{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FI3REXNWYOVC75XEW7QDR6LYPF","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":"49a9d02c123557fafab1454272abb6564ce3d295cfdfb51baa4803543fc54f78","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-11-30T17:55:27Z","title_canon_sha256":"424e479986ebcad433500cccbc6c13f9583eb1a7722fa66cbdd0911e48070d0b"},"schema_version":"1.0","source":{"id":"1711.11537","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.11537","created_at":"2026-05-18T00:29:11Z"},{"alias_kind":"arxiv_version","alias_value":"1711.11537v1","created_at":"2026-05-18T00:29:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.11537","created_at":"2026-05-18T00:29:11Z"},{"alias_kind":"pith_short_12","alias_value":"FI3REXNWYOVC","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FI3REXNWYOVC75XE","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FI3REXNW","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:278bcf65b1d55554dfcd21c103a3a5e5a772e1cd1c9e95ada3cacee57fef08bb","target":"graph","created_at":"2026-05-18T00:29:11Z","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":"The decomposability of a Cartesian product of two nondecomposable manifolds into products of lower dimensional manifolds is studied. For 3-manifolds we obtain an analog of a result due to Borsuk for surfaces, and in higher dimensions we show that similar analogs do not exist unless one imposes further restrictions such as simple connectivity.","authors_text":"Reinhard Schultz, Slawomir Kwasik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-11-30T17:55:27Z","title":"Decomposing manifolds into Cartesian products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.11537","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":"sha256:1f62c5a04bc638c1431bc37485922c5f0c4633078f9ddcb896df0c0330bd6a73","target":"record","created_at":"2026-05-18T00:29:11Z","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":"49a9d02c123557fafab1454272abb6564ce3d295cfdfb51baa4803543fc54f78","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-11-30T17:55:27Z","title_canon_sha256":"424e479986ebcad433500cccbc6c13f9583eb1a7722fa66cbdd0911e48070d0b"},"schema_version":"1.0","source":{"id":"1711.11537","kind":"arxiv","version":1}},"canonical_sha256":"2a37125db6c3aa2ff6e4b7e038f978797dc7211f9065cc1f744faa8b144f34cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a37125db6c3aa2ff6e4b7e038f978797dc7211f9065cc1f744faa8b144f34cc","first_computed_at":"2026-05-18T00:29:11.326686Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:11.326686Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TdYoUPWwVPJFZKNfJZuGpIlVk8XTScxo428RHOjQ1L8FO7NHBJykYGmk3mWsULvttty6uU73ZUwpANirMfKwBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:11.327345Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.11537","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f62c5a04bc638c1431bc37485922c5f0c4633078f9ddcb896df0c0330bd6a73","sha256:278bcf65b1d55554dfcd21c103a3a5e5a772e1cd1c9e95ada3cacee57fef08bb"],"state_sha256":"6fb4bd8c84685c225717035aadcc4a1e6e433ea58a10f432262e7ff034752175"}