{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:44IVTK2DQ5KOYMGIZ7YRLVNMVY","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"2e54f354063f43d5add512d657d7a88f091f6abb0dc3fd6586356c35356879c0","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2021-02-16T17:08:14Z","title_canon_sha256":"93bc645eb2ca310dd11f9b65c669aef0343d78e7a8c989110bebcd5156dd0a99"},"schema_version":"1.0","source":{"id":"2102.08281","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.08281","created_at":"2026-07-05T04:00:13Z"},{"alias_kind":"arxiv_version","alias_value":"2102.08281v4","created_at":"2026-07-05T04:00:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.08281","created_at":"2026-07-05T04:00:13Z"},{"alias_kind":"pith_short_12","alias_value":"44IVTK2DQ5KO","created_at":"2026-07-05T04:00:13Z"},{"alias_kind":"pith_short_16","alias_value":"44IVTK2DQ5KOYMGI","created_at":"2026-07-05T04:00:13Z"},{"alias_kind":"pith_short_8","alias_value":"44IVTK2D","created_at":"2026-07-05T04:00:13Z"}],"graph_snapshots":[{"event_id":"sha256:de9bf8445cbdc88e132b50a5b0a3316dadb6f7906af2c76a1cc9be039f90f9d8","target":"graph","created_at":"2026-07-05T04:00:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2102.08281/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that TR is corepresentable by the reduced topological Hochschild homology of the flat affine line $\\mathbf{S}[t]$ as a functor defined on the $\\infty$-category of cyclotomic spectra with values in the $\\infty$-category of spectra with Frobenius lifts, refining a result of Blumberg-Mandell. We define the notion of an integral topological Cartier module using Barwick's formalism of spectral Mackey functors on orbital $\\infty$-categories, extending the work of Antieau-Nikolaus in the $p$-typical setting. As an application, we show that TR evaluated on a connective $\\mathbf{E}_1$-ring adm","authors_text":"Jonas McCandless","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2021-02-16T17:08:14Z","title":"On curves in K-theory and TR"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.08281","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:23d6f8cfa594c5a30bb5d281fe9185c8f796d2661e78ef0f58efe61f5675307e","target":"record","created_at":"2026-07-05T04:00:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"2e54f354063f43d5add512d657d7a88f091f6abb0dc3fd6586356c35356879c0","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2021-02-16T17:08:14Z","title_canon_sha256":"93bc645eb2ca310dd11f9b65c669aef0343d78e7a8c989110bebcd5156dd0a99"},"schema_version":"1.0","source":{"id":"2102.08281","kind":"arxiv","version":4}},"canonical_sha256":"e71159ab438754ec30c8cff115d5acae2467694d6d63a85ea704fcf46ca673da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e71159ab438754ec30c8cff115d5acae2467694d6d63a85ea704fcf46ca673da","first_computed_at":"2026-07-05T04:00:13.206043Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:00:13.206043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z/P15iW+kn88mJoiJkaHg7GNWsci/ARnuEE19UpHD6iFHBQPCM42LMF90W0kOc2Af2XiWkT0fs8NFt1+EtXOAA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:00:13.206462Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.08281","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23d6f8cfa594c5a30bb5d281fe9185c8f796d2661e78ef0f58efe61f5675307e","sha256:de9bf8445cbdc88e132b50a5b0a3316dadb6f7906af2c76a1cc9be039f90f9d8"],"state_sha256":"9c66643b231e6b2a1b994e4a94ce5470365cfcf3975b60fc3d190b07394afba0"}