{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:RVGTTX7OLWC4S5SIW3Q7WP3FG7","short_pith_number":"pith:RVGTTX7O","canonical_record":{"source":{"id":"1608.07783","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-28T08:13:49Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"dd275901dcb0d9029abf19ce1741ae868a65ddb80f4537e3e3ee18ffcb8f8b9a","abstract_canon_sha256":"b9cf9691a754cc51ac08cc63f47a3a5f16055606cbc53f7a255c3919b1baa808"},"schema_version":"1.0"},"canonical_sha256":"8d4d39dfee5d85c97648b6e1fb3f6537e89ff18155bcbad7659a95becf510686","source":{"kind":"arxiv","id":"1608.07783","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.07783","created_at":"2026-05-18T01:07:49Z"},{"alias_kind":"arxiv_version","alias_value":"1608.07783v1","created_at":"2026-05-18T01:07:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.07783","created_at":"2026-05-18T01:07:49Z"},{"alias_kind":"pith_short_12","alias_value":"RVGTTX7OLWC4","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RVGTTX7OLWC4S5SI","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RVGTTX7O","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:RVGTTX7OLWC4S5SIW3Q7WP3FG7","target":"record","payload":{"canonical_record":{"source":{"id":"1608.07783","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-28T08:13:49Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"dd275901dcb0d9029abf19ce1741ae868a65ddb80f4537e3e3ee18ffcb8f8b9a","abstract_canon_sha256":"b9cf9691a754cc51ac08cc63f47a3a5f16055606cbc53f7a255c3919b1baa808"},"schema_version":"1.0"},"canonical_sha256":"8d4d39dfee5d85c97648b6e1fb3f6537e89ff18155bcbad7659a95becf510686","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:49.933764Z","signature_b64":"2WrTGd6LCwhLY0aA6h8Xa0V31U1sgUWhJJI5Yd0zJwordJ7MmKX6fIKEX68StAFo1iAS5SK7E+lRTFrCOdD8AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d4d39dfee5d85c97648b6e1fb3f6537e89ff18155bcbad7659a95becf510686","last_reissued_at":"2026-05-18T01:07:49.932988Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:49.932988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.07783","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":"2026-05-18T01:07:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yqFoP7ghzRoojsHDGfnUhjE0j5+H8SasDWkOtaRqP0ne1JM7F9FIwxTj+w4RAgk81rzW+5+skVJRvK30vXLWDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:19:05.228231Z"},"content_sha256":"269c217007d514711a16642d11e208ab86248bd0e8d5e08151c0809ab06927cf","schema_version":"1.0","event_id":"sha256:269c217007d514711a16642d11e208ab86248bd0e8d5e08151c0809ab06927cf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:RVGTTX7OLWC4S5SIW3Q7WP3FG7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A generalized lower bound theorem for balanced manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CO","authors_text":"Connor Sawaske, Isabella Novik, Martina Juhnke-Kubitzke, Satoshi Murai","submitted_at":"2016-08-28T08:13:49Z","abstract_excerpt":"A simplicial complex of dimension $d-1$ is said to be balanced if its graph is $d$-colorable. Juhnke-Kubitzke and Murai proved an analogue of the generalized lower bound theorem for balanced simplicial polytopes. We establish a generalization of their result to balanced triangulations of closed homology manifolds and balanced triangulations of orientable homology manifolds with boundary under an additional assumption that all proper links of these triangulations have the weak Lefschetz property. As a corollary, we show that if $\\Delta$ is an arbitrary balanced triangulation of any closed homol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07783","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":"2026-05-18T01:07:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KoXTcXOZ+5l+jlcnz7JIK4Wnqs2VDLgKjy7JqfuAp+alSANeFwUHK+6/EqwFkRARw92y2GdFl426n48SVWwDAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:19:05.228925Z"},"content_sha256":"0e9ad3cb1204bc1f849982fa6da3ecd4da3213550944cbace549355d359e7297","schema_version":"1.0","event_id":"sha256:0e9ad3cb1204bc1f849982fa6da3ecd4da3213550944cbace549355d359e7297"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RVGTTX7OLWC4S5SIW3Q7WP3FG7/bundle.json","state_url":"https://pith