{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:JI5AKZW4VI7KNV2DYNKYULL7ZG","short_pith_number":"pith:JI5AKZW4","canonical_record":{"source":{"id":"1202.2652","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-02-13T08:00:41Z","cross_cats_sorted":[],"title_canon_sha256":"06f05c8768f0c241553422b9335c9452e19cd71bea6e33f37874e5cf4262da87","abstract_canon_sha256":"3bc01aaa387c3775b136d0f0ad71ed2e7ce8abc7bcf854478dbd6461699c9082"},"schema_version":"1.0"},"canonical_sha256":"4a3a0566dcaa3ea6d743c3558a2d7fc9834b81c6bb2c35e806e84fcd3998444a","source":{"kind":"arxiv","id":"1202.2652","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2652","created_at":"2026-05-18T04:00:48Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2652v2","created_at":"2026-05-18T04:00:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2652","created_at":"2026-05-18T04:00:48Z"},{"alias_kind":"pith_short_12","alias_value":"JI5AKZW4VI7K","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JI5AKZW4VI7KNV2D","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JI5AKZW4","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:JI5AKZW4VI7KNV2DYNKYULL7ZG","target":"record","payload":{"canonical_record":{"source":{"id":"1202.2652","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-02-13T08:00:41Z","cross_cats_sorted":[],"title_canon_sha256":"06f05c8768f0c241553422b9335c9452e19cd71bea6e33f37874e5cf4262da87","abstract_canon_sha256":"3bc01aaa387c3775b136d0f0ad71ed2e7ce8abc7bcf854478dbd6461699c9082"},"schema_version":"1.0"},"canonical_sha256":"4a3a0566dcaa3ea6d743c3558a2d7fc9834b81c6bb2c35e806e84fcd3998444a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:00:48.967212Z","signature_b64":"auq+d0kN0bBlU87L48wXIPBk2of+l5GV+TzDsDfmNVWhy0A2BNTlkC9gNGmM4u4na/6dQEq5gaub3rx3bZlsCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a3a0566dcaa3ea6d743c3558a2d7fc9834b81c6bb2c35e806e84fcd3998444a","last_reissued_at":"2026-05-18T04:00:48.966512Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:00:48.966512Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.2652","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:00:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I70bJikCuRnANoSRFV3SC2DV2UsMF7gugXa0hk9HC8xg2gsoDEt2wESq40HTQAN2u7F9/dCVKNFiHOnN5JglCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T08:43:19.252336Z"},"content_sha256":"dc8bb609430c5a508c67963d04b3537e13982cb5972e267936a1a036f1b37474","schema_version":"1.0","event_id":"sha256:dc8bb609430c5a508c67963d04b3537e13982cb5972e267936a1a036f1b37474"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:JI5AKZW4VI7KNV2DYNKYULL7ZG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ehrhart f*-coefficients of polytopal complexes are non-negative integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Felix Breuer","submitted_at":"2012-02-13T08:00:41Z","abstract_excerpt":"The Ehrhart polynomial $L_P$ of an integral polytope $P$ counts the number of integer points in integral dilates of $P$. Ehrhart polynomials of polytopes are often described in terms of their Ehrhart $h^*$-vector (aka Ehrhart $\\delta$-vector), which is the vector of coefficients of $L_P$ with respect to a certain binomial basis and which coincides with the $h$-vector of a regular unimodular triangulation of $P$ (if one exists). One important result by Stanley about $h^*$-vectors of polytopes is that their entries are always non-negative. However, recent combinatorial applications of Ehrhart th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2652","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:00:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DNu/mlPNc6tZjcg2ZzzQMoaZrs9NOgwvA/WSw78lsMJDIPN1sZ06mFTpESh1WvSqEoMIA+vgUAFfSi0X2aKcDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T08:43:19.252690Z"},"content_sha256":"228f92421939b5319e798bc72221cfbe03e492af7e915121b572437640968ca2","schema_version":"1.0","event_id":"sha256:228f92421939b5319e798bc72221cfbe03e492af7e915121b572437640968ca2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JI5AKZW4VI7KNV2DYNKYULL7ZG/bundle.json","state_url":"https://pith.science/pith/JI5AKZW4VI7KNV2DYNKYULL7ZG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JI5AKZW4VI7KNV2DYNKYULL7ZG/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-20T08:43:19Z","links":{"resolver":"https://pith.science/pith/JI5AKZW4VI7KNV2DYNKYULL7ZG","bundle":"https://pith.science/pith/JI5AKZW4VI7KNV2DYNKYULL7ZG/bundle.json","state":"https://pith.science/pith/JI5AKZW4VI7KNV2DYNKYULL7ZG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JI5AKZW4VI7KNV2DYNKYULL7ZG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JI5AKZW4VI7KNV2DYNKYULL7ZG","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":"3bc01aaa387c3775b136d0f0ad71ed2e7ce8abc7bcf854478dbd6461699c9082","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-02-13T08:00:41Z","title_canon_sha256":"06f05c8768f0c241553422b9335c9452e19cd71bea6e33f37874e5cf4262da87"},"schema_version":"1.0","source":{"id":"1202.2652","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2652","created_at":"2026-05-18T04:00:48Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2652v2","created_at":"2026-05-18T04:00:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2652","created_at":"2026-05-18T04:00:48Z"},{"alias_kind":"pith_short_12","alias_value":"JI5AKZW4VI7K","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JI5AKZW4VI7KNV2D","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JI5AKZW4","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:228f92421939b5319e798bc72221cfbe03e492af7e915121b572437640968ca2","target":"graph","created_at":"2026-05-18T04:00:48Z","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":"The Ehrhart polynomial $L_P$ of an integral polytope $P$ counts the number of integer points in integral dilates of $P$. Ehrhart polynomials of polytopes are often described in terms of their Ehrhart $h^*$-vector (aka Ehrhart $\\delta$-vector), which is the vector of coefficients of $L_P$ with respect to a certain binomial basis and which coincides with the $h$-vector of a regular unimodular triangulation of $P$ (if one exists). One important result by Stanley about $h^*$-vectors of polytopes is that their entries are always non-negative. However, recent combinatorial applications of Ehrhart th","authors_text":"Felix Breuer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-02-13T08:00:41Z","title":"Ehrhart f*-coefficients of polytopal complexes are non-negative integers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2652","kind":"arxiv","version":2},"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:dc8bb609430c5a508c67963d04b3537e13982cb5972e267936a1a036f1b37474","target":"record","created_at":"2026-05-18T04:00:48Z","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":"3bc01aaa387c3775b136d0f0ad71ed2e7ce8abc7bcf854478dbd6461699c9082","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-02-13T08:00:41Z","title_canon_sha256":"06f05c8768f0c241553422b9335c9452e19cd71bea6e33f37874e5cf4262da87"},"schema_version":"1.0","source":{"id":"1202.2652","kind":"arxiv","version":2}},"canonical_sha256":"4a3a0566dcaa3ea6d743c3558a2d7fc9834b81c6bb2c35e806e84fcd3998444a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a3a0566dcaa3ea6d743c3558a2d7fc9834b81c6bb2c35e806e84fcd3998444a","first_computed_at":"2026-05-18T04:00:48.966512Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:00:48.966512Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"auq+d0kN0bBlU87L48wXIPBk2of+l5GV+TzDsDfmNVWhy0A2BNTlkC9gNGmM4u4na/6dQEq5gaub3rx3bZlsCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:00:48.967212Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.2652","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc8bb609430c5a508c67963d04b3537e13982cb5972e267936a1a036f1b37474","sha256:228f92421939b5319e798bc72221cfbe03e492af7e915121b572437640968ca2"],"state_sha256":"c4459716e03071d47dbb604d42e2861b1cd36906dc0af8c783f90697fdf18f7e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BILlT3a6qujZ/zpdYNgKB5XJ7vw/1az8eR4wE8Nzew8s0iTqYtyB3KYSgv38hLGOaCodFre+kLyRG0Zt26HtBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T08:43:19.254842Z","bundle_sha256":"f3593d11024e848ed73706728f45642531cfe953378b50ae948d39e8f0cb3ee8"}}