f9cb4eba5","resolution":{"observed_at":"2026-08-03T00:25:53.339172Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T00:25:53.342438Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.28811","last_updated":"2026-07-30T20:13:40Z","snapshot_observed_at":"2026-08-06T08:18:56.211874Z","submitted_at":"2026-07-30T20:13:40Z","title":"Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-03T00:25:53.342438Z"},"links":{"citing_paper":"/paper/2607.28811"},"observation_digest":"sha256:8a08424f44daf835616fe4809fda82f466f88e47cfdc2208dca315e266028dc5","observation_id":"314512ef-45e8-4dfb-a284-e00871250806","resolution":{"observed_at":"2026-08-03T00:25:53.342438Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T00:25:53.345545Z","title":"Fermionic symmetry protected topological phases and cobordisms.Journal of High Energy Physics, 2015(12):1–21, 2015","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.28811","last_updated":"2026-07-30T20:13:40Z","snapshot_observed_at":"2026-08-06T08:18:56.211874Z","submitted_at":"2026-07-30T20:13:40Z","title":"Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-03T00:25:53.345545Z"},"links":{"citing_paper":"/paper/2607.28811"},"observation_digest":"sha256:88d1a4834dbad120d94da52370fdcba859271494a8440d2e5378eae916b3d20a","observation_id":"cdca577b-5b61-4827-9267-012bd69d0ac3","resolution":{"observed_at":"2026-08-03T00:25:53.345545Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T00:25:53.348199Z","title":"Gaiotto and T","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.28811","last_updated":"2026-07-30T20:13:40Z","snapshot_observed_at":"2026-08-06T08:18:56.211874Z","submitted_at":"2026-07-30T20:13:40Z","title":"Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-03T00:25:53.348199Z"},"links":{"citing_paper":"/paper/2607.28811"},"observation_digest":"sha256:47503fc9a9ba61746d0da32b2c8637586b86d72ebf63dec456477e9de60c6e51","observation_id":"6fb12177-c5ce-4ff9-b30f-49a004e943d3","resolution":{"observed_at":"2026-08-03T00:25:53.348199Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T00:25:53.350926Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.28811","last_updated":"2026-07-30T20:13:40Z","snapshot_observed_at":"2026-08-06T08:18:56.211874Z","submitted_at":"2026-07-30T20:13:40Z","title":"Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-03T00:25:53.350926Z"},"links":{"citing_paper":"/paper/2607.28811"},"observation_digest":"sha256:0c920759a7c3aa2dd5ad9503076de2b8cc0d7bd23cae3b382dc4fa29b7253f3a","observation_id":"174d0c01-91e1-40db-a7ea-dd2171ee6c52","resolution":{"observed_at":"2026-08-03T00:25:53.350926Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T00:25:53.353530Z","title":"Stable homotopy theory of invertible gapped quantum spin systems i: Kitaev’sω-spectrum.arXiv preprint arXiv:2503.12618, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.28811","last_updated":"2026-07-30T20:13:40Z","snapshot_observed_at":"2026-08-06T08:18:56.211874Z","submitted_at":"2026-07-30T20:13:40Z","title":"Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-03T00:25:53.353530Z"},"links":{"citing_paper":"/paper/2607.28811"},"observation_digest":"sha256:5765bfbfa4c9f3c9c4e00c8294051010ccc53d58da4bb993aec034a2caa18968","observation_id":"0b249ccc-c0d7-443e-b0bc-b58eb0eada4a","resolution":{"observed_at":"2026-08-03T00:25:53.353530Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2410.10031","last_updated":"2026-07-15T14:17:47Z","snapshot_observed_at":"2026-08-05T15:15:00.152690Z","submitted_at":"2024-10-13T22:14:38Z","title":"Weak topological phases in the presence of interactions","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2410.10031","snapshot_observed_at":"2026-08-03T00:25:53.356202Z","title":"Weak topologi- cal phases in the presence of interactions.arXiv preprint arXiv:2410.10031, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.28811","last_updated":"2026-07-30T20:13:40Z","snapshot_observed_at":"2026-08-06T08:18:56.211874Z","submitted_at":"2026-07-30T20:13:40Z","title":"Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-03T00:25:53.356202Z"},"links":{"cited_paper":"/paper/2410.10031","citing_paper":"/paper/2607.28811"},"observation_digest":"sha256:b1e05c31e57f82adc2c8527a2c3d1e783395af07ae72522ed3a8af7721a06f16","observation_id":"235ed394-6f7d-451a-a0a7-8678d7519c4e","resolution":{"observed_at":"2026-08-03T00:25:53.356202Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T00:25:53.359267Z","title":"Gauging spatial symmetries and the classification of topological crystalline phases.Physical Review X, 8(1):011040, 2018","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.28811","last_updated":"2026-07-30T20:13:40Z","snapshot_observed_at":"2026-08-06T08:18:56.211874Z","submitted_at":"2026-07-30T20:13:40Z","title":"Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-03T00:25:53.359267Z"},"links":{"citing_paper":"/paper/2607.28811"},"observation_digest":"sha256:8a2f6a32214a80fdfa101baae37fcb289e7663e723dc71e119740b2e81f92cfe","observation_id":"30ec76a7-07f2-4d0e-a0d0-ea8ba1a2ff41","resolution":{"observed_at":"2026-08-03T00:25:53.359267Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T00:25:53.362169Z","title":"Failure