{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:Z7UT4VFK2X3A44Y23BEYEOJFEE","short_pith_number":"pith:Z7UT4VFK","canonical_record":{"source":{"id":"1202.3390","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-02-15T18:07:22Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"2e25b136692e99d4567e842da1a52fd842df62a82b951a087276d1aa8051bd23","abstract_canon_sha256":"dd192d09784d0e114856189264af2526ea24f95bc474b8d8207ecc6abb9610ad"},"schema_version":"1.0"},"canonical_sha256":"cfe93e54aad5f60e731ad849823925213db28d1bf2556d6c1d137f8555ffcdbb","source":{"kind":"arxiv","id":"1202.3390","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3390","created_at":"2026-05-18T03:58:24Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3390v2","created_at":"2026-05-18T03:58:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3390","created_at":"2026-05-18T03:58:24Z"},{"alias_kind":"pith_short_12","alias_value":"Z7UT4VFK2X3A","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"Z7UT4VFK2X3A44Y2","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"Z7UT4VFK","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:Z7UT4VFK2X3A44Y23BEYEOJFEE","target":"record","payload":{"canonical_record":{"source":{"id":"1202.3390","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-02-15T18:07:22Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"2e25b136692e99d4567e842da1a52fd842df62a82b951a087276d1aa8051bd23","abstract_canon_sha256":"dd192d09784d0e114856189264af2526ea24f95bc474b8d8207ecc6abb9610ad"},"schema_version":"1.0"},"canonical_sha256":"cfe93e54aad5f60e731ad849823925213db28d1bf2556d6c1d137f8555ffcdbb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:24.262562Z","signature_b64":"PMIdvv8DkyTCDrOm4Y3w3pzNQAI07QIOS8HTm6g2mPch/dRU+in+tUKP5JXitGkcmkuKBwQUhsUS90thsP04Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cfe93e54aad5f60e731ad849823925213db28d1bf2556d6c1d137f8555ffcdbb","last_reissued_at":"2026-05-18T03:58:24.261806Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:24.261806Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.3390","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:58:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SlWXwzH63rWaZczF2cH+uXk4sszhFeCOZNxH8UuLLjM0Bj1Xwyu8B3Iul9fP/+4XXcmWlmEqqrvasTuEGhq3DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T14:53:23.072993Z"},"content_sha256":"e6d7f1e97d7d7a118b16fe86e3dccafdfb1c5ad91aa2e6da32b81f06c5efa491","schema_version":"1.0","event_id":"sha256:e6d7f1e97d7d7a118b16fe86e3dccafdfb1c5ad91aa2e6da32b81f06c5efa491"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:Z7UT4VFK2X3A44Y23BEYEOJFEE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tight complexes in 3-space admit perfect discrete Morse functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GT","authors_text":"Bruno Benedetti, Karim Adiprasito","submitted_at":"2012-02-15T18:07:22Z","abstract_excerpt":"In 1967, Chillingworth proved that all convex simplicial 3-balls are collapsible. Using the classical notion of tightness, we generalize this to arbitrary manifolds: We show that all tight simplicial 3-manifolds admit some perfect discrete Morse function. We also strengthen Chillingworth's theorem by proving that all convex simplicial 3-balls are non-evasive. In contrast, we show that many non-evasive 3-balls are not convex."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3390","kind":"arxiv","version":2},"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":"2026-05-18T03:58:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rx9Bcqleh9ZIWNNwyQaLj/QzEkpd2Ly4dAb5JkEPLHcGD+JcWYvVUH5w64HpdbKdj1saIIJhGPmhis1hYep4Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T14:53:23.073636Z"},"content_sha256":"14457725e184903080ac8613de7552e9eb284c1674d33d727459530a3050312f","schema_version":"1.0","event_id":"sha256:14457725e184903080ac8613de7552e9eb284c1674d33d727459530a3050312f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z7UT4VFK2X3A44Y23BEYEOJFEE/bundle.json","state_url":"https://