{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:7HLJ7D63OGBKXH2WEXW6V66RX3","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":"d263c065dcda6ae6bb11d4e97f41f073e56cfda2c237b6471c239a4b3ed0df61","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-09-05T20:52:20Z","title_canon_sha256":"780c9db69766595df41c470ea16e9503dc1e6aaa208ad05123bfe085b89f9e54"},"schema_version":"1.0","source":{"id":"1909.02628","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.02628","created_at":"2026-07-05T02:43:50Z"},{"alias_kind":"arxiv_version","alias_value":"1909.02628v2","created_at":"2026-07-05T02:43:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.02628","created_at":"2026-07-05T02:43:50Z"},{"alias_kind":"pith_short_12","alias_value":"7HLJ7D63OGBK","created_at":"2026-07-05T02:43:50Z"},{"alias_kind":"pith_short_16","alias_value":"7HLJ7D63OGBKXH2W","created_at":"2026-07-05T02:43:50Z"},{"alias_kind":"pith_short_8","alias_value":"7HLJ7D63","created_at":"2026-07-05T02:43:50Z"}],"graph_snapshots":[{"event_id":"sha256:dedc82cb59fe37414c523af9e5b7e85eaa643fc5542dc951a1a2515397addd80","target":"graph","created_at":"2026-07-05T02:43:50Z","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/1909.02628/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The classical Kneser-Milnor theorem says that every closed oriented connected 3-dimensional manifold admits a unique connected sum decomposition into manifolds that cannot be decomposed any further. We discuss to what degree such decompositions exist in higher dimensions and we show that in many settings uniqueness fails in higher dimensions.","authors_text":"Daniel Kasprowski, Diarmuid Crowley, Fabian Hebestreit, Imre Bokor, Johnny Nicholson, Markus Land, Stefan Friedl","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-09-05T20:52:20Z","title":"Connected sum decompositions of high-dimensional manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.02628","kind":"arxiv","version":2},"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":"sha256:1b69e587b3a223d1cfc3f11325702dc477b48d94295d1aea644d6fc552d69044","target":"record","created_at":"2026-07-05T02:43:50Z","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":"d263c065dcda6ae6bb11d4e97f41f073e56cfda2c237b6471c239a4b3ed0df61","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-09-05T20:52:20Z","title_canon_sha256":"780c9db69766595df41c470ea16e9503dc1e6aaa208ad05123bfe085b89f9e54"},"schema_version":"1.0","source":{"id":"1909.02628","kind":"arxiv","version":2}},"canonical_sha256":"f9d69f8fdb7182ab9f5625edeafbd1bee1be7eb6ec2341218818494015afc10a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9d69f8fdb7182ab9f5625edeafbd1bee1be7eb6ec2341218818494015afc10a","first_computed_at":"2026-07-05T02:43:50.738780Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:43:50.738780Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rJUq1OrlhASr4ltfKCsSV7O1W/bdQ9OhWuAnRRY8AQVBxYT3rRyzEsNfP//B+qJEOWq2zy6lWrj4N26N8J+WBA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:43:50.739209Z","signed_message":"canonical_sha256_bytes"},"source_id":"1909.02628","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b69e587b3a223d1cfc3f11325702dc477b48d94295d1aea644d6fc552d69044","sha256:dedc82cb59fe37414c523af9e5b7e85eaa643fc5542dc951a1a2515397addd80"],"state_sha256":"413acc9ddcebb3394720d3b851d420eab90a85579da016efd2887ef16f34b59c"}