of the crys- talline equivalence principle for weak free fermions.Physical Review B, 111(8):L081118, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.28811","last_updated":"2026-07-30T20:13:40Z","snapshot_observed_at":"2026-08-06T08:18:56.211874Z","submitted_at":"2026-07-30T20:13:40Z","title":"Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-03T00:25:53.362169Z"},"links":{"citing_paper":"/paper/2607.28811"},"observation_digest":"sha256:d5660acbde0aac930c2612ddf59f24cddd35c0d547c3cf1414c6fd1533ab0266","observation_id":"d4a63126-1ea9-469a-847d-cdb12c62fec6","resolution":{"observed_at":"2026-08-03T00:25:53.362169Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T00:25:53.364907Z","title":"Homotopy-theoretic approach to spt phases in action: Z16 classification of three-dimensional superconductors","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.28811","last_updated":"2026-07-30T20:13:40Z","snapshot_observed_at":"2026-08-06T08:18:56.211874Z","submitted_at":"2026-07-30T20:13:40Z","title":"Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-03T00:25:53.364907Z"},"links":{"citing_paper":"/paper/2607.28811"},"observation_digest":"sha256:6836beff2712a21278460199363c14e73b0ce0f9f1c33a5c2b6d8b9d18b06391","observation_id":"3ddee03b-a5d4-4d63-9322-22eedc8d06cc","resolution":{"observed_at":"2026-08-03T00:25:53.364907Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T00:25:53.367582Z","title":"Hatcher.Algebraic Topology","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.28811","last_updated":"2026-07-30T20:13:40Z","snapshot_observed_at":"2026-08-06T08:18:56.211874Z","submitted_at":"2026-07-30T20:13:40Z","title":"Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-03T00:25:53.367582Z"},"links":{"citing_paper":"/paper/2607.28811"},"observation_digest":"sha256:fc14bf6f0065d0654075efc9c814ebc4020a83d49cb87a4c136e3e456c9d963e","observation_id":"966ee3b0-8272-48d6-83c3-31ecc0638ec9","resolution":{"observed_at":"2026-08-03T00:25:53.367582Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T00:25:53.370196Z","title":"Equivariant stable homotopy theory","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2607.28811","last_updated":"2026-07-30T20:13:40Z","snapshot_observed_at":"2026-08-06T08:18:56.211874Z","submitted_at":"2026-07-30T20:13:40Z","title":"Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-03T00:25:53.370196Z"},"links":{"citing_paper":"/paper/2607.28811"},"observation_digest":"sha256:75c715d923d5db72cfe1c0d56ba8ca5714fa84a469ce00a9f86ff4e6790cf90b","observation_id":"5805452e-2dd2-4f18-aefb-0eeb900990c6","resolution":{"observed_at":"2026-08-03T00:25:53.370196Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T00:25:53.372837Z","title":"Invertible phases for mixed spatial symmetries and the fermionic crystalline equivalence principle.arXiv preprint arXiv:2102.02941, 2021","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.28811","last_updated":"2026-07-30T20:13:40Z","snapshot_observed_at":"2026-08-06T08:18:56.211874Z","submitted_at":"2026-07-30T20:13:40Z","title":"Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-03T00:25:53.372837Z"},"links":{"citing_paper":"/paper/2607.28811"},"observation_digest":"sha256:3e88110fb8c392a6b4d62eebe20dfd190e3ce4f125a515c482b5405c59e2f0b2","observation_id":"7d5dd2dd-d6f5-4a43-b7e7-e92eac93b357","resolution":{"observed_at":"2026-08-03T00:25:53.372837Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2508.10978","last_updated":"2026-06-07T20:20:31Z","snapshot_observed_at":"2026-08-05T20:10:38.800841Z","submitted_at":"2025-08-14T18:00:00Z","title":"A Generalized Crystalline Equivalence Principle","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2508.10978","snapshot_observed_at":"2026-08-03T00:25:53.375437Z","title":"A generalized crystalline equivalence principle.arXiv preprint arXiv:2508.10978, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.28811","last_updated":"2026-07-30T20:13:40Z","snapshot_observed_at":"2026-08-06T08:18:56.211874Z","submitted_at":"2026-07-30T20:13:40Z","title":"Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-03T00:25:53.375437Z"},"links":{"cited_paper":"/paper/2508.10978","citing_paper":"/paper/2607.28811"},"observation_digest":"sha256:a135d0102e1fc709615fa298002589ab71519e4272c4b17a19b939e2828f64e4","observation_id":"a5511b74-cb3a-478e-b431-581775533870","resolution":{"observed_at":"2026-08-03T00:25:53.375437Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2605.00316","last_updated":"2026-05-01T00:55:39Z","snapshot_observed_at":"2026-07-06T23:13:47.082550Z","submitted_at":"2026-05-01T00:55:39Z","title":"Unraveling