{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:H62X2HUUMN6H7BGQLMAIV2PBJ3","short_pith_number":"pith:H62X2HUU","canonical_record":{"source":{"id":"2304.04810","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2023-04-10T18:43:26Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"9150efa1bdfdbc6eb2a7c2828ff8ac47aea2151c5914e139d6d7ea7a934714ce","abstract_canon_sha256":"87d7b9a9675e3641a30a3087370ffd7e13267785569e03c67127d33e8cffe0f9"},"schema_version":"1.0"},"canonical_sha256":"3fb57d1e94637c7f84d05b008ae9e14ee8abcfc582a3da50cfdf9bf46a3a1a10","source":{"kind":"arxiv","id":"2304.04810","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.04810","created_at":"2026-07-05T07:54:48Z"},{"alias_kind":"arxiv_version","alias_value":"2304.04810v2","created_at":"2026-07-05T07:54:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.04810","created_at":"2026-07-05T07:54:48Z"},{"alias_kind":"pith_short_12","alias_value":"H62X2HUUMN6H","created_at":"2026-07-05T07:54:48Z"},{"alias_kind":"pith_short_16","alias_value":"H62X2HUUMN6H7BGQ","created_at":"2026-07-05T07:54:48Z"},{"alias_kind":"pith_short_8","alias_value":"H62X2HUU","created_at":"2026-07-05T07:54:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:H62X2HUUMN6H7BGQLMAIV2PBJ3","target":"record","payload":{"canonical_record":{"source":{"id":"2304.04810","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2023-04-10T18:43:26Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"9150efa1bdfdbc6eb2a7c2828ff8ac47aea2151c5914e139d6d7ea7a934714ce","abstract_canon_sha256":"87d7b9a9675e3641a30a3087370ffd7e13267785569e03c67127d33e8cffe0f9"},"schema_version":"1.0"},"canonical_sha256":"3fb57d1e94637c7f84d05b008ae9e14ee8abcfc582a3da50cfdf9bf46a3a1a10","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:54:48.512301Z","signature_b64":"6Hv6iTNXKUsUlsOryqUL33A+TUXARLG24YafbZvADd1FqrbgIxxdHbijOuVoRYO7mayGJ/g/08X6HHDxTP4mCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3fb57d1e94637c7f84d05b008ae9e14ee8abcfc582a3da50cfdf9bf46a3a1a10","last_reissued_at":"2026-07-05T07:54:48.511951Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:54:48.511951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2304.04810","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":"2026-07-05T07:54:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"djA77lQfEM7WFh/cok8xLeO9c7v6CMas22miOI4BwYkWUb//XbBUdPoSPpnumiPnezQdT+oZbgAPW8xvDM6aBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T16:18:18.256777Z"},"content_sha256":"30d5c6a2273accc024728466d87382376416d1aca34458fa466e5a49a1900084","schema_version":"1.0","event_id":"sha256:30d5c6a2273accc024728466d87382376416d1aca34458fa466e5a49a1900084"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:H62X2HUUMN6H7BGQLMAIV2PBJ3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Chain algebras of finite distributive lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Lisa Nicklasson, Oleksandra Gasanova","submitted_at":"2023-04-10T18:43:26Z","abstract_excerpt":"We introduce a family of toric algebras defined by maximal chains of a finite distributive lattice. Applying results on stable set polytopes we conclude that every such algebra is normal and Cohen-Macaulay, and give an interpretation of its Krull dimension in terms of the combinatorics of the underlying lattice. When the lattice is planar, we show that the corresponding chain algebra is generated by a sortable set of monomials and is isomorphic to a Hibi ring of another finite distributive lattice. As a consequence it has a defining toric ideal with a quadratic Gr\\\"obner basis, and its $h$-vec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.04810","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2304.04810/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T07:54:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d1LQYt7fKQoNbvE2YAbt3CL87bJ/r3C1hA4MSaHNDpPfUO3dN9pOX+k0ZvrH8ZIuYx/YMduWheShH+daXOLCDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T16:18:18.257335Z"},"content_sha256":"fffba6b2520c2fe7ba7e8fa9c64b19dbfc5927f4e371a128deb62238bd397da2","schema_version":"1.0","event_id":"sha256:fffba6b2520c2fe7ba7e8fa9c64b19dbfc5927f4e371a128deb62238bd397da2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H62X2HUUMN6H7BGQLMAIV2PBJ3/bundle.json","state_url":"https://pith.