{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:G7VI6RIXKLNXJQTGHN5SY73DSP","short_pith_number":"pith:G7VI6RIX","schema_version":"1.0","canonical_sha256":"37ea8f451752db74c2663b7b2c7f6393d2c26a840017b667a0cefe577cd508d3","source":{"kind":"arxiv","id":"1102.0856","version":2},"attestation_state":"computed","paper":{"title":"On stellated spheres, shellable balls, lower bounds and a combinatorial criterion for tightness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Basudeb Datta, Bhaskar Bagchi","submitted_at":"2011-02-04T09:17:44Z","abstract_excerpt":"We introduce the $k$-stellated spheres and compare and contrast them with $k$-stacked spheres. It is shown that for $d \\geq 2k$, any $k$-stellated sphere of dimension $d$ bounds a unique and canonically defined $k$-stacked ball. In parallel, any $k$-stacked polytopal sphere of dimension $d\\geq 2k$ bounds a unique and canonically defined $k$-stacked ball. We consider the class ${\\cal W}_k(d)$ of combinatorial $d$-manifolds with $k$-stellated links. For $d\\geq 2k+2$, any member of ${\\cal W}_k(d)$ bounds a unique and canonically defined \"$k$-stacked\" $(d+1)$-manifold.\n  We introduce the mu-vector"},"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":"1102.0856","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-02-04T09:17:44Z","cross_cats_sorted":[],"title_canon_sha256":"de68f843b02c9579f1d4cf310fb4e1249db9ead8b4162458c57f9641520d100f","abstract_canon_sha256":"49c898a146d7375624ba344eafc0bed4d5446e92e4417fb26c5292d3ae559419"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:03:43.470772Z","signature_b64":"gwf27A5JsTFvsgmiWPH/Ahk6fxAMOPs8bu+ZAhryhmhwzEk1AqQY1MGfZE3Uojr6XKv9tQ7YBXPW+OuLIO6pCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"37ea8f451752db74c2663b7b2c7f6393d2c26a840017b667a0cefe577cd508d3","last_reissued_at":"2026-05-18T04:03:43.469796Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:03:43.469796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On stellated spheres, shellable balls, lower bounds and a combinatorial criterion for tightness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Basudeb Datta, Bhaskar Bagchi","submitted_at":"2011-02-04T09:17:44Z","abstract_excerpt":"We introduce the $k$-stellated spheres and compare and contrast them with $k$-stacked spheres. It is shown that for $d \\geq 2k$, any $k$-stellated sphere of dimension $d$ bounds a unique and canonically defined $k$-stacked ball. In parallel, any $k$-stacked polytopal sphere of dimension $d\\geq 2k$ bounds a unique and canonically defined $k$-stacked ball. We consider the class ${\\cal W}_k(d)$ of combinatorial $d$-manifolds with $k$-stellated links. For $d\\geq 2k+2$, any member of ${\\cal W}_k(d)$ bounds a unique and canonically defined \"$k$-stacked\" $(d+1)$-manifold.\n  We introduce the mu-vector"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0856","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":"1102.0856","created_at":"2026-05-18T04:03:43.469865+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.0856v2","created_at":"2026-05-18T04:03:43.469865+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.0856","created_at":"2026-05-18T04:03:43.469865+00:00"},{"alias_kind":"pith_short_12","alias_value":"G7VI6RIXKLNX","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_16","alias_value":"G7VI6RIXKLNXJQTG","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_8","alias_value":"G7VI6RIX","created_at":"2026-05-18T12:26:28.662955+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/G7VI6RIXKLNXJQTGHN5SY73DSP","json":"https://pith.science/pith/G7VI6RIXKLNXJQTGHN5SY73DSP.json","graph_json":"https://pith.science/api/pith-number/G7VI6RIXKLNXJQTGHN5SY73DSP/graph.json","events_json":"https://pith.science/api/pith-number/G7VI6RIXKLNXJQTGHN5SY73DSP/events.json","paper":"https://pith.science/paper/G7VI6RIX"},"agent_actions":{"view_html":"https://pith.science/pith/G7VI6RIXKLNXJQTGHN5SY73DSP","download_json":"https://pith.science/pith/G7VI6RIXKLNXJQTGHN5SY73DSP.json","view_paper":"https://pith.science/paper/G7VI6RIX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.0856&json=true","fetch_graph":"https://pith.science/api/pith-number/G7VI6RIXKLNXJQTGHN5SY73DSP/graph.json","fetch_events":"https://pith.science/api/pith-number/G7VI6RIXKLNXJQTGHN5SY73DSP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G7VI6RIXKLNXJQTGHN5SY73DSP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G7VI6RIXKLNXJQTGHN5SY73DSP/action/storage_attestation","attest_author":"https://pith.science/pith/G7VI6RIXKLNXJQTGHN5SY73DSP/action/author_attestation","sign_citation":"https://pith.science/pith/G7VI6RIXKLNXJQTGHN5SY73DSP/action/citation_signature","submit_replication":"https://pith.science/pith/G7VI6RIXKLNXJQTGHN5SY73DSP/action/replication_record"}},"created_at":"2026-05-18T04:03:43.469865+00:00","updated_at":"2026-05-18T04:03:43.469865+00:00"}