{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:KKMKTA7DSUVPSCGAZPMN6EWBV2","short_pith_number":"pith:KKMKTA7D","schema_version":"1.0","canonical_sha256":"5298a983e3952af908c0cbd8df12c1aeb99318abfb11180cd354bc0a0834c2ab","source":{"kind":"arxiv","id":"1201.3377","version":2},"attestation_state":"computed","paper":{"title":"Euler flag enumeration of Whitney stratified spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CO","authors_text":"Margaret Readdy, Mark Goresky, Richard Ehrenborg","submitted_at":"2012-01-16T21:24:09Z","abstract_excerpt":"The flag vector contains all the face incidence data of a polytope, and in the poset setting, the chain enumerative data. It is a classical result due to Bayer and Klapper that for face lattices of polytopes, and more generally, Eulerian graded posets, the flag vector can be written as a cd-index, a non-commutative polynomial which removes all the linear redundancies among the flag vector entries. This result holds for regular CW complexes.\n  We relax the regularity condition to show the cd-index exists for Whitney stratified manifolds by extending the notion of a graded poset to that of a qua"},"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":"1201.3377","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-16T21:24:09Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"474775e68900b231b94d6710311a53cd28a47b4657540a7f142fb0a501825d8c","abstract_canon_sha256":"ffa34a247bd87fa4e60a24482dafaa2e7fbb8185b5018c4a2d087ba56642bdfa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:01.813664Z","signature_b64":"q7BBzCciGtHgDyhk9TRT8vp7TaTIpXO7Vh4JWU9WO3BQHkLPs5CKdzpzlZeqEz7NyM9/XEB7P8iUv0LhcU8DBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5298a983e3952af908c0cbd8df12c1aeb99318abfb11180cd354bc0a0834c2ab","last_reissued_at":"2026-05-18T02:41:01.813234Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:01.813234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Euler flag enumeration of Whitney stratified spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CO","authors_text":"Margaret Readdy, Mark Goresky, Richard Ehrenborg","submitted_at":"2012-01-16T21:24:09Z","abstract_excerpt":"The flag vector contains all the face incidence data of a polytope, and in the poset setting, the chain enumerative data. It is a classical result due to Bayer and Klapper that for face lattices of polytopes, and more generally, Eulerian graded posets, the flag vector can be written as a cd-index, a non-commutative polynomial which removes all the linear redundancies among the flag vector entries. This result holds for regular CW complexes.\n  We relax the regularity condition to show the cd-index exists for Whitney stratified manifolds by extending the notion of a graded poset to that of a qua"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3377","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":"1201.3377","created_at":"2026-05-18T02:41:01.813295+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.3377v2","created_at":"2026-05-18T02:41:01.813295+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3377","created_at":"2026-05-18T02:41:01.813295+00:00"},{"alias_kind":"pith_short_12","alias_value":"KKMKTA7DSUVP","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_16","alias_value":"KKMKTA7DSUVPSCGA","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_8","alias_value":"KKMKTA7D","created_at":"2026-05-18T12:27:11.947152+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/KKMKTA7DSUVPSCGAZPMN6EWBV2","json":"https://pith.science/pith/KKMKTA7DSUVPSCGAZPMN6EWBV2.json","graph_json":"https://pith.science/api/pith-number/KKMKTA7DSUVPSCGAZPMN6EWBV2/graph.json","events_json":"https://pith.science/api/pith-number/KKMKTA7DSUVPSCGAZPMN6EWBV2/events.json","paper":"https://pith.science/paper/KKMKTA7D"},"agent_actions":{"view_html":"https://pith.science/pith/KKMKTA7DSUVPSCGAZPMN6EWBV2","download_json":"https://pith.science/pith/KKMKTA7DSUVPSCGAZPMN6EWBV2.json","view_paper":"https://pith.science/paper/KKMKTA7D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.3377&json=true","fetch_graph":"https://pith.science/api/pith-number/KKMKTA7DSUVPSCGAZPMN6EWBV2/graph.json","fetch_events":"https://pith.science/api/pith-number/KKMKTA7DSUVPSCGAZPMN6EWBV2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KKMKTA7DSUVPSCGAZPMN6EWBV2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KKMKTA7DSUVPSCGAZPMN6EWBV2/action/storage_attestation","attest_author":"https://pith.science/pith/KKMKTA7DSUVPSCGAZPMN6EWBV2/action/author_attestation","sign_citation":"https://pith.science/pith/KKMKTA7DSUVPSCGAZPMN6EWBV2/action/citation_signature","submit_replication":"https://pith.science/pith/KKMKTA7DSUVPSCGAZPMN6EWBV2/action/replication_record"}},"created_at":"2026-05-18T02:41:01.813295+00:00","updated_at":"2026-05-18T02:41:01.813295+00:00"}