{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:JEG7S6UGFBXHFXCMFR36BFJWP5","short_pith_number":"pith:JEG7S6UG","canonical_record":{"source":{"id":"0802.3747","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2008-02-26T05:26:11Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"190dec85fec30a3617a5198548dfd88a35473b8aec113a1c5190df7b218d1766","abstract_canon_sha256":"071a01cb4bd25e0d030e93f9d3f5cdff54c2a918553966f6d046f58664f44834"},"schema_version":"1.0"},"canonical_sha256":"490df97a86286e72dc4c2c77e095367f772f3d2b9ba3dc2b008f9be4c58d2a94","source":{"kind":"arxiv","id":"0802.3747","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0802.3747","created_at":"2026-05-18T04:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"0802.3747v3","created_at":"2026-05-18T04:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0802.3747","created_at":"2026-05-18T04:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"JEG7S6UGFBXH","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"JEG7S6UGFBXHFXCM","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"JEG7S6UG","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:JEG7S6UGFBXHFXCMFR36BFJWP5","target":"record","payload":{"canonical_record":{"source":{"id":"0802.3747","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2008-02-26T05:26:11Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"190dec85fec30a3617a5198548dfd88a35473b8aec113a1c5190df7b218d1766","abstract_canon_sha256":"071a01cb4bd25e0d030e93f9d3f5cdff54c2a918553966f6d046f58664f44834"},"schema_version":"1.0"},"canonical_sha256":"490df97a86286e72dc4c2c77e095367f772f3d2b9ba3dc2b008f9be4c58d2a94","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:03:44.122812Z","signature_b64":"LcJ3n7gokH5FCGGbtIWiIhemHO0+FZmNXBMRIGSVQf+Zru+nl0R96xGgJZRlq0XPS99KbZq4D5fPf56oMAX5Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"490df97a86286e72dc4c2c77e095367f772f3d2b9ba3dc2b008f9be4c58d2a94","last_reissued_at":"2026-05-18T04:03:44.122050Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:03:44.122050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0802.3747","source_version":3,"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":"yLwdmtodo8kV9Cs3XhTQt9/bgs2MIquNG9N/R26UaMXJj1UmXUY++AdhE/b6DQq+QWuELzQsXCRaGORkAm+dCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:30:11.562988Z"},"content_sha256":"01727ed0e32abfc8ea6347fc3467bd780e288f59bfbb5b65a5de99b9a8ce472c","schema_version":"1.0","event_id":"sha256:01727ed0e32abfc8ea6347fc3467bd780e288f59bfbb5b65a5de99b9a8ce472c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:JEG7S6UGFBXHFXCMFR36BFJWP5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lower bound theorem for normal pseudomanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GT","authors_text":"Basudeb Datta, Bhaskar Bagchi","submitted_at":"2008-02-26T05:26:11Z","abstract_excerpt":"In this paper we present a self-contained combinatorial proof of the lower bound theorem for normal pseudomanifolds, including a treatment of the cases of equality in this theorem. We also discuss McMullen and Walkup's generalised lower bound conjecture for triangulated spheres in the context of the lower bound theorem. Finally, we pose a new lower bound conjecture for non-simply connected triangulated manifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.3747","kind":"arxiv","version":3},"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":"8ctslXsKN2Qqze9fFAIHA7+M5o2lmqZ7vG+q+bdcUv3Ela9WWDPmVH4Xo1YYcCAtkW5sN2yK8JLNuFFwTAH4Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:30:11.563705Z"},"content_sha256":"4418ae33c726d4c531a7c8e887bbc816a31a3b6f2182e1102f9962e84bf6b53a","schema_version":"1.0","event_id":"sha256:4418ae33c726d4c531a7c8e887bbc816a31a3b6f2182e1102f9962e84bf6b53a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JEG7S6UGFBXHFXCMFR36BFJWP5/bundle.json","state_url":"https://pith.science/pith/JEG7S6UGFBXHFXCMFR36BFJWP5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JEG7S6UGFBXHFXCMFR36BFJWP5/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":"2026-05-26T07:30:11Z","links":{"resolver":"https://pith.science/pith/JEG7S6UGFBXHFXCMFR36BFJWP5","bundle":"https://pith.science/pith/JEG7S6UGFBXHFXCMFR36BFJWP5/bundle.json","state":"https://pith.science/pith/JEG7S6UGFBXHFXCMFR36BFJWP5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JEG7S6UGFBXHFXCMFR36BFJWP5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:JEG7S6UGFBXHFXCMFR36BFJWP5","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":"071a01cb4bd25e0d030e93f9d3f5cdff54c2a918553966f6d046f58664f44834","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2008-02-26T05:26:11Z","title_canon_sha256":"190dec85fec30a3617a5198548dfd88a35473b8aec113a1c5190df7b218d1766"},"schema_version":"1.0","source":{"id":"0802.3747","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0802.3747","created_at":"2026-05-18T04:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"0802.3747v3","created_at":"2026-05-18T04:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0802.3747","created_at":"2026-05-18T04:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"JEG7S6UGFBXH","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"JEG7S6UGFBXHFXCM","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"JEG7S6UG","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:4418ae33c726d4c531a7c8e887bbc816a31a3b6f2182e1102f9962e84bf6b53a","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":"In this paper we present a self-contained combinatorial proof of the lower bound theorem for normal pseudomanifolds, including a treatment of the cases of equality in this theorem. We also discuss McMullen and Walkup's generalised lower bound conjecture for triangulated spheres in the context of the lower bound theorem. Finally, we pose a new lower bound conjecture for non-simply connected triangulated manifolds.","authors_text":"Basudeb Datta, Bhaskar Bagchi","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2008-02-26T05:26:11Z","title":"Lower bound theorem for normal pseudomanifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.3747","kind":"arxiv","version":3},"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":"sha256:01727ed0e32abfc8ea6347fc3467bd780e288f59bfbb5b65a5de99b9a8ce472c","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":"071a01cb4bd25e0d030e93f9d3f5cdff54c2a918553966f6d046f58664f44834","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2008-02-26T05:26:11Z","title_canon_sha256":"190dec85fec30a3617a5198548dfd88a35473b8aec113a1c5190df7b218d1766"},"schema_version":"1.0","source":{"id":"0802.3747","kind":"arxiv","version":3}},"canonical_sha256":"490df97a86286e72dc4c2c77e095367f772f3d2b9ba3dc2b008f9be4c58d2a94","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"490df97a86286e72dc4c2c77e095367f772f3d2b9ba3dc2b008f9be4c58d2a94","first_computed_at":"2026-05-18T04:03:44.122050Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:44.122050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LcJ3n7gokH5FCGGbtIWiIhemHO0+FZmNXBMRIGSVQf+Zru+nl0R96xGgJZRlq0XPS99KbZq4D5fPf56oMAX5Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:44.122812Z","signed_message":"canonical_sha256_bytes"},"source_id":"0802.3747","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01727ed0e32abfc8ea6347fc3467bd780e288f59bfbb5b65a5de99b9a8ce472c","sha256:4418ae33c726d4c531a7c8e887bbc816a31a3b6f2182e1102f9962e84bf6b53a"],"state_sha256":"3c85ea5f20070b185f4c17f1e946a2a8670d9290a41de4361c3f5550a8953ec4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cBHJlm/PQ4emyJHrnmvo7mbFm5ru24k0p0Z1HkPG5xHDuGhGfKHuSNVQDp2fz/PK774dcPXRwA3SCI/h/ZQtDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T07:30:11.567169Z","bundle_sha256":"5cd1efb61123338bdf1e5c65ad70f3df3b7d5acca63e7576c993906037eff158"}}