{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZCNTX33WRGLNEWHG5WAY5RGA2B","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":"14b3d80f263ef491feb1196eeb615e50cbedf4703b35417cc13043d604f1ad1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-09-01T09:58:12Z","title_canon_sha256":"e31dab064a0f440117339c219af08a6f04682958f86b23f97ec4ba3ef797b3d5"},"schema_version":"1.0","source":{"id":"1509.00204","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.00204","created_at":"2026-05-18T01:34:14Z"},{"alias_kind":"arxiv_version","alias_value":"1509.00204v1","created_at":"2026-05-18T01:34:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.00204","created_at":"2026-05-18T01:34:14Z"},{"alias_kind":"pith_short_12","alias_value":"ZCNTX33WRGLN","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZCNTX33WRGLNEWHG","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZCNTX33W","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:1a8add7120c15357a4dd3a39fe0dcd5b943158847d6565490e3433af0edd2d4e","target":"graph","created_at":"2026-05-18T01:34:14Z","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":"Integral simplicial volume is a homotopy invariant of oriented closed connected manifolds, defined as the minimal weighted number of singular simplices needed to represent the fundamental class with integral coefficients. We show that odd-dimensional spheres are the only manifolds with integral simplicial volume equal to 1. Consequently, we obtain an elementary proof that, in general, the integral simplicial volume of (triangulated) manifolds is not computable.","authors_text":"Clara Loeh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-09-01T09:58:12Z","title":"Odd manifolds of small integral simplicial volume"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00204","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:ef40a1e9b39bbc04948c34a95f7849717be881622c3f58120bf0361cc06e2614","target":"record","created_at":"2026-05-18T01:34:14Z","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":"14b3d80f263ef491feb1196eeb615e50cbedf4703b35417cc13043d604f1ad1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-09-01T09:58:12Z","title_canon_sha256":"e31dab064a0f440117339c219af08a6f04682958f86b23f97ec4ba3ef797b3d5"},"schema_version":"1.0","source":{"id":"1509.00204","kind":"arxiv","version":1}},"canonical_sha256":"c89b3bef768996d258e6ed818ec4c0d045db016546c89c6e9e0f430dd499b634","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c89b3bef768996d258e6ed818ec4c0d045db016546c89c6e9e0f430dd499b634","first_computed_at":"2026-05-18T01:34:14.861800Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:14.861800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uO6omv72HNcs8ZAahpXu0MeOGEjnXKHYMJLs0MHCpvvykykQd9oMKn+0NqzfFey/aEeL4PEAGmUhVdmPwhYeBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:14.862562Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.00204","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef40a1e9b39bbc04948c34a95f7849717be881622c3f58120bf0361cc06e2614","sha256:1a8add7120c15357a4dd3a39fe0dcd5b943158847d6565490e3433af0edd2d4e"],"state_sha256":"12621d9bcefa419bb069bc9dbb57fbdc67502f122c564169cf0d2d69bc25cc77"}