{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:JHXOLCTOB7XX3AXTVAMNWF7RA2","short_pith_number":"pith:JHXOLCTO","canonical_record":{"source":{"id":"2009.07224","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2020-09-15T17:04:15Z","cross_cats_sorted":["math.AT","math.CT"],"title_canon_sha256":"00b7e0936097b0fd0043d4fe7091e383adb4859a74c22e7b24015b824fac41c2","abstract_canon_sha256":"2e9ca297c918489cee0a56100b8837192a1a10ef837d0144880d0dbd1be809dc"},"schema_version":"1.0"},"canonical_sha256":"49eee58a6e0fef7d82f3a818db17f1068082f09107c9044b10dc82ad9fd1cd4c","source":{"kind":"arxiv","id":"2009.07224","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.07224","created_at":"2026-07-05T10:47:22Z"},{"alias_kind":"arxiv_version","alias_value":"2009.07224v5","created_at":"2026-07-05T10:47:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.07224","created_at":"2026-07-05T10:47:22Z"},{"alias_kind":"pith_short_12","alias_value":"JHXOLCTOB7XX","created_at":"2026-07-05T10:47:22Z"},{"alias_kind":"pith_short_16","alias_value":"JHXOLCTOB7XX3AXT","created_at":"2026-07-05T10:47:22Z"},{"alias_kind":"pith_short_8","alias_value":"JHXOLCTO","created_at":"2026-07-05T10:47:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:JHXOLCTOB7XX3AXTVAMNWF7RA2","target":"record","payload":{"canonical_record":{"source":{"id":"2009.07224","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2020-09-15T17:04:15Z","cross_cats_sorted":["math.AT","math.CT"],"title_canon_sha256":"00b7e0936097b0fd0043d4fe7091e383adb4859a74c22e7b24015b824fac41c2","abstract_canon_sha256":"2e9ca297c918489cee0a56100b8837192a1a10ef837d0144880d0dbd1be809dc"},"schema_version":"1.0"},"canonical_sha256":"49eee58a6e0fef7d82f3a818db17f1068082f09107c9044b10dc82ad9fd1cd4c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:47:22.973417Z","signature_b64":"6qJCl2widDC2Mf0bNTe1gHA3LiX/l03crW4ulEuCyDe54KmsnMtP7pkLjnBdGFKkMl3K8xne4IBgUla24L7DCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49eee58a6e0fef7d82f3a818db17f1068082f09107c9044b10dc82ad9fd1cd4c","last_reissued_at":"2026-07-05T10:47:22.972792Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:47:22.972792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2009.07224","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:47:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fjAMgnpbfdcPi/ONHVh4J8K0zk0UH6bSu9IVGZSKrXtZ12RvIJorsaWlYZ1yyr9xYaAT7EMhVLZxEZgRHiVrBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T02:06:51.583009Z"},"content_sha256":"e3092549f757995abd0d1f2c817fff765e5ab7c9c3dc50f1485513a77308ba4a","schema_version":"1.0","event_id":"sha256:e3092549f757995abd0d1f2c817fff765e5ab7c9c3dc50f1485513a77308ba4a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:JHXOLCTOB7XX3AXTVAMNWF7RA2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hermitian K-theory for stable $\\infty$-categories II: Cobordism categories and additivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CT"],"primary_cat":"math.KT","authors_text":"Baptiste Calm\\`es, Denis Nardin, Emanuele Dotto, Fabian Hebestreit, Kristian Moi, Markus Land, Thomas Nikolaus, Wolfgang Steimle, Yonatan Harpaz","submitted_at":"2020-09-15T17:04:15Z","abstract_excerpt":"We define Grothendieck-Witt spectra in the setting of Poincar\\'e $\\infty$-categories and show that they fit into an extension with a K- and an L-theoretic part. As consequences we deduce localisation sequences for Verdier quotients, and generalisations of Karoubi's fundamental and periodicity theorems for rings in which 2 need not be invertible. Our set-up allows for the uniform treatment of such algebraic examples alongside homotopy-theoretic generalisations: For example, the periodicity theorem holds for complex oriented $\\mathrm{E}_1$-rings, and we show that the Grothendieck-Witt theory of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.07224","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2009.07224/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:47:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yfzd8Pq8u2lS4FFHH31yb0Nt8VL87f33tAdnXdpHPvpF8yWM/vCqYVOwjOyfeWWHkkeydAYHdt+vpDa/7NFtCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T02:06:51.583505Z"},"content_sha256":"fea98cafb26b185512801b1befba47879ddc64de4f47376328e5f9ac68727576","schema_version":"1.0","event_id":"sha256:fea98cafb26b185512801b1befba47879ddc64de4f47376328e5f9ac68727576"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JHXOLCTOB7XX3AXTVAMNWF7RA2/bundle.json","state_url":"https://pith.science/pith/JHXOLCTOB7XX3AXTVAMNWF7RA2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JHXOLCTOB7XX3AXTVAMNWF7RA2/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-09T02:06:51Z","links":{"resolver":"https://pith.science/pith/JHXOLCTOB7XX3AXTVAMNWF7RA2","bundle":"https://pith.science/pith/JHXOLCTOB7XX3AXTVAMNWF7RA2/bundle.json","state":"https://pith.science/pith/JHXOLCTOB7XX3AXTVAMNWF7RA2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JHXOLCTOB7XX3AXTVAMNWF7RA2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:JHXOLCTOB7XX3AXTVAMNWF7RA2","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":"2e9ca297c918489cee0a56100b8837192a1a10ef837d0144880d0dbd1be809dc","cross_cats_sorted":["math.AT","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2020-09-15T17:04:15Z","title_canon_sha256":"00b7e0936097b0fd0043d4fe7091e383adb4859a74c22e7b24015b824fac41c2"},"schema_version":"1.0","source":{"id":"2009.07224","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.07224","created_at":"2026-07-05T10:47:22Z"},{"alias_kind":"arxiv_version","alias_value":"2009.07224v5","created_at":"2026-07-05T10:47:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.07224","created_at":"2026-07-05T10:47:22Z"},{"alias_kind":"pith_short_12","alias_value":"JHXOLCTOB7XX","created_at":"2026-07-05T10:47:22Z"},{"alias_kind":"pith_short_16","alias_value":"JHXOLCTOB7XX3AXT","created_at":"2026-07-05T10:47:22Z"},{"alias_kind":"pith_short_8","alias_value":"JHXOLCTO","created_at":"2026-07-05T10:47:22Z"}],"graph_snapshots":[{"event_id":"sha256:fea98cafb26b185512801b1befba47879ddc64de4f47376328e5f9ac68727576","target":"graph","created_at":"2026-07-05T10:47:22Z","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/2009.07224/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We define Grothendieck-Witt spectra in the setting of Poincar\\'e $\\infty$-categories and show that they fit into an extension with a K- and an L-theoretic part. As consequences we deduce localisation sequences for Verdier quotients, and generalisations of Karoubi's fundamental and periodicity theorems for rings in which 2 need not be invertible. Our set-up allows for the uniform treatment of such algebraic examples alongside homotopy-theoretic generalisations: For example, the periodicity theorem holds for complex oriented $\\mathrm{E}_1$-rings, and we show that the Grothendieck-Witt theory of ","authors_text":"Baptiste Calm\\`es, Denis Nardin, Emanuele Dotto, Fabian Hebestreit, Kristian Moi, Markus Land, Thomas Nikolaus, Wolfgang Steimle, Yonatan Harpaz","cross_cats":["math.AT","math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2020-09-15T17:04:15Z","title":"Hermitian K-theory for stable $\\infty$-categories II: Cobordism categories and additivity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.07224","kind":"arxiv","version":5},"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:e3092549f757995abd0d1f2c817fff765e5ab7c9c3dc50f1485513a77308ba4a","target":"record","created_at":"2026-07-05T10:47:22Z","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":"2e9ca297c918489cee0a56100b8837192a1a10ef837d0144880d0dbd1be809dc","cross_cats_sorted":["math.AT","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2020-09-15T17:04:15Z","title_canon_sha256":"00b7e0936097b0fd0043d4fe7091e383adb4859a74c22e7b24015b824fac41c2"},"schema_version":"1.0","source":{"id":"2009.07224","kind":"arxiv","version":5}},"canonical_sha256":"49eee58a6e0fef7d82f3a818db17f1068082f09107c9044b10dc82ad9fd1cd4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"49eee58a6e0fef7d82f3a818db17f1068082f09107c9044b10dc82ad9fd1cd4c","first_computed_at":"2026-07-05T10:47:22.972792Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:47:22.972792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6qJCl2widDC2Mf0bNTe1gHA3LiX/l03crW4ulEuCyDe54KmsnMtP7pkLjnBdGFKkMl3K8xne4IBgUla24L7DCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:47:22.973417Z","signed_message":"canonical_sha256_bytes"},"source_id":"2009.07224","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3092549f757995abd0d1f2c817fff765e5ab7c9c3dc50f1485513a77308ba4a","sha256:fea98cafb26b185512801b1befba47879ddc64de4f47376328e5f9ac68727576"],"state_sha256":"2e5b23c0f83bd7e3e33c113bfd131bb756f39cca33a3ff79b59e61291d17884d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Z6UlrIHraTE1RT5aHTN1RfdtbxtrmUiafadVvtuXSk2+WX8MLZmDJz1nZbSLTHhZJvmgkHtEXB3UJTN9iFrDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T02:06:51.588600Z","bundle_sha256":"7f03f364d52003ff97e1bb55b0fb3688a4d6d2fad67218c66890fbc503265826"}}