.science/pith/RVGTTX7OLWC4S5SIW3Q7WP3FG7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RVGTTX7OLWC4S5SIW3Q7WP3FG7/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":"2026-06-08T17:19:05Z","links":{"resolver":"https://pith.science/pith/RVGTTX7OLWC4S5SIW3Q7WP3FG7","bundle":"https://pith.science/pith/RVGTTX7OLWC4S5SIW3Q7WP3FG7/bundle.json","state":"https://pith.science/pith/RVGTTX7OLWC4S5SIW3Q7WP3FG7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RVGTTX7OLWC4S5SIW3Q7WP3FG7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RVGTTX7OLWC4S5SIW3Q7WP3FG7","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":"b9cf9691a754cc51ac08cc63f47a3a5f16055606cbc53f7a255c3919b1baa808","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-28T08:13:49Z","title_canon_sha256":"dd275901dcb0d9029abf19ce1741ae868a65ddb80f4537e3e3ee18ffcb8f8b9a"},"schema_version":"1.0","source":{"id":"1608.07783","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.07783","created_at":"2026-05-18T01:07:49Z"},{"alias_kind":"arxiv_version","alias_value":"1608.07783v1","created_at":"2026-05-18T01:07:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.07783","created_at":"2026-05-18T01:07:49Z"},{"alias_kind":"pith_short_12","alias_value":"RVGTTX7OLWC4","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RVGTTX7OLWC4S5SI","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RVGTTX7O","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:0e9ad3cb1204bc1f849982fa6da3ecd4da3213550944cbace549355d359e7297","target":"graph","created_at":"2026-05-18T01:07:49Z","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":"A simplicial complex of dimension $d-1$ is said to be balanced if its graph is $d$-colorable. Juhnke-Kubitzke and Murai proved an analogue of the generalized lower bound theorem for balanced simplicial polytopes. We establish a generalization of their result to balanced triangulations of closed homology manifolds and balanced triangulations of orientable homology manifolds with boundary under an additional assumption that all proper links of these triangulations have the weak Lefschetz property. As a corollary, we show that if $\\Delta$ is an arbitrary balanced triangulation of any closed homol","authors_text":"Connor Sawaske, Isabella Novik, Martina Juhnke-Kubitzke, Satoshi Murai","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-28T08:13:49Z","title":"A generalized lower bound theorem for balanced manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07783","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":"sha256:269c217007d514711a16642d11e208ab86248bd0e8d5e08151c0809ab06927cf","target":"record","created_at":"2026-05-18T01:07:49Z","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":"b9cf9691a754cc51ac08cc63f47a3a5f16055606cbc53f7a255c3919b1baa808","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-28T08:13:49Z","title_canon_sha256":"dd275901dcb0d9029abf19ce1741ae868a65ddb80f4537e3e3ee18ffcb8f8b9a"},"schema_version":"1.0","source":{"id":"1608.07783","kind":"arxiv","version":1}},"canonical_sha256":"8d4d39dfee5d85c97648b6e1fb3f6537e89ff18155bcbad7659a95becf510686","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d4d39dfee5d85c97648b6e1fb3f6537e89ff18155bcbad7659a95becf510686","first_computed_at":"2026-05-18T01:07:49.932988Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:07:49.932988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2WrTGd6LCwhLY0aA6h8Xa0V31U1sgUWhJJI5Yd0zJwordJ7MmKX6fIKEX68StAFo1iAS5SK7E+lRTFrCOdD8AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:07:49.933764Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.07783","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:269c217007d514711a16642d11e208ab86248bd0e8d5e08151c0809ab06927cf","sha256:0e9ad3cb1204bc1f849982fa6da3ecd4da3213550944cbace549355d359e7297"],"state_sha256":"354feda8cb8b736e205258cd140a414fdc9e7170f83462d5f1679564f50efd0c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cZjhOqtf02UmP4q8BoPZuOID4YKFMwGh+O/gO88TTNBA2Nksu+RpuAlpJKmB7Vpy2frpyfovcoqElYRoN8I5AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T17:19:05.232841Z","bundle_sha256":"cbd24e8f6b2a4f90d3bda292836743fe02d1153952dbc138d857e386e36557ca"}}