{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:A4NPKAH5W6TF2SYTUNUDP4CICZ","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":"276b54e33f08bb42f2d74dbbb0aa060372066abde5fd53a597c3ce104d64915e","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2009-10-29T14:30:12Z","title_canon_sha256":"b2bf75e62d18f3a255ff9112e58b09c3402ad8d554d55cb6a464baa7d8b220b4"},"schema_version":"1.0","source":{"id":"0910.5650","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.5650","created_at":"2026-05-18T04:21:21Z"},{"alias_kind":"arxiv_version","alias_value":"0910.5650v3","created_at":"2026-05-18T04:21:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.5650","created_at":"2026-05-18T04:21:21Z"},{"alias_kind":"pith_short_12","alias_value":"A4NPKAH5W6TF","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"A4NPKAH5W6TF2SYT","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"A4NPKAH5","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:1c513695d3e5d338e6b9b8842751db952ec2b43e85210b4dab70c06a3bdfb0b9","target":"graph","created_at":"2026-05-18T04:21:21Z","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"},"paper":{"abstract_excerpt":"We propose a homology theory for locally compact spaces with ends in which the ends play a special role. The approach is motivated by results for graphs with ends, where it has been highly successful. But it was unclear how the original graph-theoretical definition could be captured in the usual language for homology theories, so as to make it applicable to more general spaces. In this paper we provide such a general topological framework: we define a homology theory which satisfies the usual axioms, but which maintains the special role for ends that has made this homology work so well for gra","authors_text":"Philipp Spr\\\"ussel, Reinhard Diestel","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2009-10-29T14:30:12Z","title":"On the homology of locally compact spaces with ends"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.5650","kind":"arxiv","version":3},"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":"sha256:2ab965e803f041cb44afb82c4dc17f2a411e4807112b016f3911d921ec243c9a","target":"record","created_at":"2026-05-18T04:21:21Z","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":"276b54e33f08bb42f2d74dbbb0aa060372066abde5fd53a597c3ce104d64915e","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2009-10-29T14:30:12Z","title_canon_sha256":"b2bf75e62d18f3a255ff9112e58b09c3402ad8d554d55cb6a464baa7d8b220b4"},"schema_version":"1.0","source":{"id":"0910.5650","kind":"arxiv","version":3}},"canonical_sha256":"071af500fdb7a65d4b13a36837f048167f3821d5f67e73ca8967a4bd34a58674","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"071af500fdb7a65d4b13a36837f048167f3821d5f67e73ca8967a4bd34a58674","first_computed_at":"2026-05-18T04:21:21.574168Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:21:21.574168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2zmlSxJGHt0GOM7Z3gtJF4RUOstjiHemYMjWJO80/7U8LP95dgqq/espoBTxKAIxE+Hvj1K3GVlH+YXFkpncAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:21:21.574656Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.5650","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ab965e803f041cb44afb82c4dc17f2a411e4807112b016f3911d921ec243c9a","sha256:1c513695d3e5d338e6b9b8842751db952ec2b43e85210b4dab70c06a3bdfb0b9"],"state_sha256":"77e842bac5d9a3d31bf42153d02c36bfa515f6437394beea8a95b64f72c507ab"}