{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:AZ7KWVKFQLXVVXAYW7R6C6BB6F","short_pith_number":"pith:AZ7KWVKF","schema_version":"1.0","canonical_sha256":"067eab554582ef5adc18b7e3e17821f17f88ee659a4a89b0daf3b59c3aa33aaf","source":{"kind":"arxiv","id":"0902.0436","version":4},"attestation_state":"computed","paper":{"title":"On locally constructible spheres and balls","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.AT","math.MG"],"primary_cat":"math.CO","authors_text":"Bruno Benedetti, G\\\"unter M. Ziegler","submitted_at":"2009-02-03T07:15:19Z","abstract_excerpt":"Durhuus and Jonsson (1995) introduced the class of \"locally constructible\" (LC) 3-spheres and showed that there are only exponentially-many combinatorial types of simplicial LC 3-spheres. Such upper bounds are crucial for the convergence of models for 3D quantum gravity.\n  We characterize the LC property for d-spheres (\"the sphere minus a facet collapses to a (d-2)-complex\") and for d-balls. In particular, we link it to the classical notions of collapsibility, shellability and constructibility, and obtain hierarchies of such properties for simplicial balls and spheres. The main corollaries fro"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0902.0436","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-02-03T07:15:19Z","cross_cats_sorted":["hep-th","math.AT","math.MG"],"title_canon_sha256":"c8c1ec5f99da189d34b4b4950930b5ce2b8a8488f1178cbcaaa7c8560a126d60","abstract_canon_sha256":"47ac88c334cd59d0f91e290595fc8487c2ba11c4022f5853c1c05b8a828635f5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:15:17.174706Z","signature_b64":"+0pu+nyMAjY0+aQcpm0Y7in1qgBrrzkXpory3HMlUYJKqCq9F9BAICLLGqdJk0zhuTYX3OwZ8v0jSov9/aGCDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"067eab554582ef5adc18b7e3e17821f17f88ee659a4a89b0daf3b59c3aa33aaf","last_reissued_at":"2026-05-18T04:15:17.173946Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:15:17.173946Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On locally constructible spheres and balls","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.AT","math.MG"],"primary_cat":"math.CO","authors_text":"Bruno Benedetti, G\\\"unter M. Ziegler","submitted_at":"2009-02-03T07:15:19Z","abstract_excerpt":"Durhuus and Jonsson (1995) introduced the class of \"locally constructible\" (LC) 3-spheres and showed that there are only exponentially-many combinatorial types of simplicial LC 3-spheres. Such upper bounds are crucial for the convergence of models for 3D quantum gravity.\n  We characterize the LC property for d-spheres (\"the sphere minus a facet collapses to a (d-2)-complex\") and for d-balls. In particular, we link it to the classical notions of collapsibility, shellability and constructibility, and obtain hierarchies of such properties for simplicial balls and spheres. The main corollaries fro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.0436","kind":"arxiv","version":4},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0902.0436","created_at":"2026-05-18T04:15:17.174072+00:00"},{"alias_kind":"arxiv_version","alias_value":"0902.0436v4","created_at":"2026-05-18T04:15:17.174072+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.0436","created_at":"2026-05-18T04:15:17.174072+00:00"},{"alias_kind":"pith_short_12","alias_value":"AZ7KWVKFQLXV","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_16","alias_value":"AZ7KWVKFQLXVVXAY","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_8","alias_value":"AZ7KWVKF","created_at":"2026-05-18T12:25:58.837520+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AZ7KWVKFQLXVVXAYW7R6C6BB6F","json":"https://pith.science/pith/AZ7KWVKFQLXVVXAYW7R6C6BB6F.json","graph_json":"https://pith.science/api/pith-number/AZ7KWVKFQLXVVXAYW7R6C6BB6F/graph.json","events_json":"https://pith.science/api/pith-number/AZ7KWVKFQLXVVXAYW7R6C6BB6F/events.json","paper":"https://pith.science/paper/AZ7KWVKF"},"agent_actions":{"view_html":"https://pith.science/pith/AZ7KWVKFQLXVVXAYW7R6C6BB6F","download_json":"https://pith.science/pith/AZ7KWVKFQLXVVXAYW7R6C6BB6F.json","view_paper":"https://pith.science/paper/AZ7KWVKF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0902.0436&json=true","fetch_graph":"https://pith.science/api/pith-number/AZ7KWVKFQLXVVXAYW7R6C6BB6F/graph.json","fetch_events":"https://pith.science/api/pith-number/AZ7KWVKFQLXVVXAYW7R6C6BB6F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AZ7KWVKFQLXVVXAYW7R6C6BB6F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AZ7KWVKFQLXVVXAYW7R6C6BB6F/action/storage_attestation","attest_author":"https://pith.science/pith/AZ7KWVKFQLXVVXAYW7R6C6BB6F/action/author_attestation","sign_citation":"https://pith.science/pith/AZ7KWVKFQLXVVXAYW7R6C6BB6F/action/citation_signature","submit_replication":"https://pith.science/pith/AZ7KWVKFQLXVVXAYW7R6C6BB6F/action/replication_record"}},"created_at":"2026-05-18T04:15:17.174072+00:00","updated_at":"2026-05-18T04:15:17.174072+00:00"}