pith.science/pith/Z7UT4VFK2X3A44Y23BEYEOJFEE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z7UT4VFK2X3A44Y23BEYEOJFEE/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":"2026-06-10T14:53:23Z","links":{"resolver":"https://pith.science/pith/Z7UT4VFK2X3A44Y23BEYEOJFEE","bundle":"https://pith.science/pith/Z7UT4VFK2X3A44Y23BEYEOJFEE/bundle.json","state":"https://pith.science/pith/Z7UT4VFK2X3A44Y23BEYEOJFEE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z7UT4VFK2X3A44Y23BEYEOJFEE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Z7UT4VFK2X3A44Y23BEYEOJFEE","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":"dd192d09784d0e114856189264af2526ea24f95bc474b8d8207ecc6abb9610ad","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-02-15T18:07:22Z","title_canon_sha256":"2e25b136692e99d4567e842da1a52fd842df62a82b951a087276d1aa8051bd23"},"schema_version":"1.0","source":{"id":"1202.3390","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3390","created_at":"2026-05-18T03:58:24Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3390v2","created_at":"2026-05-18T03:58:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3390","created_at":"2026-05-18T03:58:24Z"},{"alias_kind":"pith_short_12","alias_value":"Z7UT4VFK2X3A","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"Z7UT4VFK2X3A44Y2","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"Z7UT4VFK","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:14457725e184903080ac8613de7552e9eb284c1674d33d727459530a3050312f","target":"graph","created_at":"2026-05-18T03:58:24Z","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 1967, Chillingworth proved that all convex simplicial 3-balls are collapsible. Using the classical notion of tightness, we generalize this to arbitrary manifolds: We show that all tight simplicial 3-manifolds admit some perfect discrete Morse function. We also strengthen Chillingworth's theorem by proving that all convex simplicial 3-balls are non-evasive. In contrast, we show that many non-evasive 3-balls are not convex.","authors_text":"Bruno Benedetti, Karim Adiprasito","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-02-15T18:07:22Z","title":"Tight complexes in 3-space admit perfect discrete Morse functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3390","kind":"arxiv","version":2},"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:e6d7f1e97d7d7a118b16fe86e3dccafdfb1c5ad91aa2e6da32b81f06c5efa491","target":"record","created_at":"2026-05-18T03:58:24Z","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":"dd192d09784d0e114856189264af2526ea24f95bc474b8d8207ecc6abb9610ad","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-02-15T18:07:22Z","title_canon_sha256":"2e25b136692e99d4567e842da1a52fd842df62a82b951a087276d1aa8051bd23"},"schema_version":"1.0","source":{"id":"1202.3390","kind":"arxiv","version":2}},"canonical_sha256":"cfe93e54aad5f60e731ad849823925213db28d1bf2556d6c1d137f8555ffcdbb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cfe93e54aad5f60e731ad849823925213db28d1bf2556d6c1d137f8555ffcdbb","first_computed_at":"2026-05-18T03:58:24.261806Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:24.261806Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PMIdvv8DkyTCDrOm4Y3w3pzNQAI07QIOS8HTm6g2mPch/dRU+in+tUKP5JXitGkcmkuKBwQUhsUS90thsP04Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:24.262562Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.3390","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6d7f1e97d7d7a118b16fe86e3dccafdfb1c5ad91aa2e6da32b81f06c5efa491","sha256:14457725e184903080ac8613de7552e9eb284c1674d33d727459530a3050312f"],"state_sha256":"2130c35e20f69f6a4a1547a3e935e0f405324a421866092de7e46e74f3fd4430"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"utGWRYG5iQ+yYz1TcgGThZtjYRlXm7MnMDx3yNb3Mb/A+/0uGWGPPKTxGY+rLZ98uO0flHSrgEQWrQUAS9LYCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T14:53:23.077190Z","bundle_sha256":"51e6db36ed1f6a5ca796aa6b7d7c11dc2a9bf42dafa321d454f9ec2ba6526ce9"}}