{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:UO3SYJKVQVW5FCJATJAQADAGX4","short_pith_number":"pith:UO3SYJKV","canonical_record":{"source":{"id":"1201.5790","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-01-27T15:13:57Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"de0c3e2b9a4cb35df14896b52a8ab5e3bb206679d0f320544a25c00eade81747","abstract_canon_sha256":"00c5044bc7121fe9cd463e78fd9bf15ee64242f5ccadd0ed0a28fa0edc62ef13"},"schema_version":"1.0"},"canonical_sha256":"a3b72c2555856dd289209a41000c06bf0234b18daf7388adf9e38013515c0986","source":{"kind":"arxiv","id":"1201.5790","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.5790","created_at":"2026-05-18T04:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"1201.5790v1","created_at":"2026-05-18T04:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.5790","created_at":"2026-05-18T04:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"UO3SYJKVQVW5","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UO3SYJKVQVW5FCJA","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UO3SYJKV","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:UO3SYJKVQVW5FCJATJAQADAGX4","target":"record","payload":{"canonical_record":{"source":{"id":"1201.5790","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-01-27T15:13:57Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"de0c3e2b9a4cb35df14896b52a8ab5e3bb206679d0f320544a25c00eade81747","abstract_canon_sha256":"00c5044bc7121fe9cd463e78fd9bf15ee64242f5ccadd0ed0a28fa0edc62ef13"},"schema_version":"1.0"},"canonical_sha256":"a3b72c2555856dd289209a41000c06bf0234b18daf7388adf9e38013515c0986","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:03:44.504173Z","signature_b64":"k3WX3lTLDJM3Bs+3hf/IXo/bBJP+dEBed6KSnQdE1V+vPq6mCVUXofW+a4oGtEjEDUsNUz9YrQJXUbGkpxifBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3b72c2555856dd289209a41000c06bf0234b18daf7388adf9e38013515c0986","last_reissued_at":"2026-05-18T04:03:44.503375Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:03:44.503375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.5790","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:03:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dWJejLfBETqaxli1MssCmnN14SVuBFEsNZFKHMwwr7Avmz8sEIuULQgQ6AaLwMg/T7bzadOkHHVm1DnjotRpDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T00:09:05.924132Z"},"content_sha256":"b8f8f9b40d2b475bdcc6d09edfad72d9a09ea5bbf94323454862589372395b7a","schema_version":"1.0","event_id":"sha256:b8f8f9b40d2b475bdcc6d09edfad72d9a09ea5bbf94323454862589372395b7a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:UO3SYJKVQVW5FCJATJAQADAGX4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Face numbers of centrally symmetric polytopes from split graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"G\\\"unter M. Ziegler, Matthias Henze, Moritz W. Schmitt, Ragnar Freij","submitted_at":"2012-01-27T15:13:57Z","abstract_excerpt":"We analyze a remarkable class of centrally symmetric polytopes, the Hansen polytopes of split graphs. We confirm Kalai's 3^d-conjecture for such polytopes (they all have at least 3^d nonempty faces) and show that the Hanner polytopes among them (which have exactly 3^d nonempty faces) correspond to threshold graphs. Our study produces a new family of Hansen polytopes that have only 3^d+16 nonempty faces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5790","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:03:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vBmfe5RVvjDOK6FKNtuF0dcAhc6mpmw9k5cHklrwhzazHpAuq81OJSPqfHyLbHMBYc9GdDhFaEtGsK3wjGe9DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T00:09:05.924573Z"},"content_sha256":"f6a7ca205e6228ce30230b515ba0f579867bdb484438849e272863155cf52b0f","schema_version":"1.0","event_id":"sha256:f6a7ca205e6228ce30230b515ba0f579867bdb484438849e272863155cf52b0f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UO3SYJKVQVW5FCJATJAQADAGX4/bundle.json","state_url":"https://pith.science/pith/UO3SYJKVQVW5FCJATJAQADAGX4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UO3SYJKVQVW5FCJATJAQADAGX4/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T00:09:05Z","links":{"resolver":"https://pith.science/pith/UO3SYJKVQVW5FCJATJAQADAGX4","bundle":"https://pith.science/pith/UO3SYJKVQVW5FCJATJAQADAGX4/bundle.json","state":"https://pith.science/pith/UO3SYJKVQVW5FCJATJAQADAGX4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UO3SYJKVQVW5FCJATJAQADAGX4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UO3SYJKVQVW5FCJATJAQADAGX4","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":"00c5044bc7121fe9cd463e78fd9bf15ee64242f5ccadd0ed0a28fa0edc62ef13","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-01-27T15:13:57Z","title_canon_sha256":"de0c3e2b9a4cb35df14896b52a8ab5e3bb206679d0f320544a25c00eade81747"},"schema_version":"1.0","source":{"id":"1201.5790","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.5790","created_at":"2026-05-18T04:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"1201.5790v1","created_at":"2026-05-18T04:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.5790","created_at":"2026-05-18T04:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"UO3SYJKVQVW5","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UO3SYJKVQVW5FCJA","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UO3SYJKV","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:f6a7ca205e6228ce30230b515ba0f579867bdb484438849e272863155cf52b0f","target":"graph","created_at":"2026-05-18T04:03:44Z","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 analyze a remarkable class of centrally symmetric polytopes, the Hansen polytopes of split graphs. We confirm Kalai's 3^d-conjecture for such polytopes (they all have at least 3^d nonempty faces) and show that the Hanner polytopes among them (which have exactly 3^d nonempty faces) correspond to threshold graphs. Our study produces a new family of Hansen polytopes that have only 3^d+16 nonempty faces.","authors_text":"G\\\"unter M. Ziegler, Matthias Henze, Moritz W. Schmitt, Ragnar Freij","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-01-27T15:13:57Z","title":"Face numbers of centrally symmetric polytopes from split graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5790","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:b8f8f9b40d2b475bdcc6d09edfad72d9a09ea5bbf94323454862589372395b7a","target":"record","created_at":"2026-05-18T04:03:44Z","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":"00c5044bc7121fe9cd463e78fd9bf15ee64242f5ccadd0ed0a28fa0edc62ef13","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-01-27T15:13:57Z","title_canon_sha256":"de0c3e2b9a4cb35df14896b52a8ab5e3bb206679d0f320544a25c00eade81747"},"schema_version":"1.0","source":{"id":"1201.5790","kind":"arxiv","version":1}},"canonical_sha256":"a3b72c2555856dd289209a41000c06bf0234b18daf7388adf9e38013515c0986","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3b72c2555856dd289209a41000c06bf0234b18daf7388adf9e38013515c0986","first_computed_at":"2026-05-18T04:03:44.503375Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:44.503375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k3WX3lTLDJM3Bs+3hf/IXo/bBJP+dEBed6KSnQdE1V+vPq6mCVUXofW+a4oGtEjEDUsNUz9YrQJXUbGkpxifBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:44.504173Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.5790","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b8f8f9b40d2b475bdcc6d09edfad72d9a09ea5bbf94323454862589372395b7a","sha256:f6a7ca205e6228ce30230b515ba0f579867bdb484438849e272863155cf52b0f"],"state_sha256":"47c0c20c9fe40bbbc67c64038ec56894e4581d834ed1b86edc83af1817a9685b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/kgZPZ32g1gefMHxMDMEMT3YJhpKj2CRxIb58gs1NDib1dRU6+hzKfz1KSbIsmM5mN/Zd54uuSCni3MxVL0lBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T00:09:05.927809Z","bundle_sha256":"95673c1f8beb0e4ab9372b1f64f6c9ded0e5d22c2b93cdb5a060cbc196f1d682"}}