the Bott spiral","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2605.00316","snapshot_observed_at":"2026-08-03T00:25:53.378483Z","title":"Unraveling the bott spiral.arXiv preprint arXiv:2605.00316, 2026","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.28811","last_updated":"2026-07-30T20:13:40Z","snapshot_observed_at":"2026-08-06T08:18:56.211874Z","submitted_at":"2026-07-30T20:13:40Z","title":"Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-03T00:25:53.378483Z"},"links":{"cited_paper":"/paper/2605.00316","citing_paper":"/paper/2607.28811"},"observation_digest":"sha256:54d8a959a9949eec5a64a8949b7701c6bd6c368a0d09ec17242c766684eb967a","observation_id":"28cc2b84-e2a9-4191-a931-70d1b9ea7c64","resolution":{"observed_at":"2026-08-03T00:25:53.378483Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T00:25:53.381685Z","title":"Crystallographic t-duality.Journal of Geometry and Physics, 139:50–77, 2019","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.28811","last_updated":"2026-07-30T20:13:40Z","snapshot_observed_at":"2026-08-06T08:18:56.211874Z","submitted_at":"2026-07-30T20:13:40Z","title":"Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-03T00:25:53.381685Z"},"links":{"citing_paper":"/paper/2607.28811"},"observation_digest":"sha256:452ccebf3022df9cc36328dd2a265cd07a634ef0afaa69ed834406d52272788b","observation_id":"7bec86a5-4256-4e13-ba1f-0248561c89f9","resolution":{"observed_at":"2026-08-03T00:25:53.381685Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T00:25:53.384535Z","title":"The equivariant cobordism category","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.28811","last_updated":"2026-07-30T20:13:40Z","snapshot_observed_at":"2026-08-06T08:18:56.211874Z","submitted_at":"2026-07-30T20:13:40Z","title":"Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-03T00:25:53.384535Z"},"links":{"citing_paper":"/paper/2607.28811"},"observation_digest":"sha256:c824c248a2a922180fae0757668a45ffd312a26127506d893d912565eb1c8881","observation_id":"2b9f9b89-9697-48eb-818e-03858fb47f20","resolution":{"observed_at":"2026-08-03T00:25:53.384535Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T00:25:53.387155Z","title":"Higher coherences for equivariant k-theory.Structured ring spectra, 315:87–114, 2004","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2607.28811","last_updated":"2026-07-30T20:13:40Z","snapshot_observed_at":"2026-08-06T08:18:56.211874Z","submitted_at":"2026-07-30T20:13:40Z","title":"Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-03T00:25:53.387155Z"},"links":{"citing_paper":"/paper/2607.28811"},"observation_digest":"sha256:b32edc801d255f8ebe676f229dfa3ae1ed5a31b63e69f47a432e916c251783d4","observation_id":"447b78a3-4279-4eb5-bf28-310b931e7700","resolution":{"observed_at":"2026-08-03T00:25:53.387155Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T00:25:53.389740Z","title":"Topological k–(co) homology of clas- sifying spaces of discrete groups.Algebraic & Geometric Topology, 13(1):1– 34, 2013","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.28811","last_updated":"2026-07-30T20:13:40Z","snapshot_observed_at":"2026-08-06T08:18:56.211874Z","submitted_at":"2026-07-30T20:13:40Z","title":"Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-03T00:25:53.389740Z"},"links":{"citing_paper":"/paper/2607.28811"},"observation_digest":"sha256:cd929989ddf50ae9e5ea3ce1dd500bb35f427725d992d163624c1c06e371df09","observation_id":"d1d75d67-2797-4318-9fc9-242c6dfff434","resolution":{"observed_at":"2026-08-03T00:25:53.389740Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T00:25:53.392478Z","title":"Twisted crystallo- graphic t-duality via the baum–connes isomorphism.International Journal of Mathematics, 32(10):2150078, 2021","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.28811","last_updated":"2026-07-30T20:13:40Z","snapshot_observed_at":"2026-08-06T08:18:56.211874Z","submitted_at":"2026-07-30T20:13:40Z","title":"Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-03T00:25:53.392478Z"},"links":{"citing_paper":"/paper/2607.28811"},"observation_digest":"sha256:e939342ba181d77dcd6643168875ef89c43b9e915b5eeab6ef9c0df404a9c895","observation_id":"6bf59116-adf1-4cb1-9a6c-4112affb72fd","resolution":{"observed_at":"2026-08-03T00:25:53.392478Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.28811","last_updated":"2026-07-30T20:13:40Z","latest_version":1,"primary_category":"math-ph","snapshot_observed_at":"2026-08-06T08:18:56.211874Z","submitted_at":"2026-07-30T20:13:40Z","title":"Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence"},"reference_resolution":{"displayed":24,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":24,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":24},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 0 inbound Pith citation observations for arXiv:2607.28811."}