{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:4EDEZPLYGAERQTXWDQNIOJSQE3","short_pith_number":"pith:4EDEZPLY","schema_version":"1.0","canonical_sha256":"e1064cbd783009184ef61c1a87265026fcbf2e0eec4139ada94aa8c35645027e","source":{"kind":"arxiv","id":"1207.5599","version":2},"attestation_state":"computed","paper":{"title":"On stellated spheres and a tightness criterion for combinatorial manifolds","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":"2012-07-24T06:40:05Z","abstract_excerpt":"We introduce the $k$-stellated spheres and consider the class ${\\cal W}_k(d)$ of triangulated $d$-manifolds all whose vertex links are $k$-stellated, and its subclass ${\\cal W}^{\\ast}_k(d)$ consisting of the $(k+1)$-neighbourly members of ${\\cal W}_k(d)$. We introduce the mu-vector of any simplicial complex and show that, in the case of 2-neighbourly simplicial complexes, the mu-vector dominates the vector of its Betti numbers componentwise; the two vectors are equal precisely for tight simplicial complexes. We are able to estimate/compute certain alternating sums of the components of the mu-v"},"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":"1207.5599","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-07-24T06:40:05Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"a10bf158698d5077bf1384e309e3230e847db20fa043e109c980852f93824a7a","abstract_canon_sha256":"abe15c9f7c648808fffaf265355a8ff4bfc8b56167f155513df624cfb9c1a54a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:35.069489Z","signature_b64":"3r5QiQUwSqB/fk0vRLURNABtXfeRfSy7el/hLx6Uvn+HDe3C3IVCd78iziBK0b1cGkxFu6vDEsmyYVyDSAaaBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1064cbd783009184ef61c1a87265026fcbf2e0eec4139ada94aa8c35645027e","last_reissued_at":"2026-05-18T03:25:35.069020Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:35.069020Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On stellated spheres and a tightness criterion for combinatorial manifolds","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":"2012-07-24T06:40:05Z","abstract_excerpt":"We introduce the $k$-stellated spheres and consider the class ${\\cal W}_k(d)$ of triangulated $d$-manifolds all whose vertex links are $k$-stellated, and its subclass ${\\cal W}^{\\ast}_k(d)$ consisting of the $(k+1)$-neighbourly members of ${\\cal W}_k(d)$. We introduce the mu-vector of any simplicial complex and show that, in the case of 2-neighbourly simplicial complexes, the mu-vector dominates the vector of its Betti numbers componentwise; the two vectors are equal precisely for tight simplicial complexes. We are able to estimate/compute certain alternating sums of the components of the mu-v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5599","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1207.5599","created_at":"2026-05-18T03:25:35.069092+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.5599v2","created_at":"2026-05-18T03:25:35.069092+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5599","created_at":"2026-05-18T03:25:35.069092+00:00"},{"alias_kind":"pith_short_12","alias_value":"4EDEZPLYGAER","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_16","alias_value":"4EDEZPLYGAERQTXW","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_8","alias_value":"4EDEZPLY","created_at":"2026-05-18T12:26:53.410803+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/4EDEZPLYGAERQTXWDQNIOJSQE3","json":"https://pith.science/pith/4EDEZPLYGAERQTXWDQNIOJSQE3.json","graph_json":"https://pith.science/api/pith-number/4EDEZPLYGAERQTXWDQNIOJSQE3/graph.json","events_json":"https://pith.science/api/pith-number/4EDEZPLYGAERQTXWDQNIOJSQE3/events.json","paper":"https://pith.science/paper/4EDEZPLY"},"agent_actions":{"view_html":"https://pith.science/pith/4EDEZPLYGAERQTXWDQNIOJSQE3","download_json":"https://pith.science/pith/4EDEZPLYGAERQTXWDQNIOJSQE3.json","view_paper":"https://pith.science/paper/4EDEZPLY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.5599&json=true","fetch_graph":"https://pith.science/api/pith-number/4EDEZPLYGAERQTXWDQNIOJSQE3/graph.json","fetch_events":"https://pith.science/api/pith-number/4EDEZPLYGAERQTXWDQNIOJSQE3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4EDEZPLYGAERQTXWDQNIOJSQE3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4EDEZPLYGAERQTXWDQNIOJSQE3/action/storage_attestation","attest_author":"https://pith.science/pith/4EDEZPLYGAERQTXWDQNIOJSQE3/action/author_attestation","sign_citation":"https://pith.science/pith/4EDEZPLYGAERQTXWDQNIOJSQE3/action/citation_signature","submit_replication":"https://pith.science/pith/4EDEZPLYGAERQTXWDQNIOJSQE3/action/replication_record"}},"created_at":"2026-05-18T03:25:35.069092+00:00","updated_at":"2026-05-18T03:25:35.069092+00:00"}