{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HKJ6UORMR5T5LAP257MT2NN4ME","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":"db3a2a645af199ed368dbf1c953cbced05a8c98470fcb42254308932b63bb219","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-09-09T10:53:14Z","title_canon_sha256":"4f2654524104aebc0bcebcdaa9b485b0d06674de2ab70d08c39a7f881114a9d9"},"schema_version":"1.0","source":{"id":"1209.1789","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.1789","created_at":"2026-05-18T03:45:54Z"},{"alias_kind":"arxiv_version","alias_value":"1209.1789v1","created_at":"2026-05-18T03:45:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.1789","created_at":"2026-05-18T03:45:54Z"},{"alias_kind":"pith_short_12","alias_value":"HKJ6UORMR5T5","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HKJ6UORMR5T5LAP2","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HKJ6UORM","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:cd9c7bd33670cac00461a851ff8af6cd34772e8268a6206ad6305f57023897de","target":"graph","created_at":"2026-05-18T03:45:54Z","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":"For any flag simplicial complex $\\Theta$ obtained by stellar subdividing the boundary of the cross polytope in edges, we define a flag simplicial complex $\\Gamma(\\Theta)$ (dependent on the sequence of subdivisions) whose $f$-vector is the $\\gamma$-vector of $\\Theta$. This proves that the $\\gamma$-vector of any such simplicial complex satisfies the Frankl-F\\\"{u}redi-Kalai inequalities, partially solving a conjecture by Nevo and Petersen \\cite{np}. We show that when $\\Theta$ is the dual simplicial complex to a nestohedron, and the sequence of subdivisions corresponds to a flag ordering as define","authors_text":"Natalie Aisbett","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-09-09T10:53:14Z","title":"gamma-vectors of edge subdivisions of the boundary of the cross polytope"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1789","kind":"arxiv","version":1},"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":"sha256:6d467bde9c7564e740c7a0c9cf9d1485295d986ff42c1c9d87c7bd5235d4c1f6","target":"record","created_at":"2026-05-18T03:45:54Z","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":"db3a2a645af199ed368dbf1c953cbced05a8c98470fcb42254308932b63bb219","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-09-09T10:53:14Z","title_canon_sha256":"4f2654524104aebc0bcebcdaa9b485b0d06674de2ab70d08c39a7f881114a9d9"},"schema_version":"1.0","source":{"id":"1209.1789","kind":"arxiv","version":1}},"canonical_sha256":"3a93ea3a2c8f67d581faefd93d35bc613f29d332afc9ed475da9d68c62cd3a78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a93ea3a2c8f67d581faefd93d35bc613f29d332afc9ed475da9d68c62cd3a78","first_computed_at":"2026-05-18T03:45:54.374463Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:54.374463Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mQVgcITtZ64cHrnWian/g4DHKI2XAgWYLJtKtnApifURYlEmBN4Hj1rxy0PeiATY9qaQJwRWsGVCFN/vXo8IAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:54.374934Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.1789","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d467bde9c7564e740c7a0c9cf9d1485295d986ff42c1c9d87c7bd5235d4c1f6","sha256:cd9c7bd33670cac00461a851ff8af6cd34772e8268a6206ad6305f57023897de"],"state_sha256":"dcba9cbee686f004771008ac70dbfb33d422746ff0347bfa388836cf0f0779f2"}