{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:X3SJNEZSKZW4CPULHOLACZAPFT","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":"2e33a64b9534ec02cbc0a7a5c0226fb407ba2de12b65a8d991a768bc99cebf30","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-20T16:20:31Z","title_canon_sha256":"cc56897dfd97efb54180e8e87a1e0d0629f30f7d1ba6ae3b02fcff717d6446d3"},"schema_version":"1.0","source":{"id":"1408.4713","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.4713","created_at":"2026-05-18T01:19:00Z"},{"alias_kind":"arxiv_version","alias_value":"1408.4713v3","created_at":"2026-05-18T01:19:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.4713","created_at":"2026-05-18T01:19:00Z"},{"alias_kind":"pith_short_12","alias_value":"X3SJNEZSKZW4","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"X3SJNEZSKZW4CPUL","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"X3SJNEZS","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:b3cf4367fc043f11c213ea908497b09a0207eaae22a8ac7a34bf3755b0a14ec5","target":"graph","created_at":"2026-05-18T01:19:00Z","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":"Hypersimplices are well-studied objects in combinatorics, optimization, and representation theory. For each hypersimplex, we define a new family of subpolytopes, called r-stable hypersimplices, and show that a well-known regular unimodular triangulation of the hypersimplex restricts to a triangulation of each r-stable hypersimplex. For the case of the second hypersimplex defined by the two-element subsets of an n-set, we provide a shelling of this triangulation that sequentially shells each r-stable sub-hypersimplex. In this case, we utilize the shelling to compute the Ehrhart h*-polynomials o","authors_text":"Benjamin Braun, Liam Solus","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-20T16:20:31Z","title":"Shellability, Ehrhart Theory, and $r$-stable Hypersimplices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4713","kind":"arxiv","version":3},"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":"sha256:7d124302a31c0aca0a57c57ef8a190e5bd58771d76d63100bf76f1161f5fa915","target":"record","created_at":"2026-05-18T01:19:00Z","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":"2e33a64b9534ec02cbc0a7a5c0226fb407ba2de12b65a8d991a768bc99cebf30","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-20T16:20:31Z","title_canon_sha256":"cc56897dfd97efb54180e8e87a1e0d0629f30f7d1ba6ae3b02fcff717d6446d3"},"schema_version":"1.0","source":{"id":"1408.4713","kind":"arxiv","version":3}},"canonical_sha256":"bee4969332566dc13e8b3b9601640f2cc525904fc3cab15249a259fabebf124c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bee4969332566dc13e8b3b9601640f2cc525904fc3cab15249a259fabebf124c","first_computed_at":"2026-05-18T01:19:00.608763Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:00.608763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LaA45mwQt+TTmg1ginYkCzFpPv5NlzDAQeVK6Ch79vTZlVsjMYLFx69Mu876/s1OhoVpOJovKuiSlBmi9bFJAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:00.609227Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.4713","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d124302a31c0aca0a57c57ef8a190e5bd58771d76d63100bf76f1161f5fa915","sha256:b3cf4367fc043f11c213ea908497b09a0207eaae22a8ac7a34bf3755b0a14ec5"],"state_sha256":"04f25a51e60a2e36d23b8cc72e4dcdd4d4f590067a44d9b6a8e7e28d994290fd"}