science/pith/H62X2HUUMN6H7BGQLMAIV2PBJ3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H62X2HUUMN6H7BGQLMAIV2PBJ3/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":"2026-08-04T16:18:18Z","links":{"resolver":"https://pith.science/pith/H62X2HUUMN6H7BGQLMAIV2PBJ3","bundle":"https://pith.science/pith/H62X2HUUMN6H7BGQLMAIV2PBJ3/bundle.json","state":"https://pith.science/pith/H62X2HUUMN6H7BGQLMAIV2PBJ3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H62X2HUUMN6H7BGQLMAIV2PBJ3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:H62X2HUUMN6H7BGQLMAIV2PBJ3","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":"87d7b9a9675e3641a30a3087370ffd7e13267785569e03c67127d33e8cffe0f9","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2023-04-10T18:43:26Z","title_canon_sha256":"9150efa1bdfdbc6eb2a7c2828ff8ac47aea2151c5914e139d6d7ea7a934714ce"},"schema_version":"1.0","source":{"id":"2304.04810","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.04810","created_at":"2026-07-05T07:54:48Z"},{"alias_kind":"arxiv_version","alias_value":"2304.04810v2","created_at":"2026-07-05T07:54:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.04810","created_at":"2026-07-05T07:54:48Z"},{"alias_kind":"pith_short_12","alias_value":"H62X2HUUMN6H","created_at":"2026-07-05T07:54:48Z"},{"alias_kind":"pith_short_16","alias_value":"H62X2HUUMN6H7BGQ","created_at":"2026-07-05T07:54:48Z"},{"alias_kind":"pith_short_8","alias_value":"H62X2HUU","created_at":"2026-07-05T07:54:48Z"}],"graph_snapshots":[{"event_id":"sha256:fffba6b2520c2fe7ba7e8fa9c64b19dbfc5927f4e371a128deb62238bd397da2","target":"graph","created_at":"2026-07-05T07:54:48Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2304.04810/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a family of toric algebras defined by maximal chains of a finite distributive lattice. Applying results on stable set polytopes we conclude that every such algebra is normal and Cohen-Macaulay, and give an interpretation of its Krull dimension in terms of the combinatorics of the underlying lattice. When the lattice is planar, we show that the corresponding chain algebra is generated by a sortable set of monomials and is isomorphic to a Hibi ring of another finite distributive lattice. As a consequence it has a defining toric ideal with a quadratic Gr\\\"obner basis, and its $h$-vec","authors_text":"Lisa Nicklasson, Oleksandra Gasanova","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2023-04-10T18:43:26Z","title":"Chain algebras of finite distributive lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.04810","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":"sha256:30d5c6a2273accc024728466d87382376416d1aca34458fa466e5a49a1900084","target":"record","created_at":"2026-07-05T07:54:48Z","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":"87d7b9a9675e3641a30a3087370ffd7e13267785569e03c67127d33e8cffe0f9","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2023-04-10T18:43:26Z","title_canon_sha256":"9150efa1bdfdbc6eb2a7c2828ff8ac47aea2151c5914e139d6d7ea7a934714ce"},"schema_version":"1.0","source":{"id":"2304.04810","kind":"arxiv","version":2}},"canonical_sha256":"3fb57d1e94637c7f84d05b008ae9e14ee8abcfc582a3da50cfdf9bf46a3a1a10","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3fb57d1e94637c7f84d05b008ae9e14ee8abcfc582a3da50cfdf9bf46a3a1a10","first_computed_at":"2026-07-05T07:54:48.511951Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:54:48.511951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6Hv6iTNXKUsUlsOryqUL33A+TUXARLG24YafbZvADd1FqrbgIxxdHbijOuVoRYO7mayGJ/g/08X6HHDxTP4mCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:54:48.512301Z","signed_message":"canonical_sha256_bytes"},"source_id":"2304.04810","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30d5c6a2273accc024728466d87382376416d1aca34458fa466e5a49a1900084","sha256:fffba6b2520c2fe7ba7e8fa9c64b19dbfc5927f4e371a128deb62238bd397da2"],"state_sha256":"0792cc27af292a4b75999354f3326ad5692fa5a279154c156b308d0c91f92c1d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6OJ2CjunauwdyMnnbvBsdpZGNS2ZGuIHbkv89Eynb3BcoDRjPBtGORXwiJOwbQu/3pjts1bFX0yq8nB7hQkoCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T16:18:18.262000Z","bundle_sha256":"c8a1f171af0bbd8fdc32f485b4ba9af289823d45d93a01406b259301974cda1f"}}