{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:O4ZMLME3ZUCUJM6GIEDXRIADQJ","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":"efdb862b4ec89faa89696ab6a2f3a8fe1c19cd41000c1736449a241202a86c35","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-04-27T13:04:28Z","title_canon_sha256":"fe96c80078d49b318ce16ff0b747cc0e6c87679b14eb8116cc45fcad8674d755"},"schema_version":"1.0","source":{"id":"1204.6198","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.6198","created_at":"2026-05-18T03:56:46Z"},{"alias_kind":"arxiv_version","alias_value":"1204.6198v1","created_at":"2026-05-18T03:56:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.6198","created_at":"2026-05-18T03:56:46Z"},{"alias_kind":"pith_short_12","alias_value":"O4ZMLME3ZUCU","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"O4ZMLME3ZUCUJM6G","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"O4ZMLME3","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:90f52a589974e2f2bf5b31dcd3a2b869c00171d5e016c77c83eb161f418dff5f","target":"graph","created_at":"2026-05-18T03:56:46Z","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":"Measure homology was introduced by Thurston in order to compute the simplicial volume of hyperbolic manifolds. Berlanga endowed measure homology with a structure of graded locally convex (possibly non-Hausdorff) topological vector space. In this note we completely characterize Berlanga's topology on measure homology of CW-complexes, showing in particular that it is Hausdorff. This answers a question posed by Berlanga.","authors_text":"Roberto Frigerio","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-04-27T13:04:28Z","title":"A note on measure homology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.6198","kind":"arxiv","version":1},"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":"sha256:56d1cf70ec6bd176ebe920a57cf424806c2a554f86ffa5aa41b87ad7a0d807fa","target":"record","created_at":"2026-05-18T03:56:46Z","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":"efdb862b4ec89faa89696ab6a2f3a8fe1c19cd41000c1736449a241202a86c35","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-04-27T13:04:28Z","title_canon_sha256":"fe96c80078d49b318ce16ff0b747cc0e6c87679b14eb8116cc45fcad8674d755"},"schema_version":"1.0","source":{"id":"1204.6198","kind":"arxiv","version":1}},"canonical_sha256":"7732c5b09bcd0544b3c6410778a0038278d52cbdb4542283b524a76ad3e54055","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7732c5b09bcd0544b3c6410778a0038278d52cbdb4542283b524a76ad3e54055","first_computed_at":"2026-05-18T03:56:46.791687Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:46.791687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Noitgpc7McKLPuTQdiY28xupaYmKrlYicDVVErjvqAXZiINtvfJ2P49JKnX/Y3yCiT2NpdRdJeKl2j2MCx+vBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:46.792233Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.6198","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56d1cf70ec6bd176ebe920a57cf424806c2a554f86ffa5aa41b87ad7a0d807fa","sha256:90f52a589974e2f2bf5b31dcd3a2b869c00171d5e016c77c83eb161f418dff5f"],"state_sha256":"e48f0bf7f51f012ece6ef9a40c462c264aeb5f06ef08b1ef9b5e90169b8a04cc"}