{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:FFOOXAK2WTL7UGH2FPS6JZIBEB","short_pith_number":"pith:FFOOXAK2","canonical_record":{"source":{"id":"1504.01520","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-04-07T08:43:35Z","cross_cats_sorted":[],"title_canon_sha256":"dbdc5b9cd86258087a7a480a07bc75293bb0d40124a4c36fe695a95308fb904b","abstract_canon_sha256":"99261d965585fb086658fa1efc01e79290dcfaf6303a318efbaa4df8895d3dc1"},"schema_version":"1.0"},"canonical_sha256":"295ceb815ab4d7fa18fa2be5e4e5012049b62f26fcc2cd19e7dd968e70c81f33","source":{"kind":"arxiv","id":"1504.01520","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.01520","created_at":"2026-05-18T01:55:59Z"},{"alias_kind":"arxiv_version","alias_value":"1504.01520v3","created_at":"2026-05-18T01:55:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01520","created_at":"2026-05-18T01:55:59Z"},{"alias_kind":"pith_short_12","alias_value":"FFOOXAK2WTL7","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FFOOXAK2WTL7UGH2","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FFOOXAK2","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:FFOOXAK2WTL7UGH2FPS6JZIBEB","target":"record","payload":{"canonical_record":{"source":{"id":"1504.01520","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-04-07T08:43:35Z","cross_cats_sorted":[],"title_canon_sha256":"dbdc5b9cd86258087a7a480a07bc75293bb0d40124a4c36fe695a95308fb904b","abstract_canon_sha256":"99261d965585fb086658fa1efc01e79290dcfaf6303a318efbaa4df8895d3dc1"},"schema_version":"1.0"},"canonical_sha256":"295ceb815ab4d7fa18fa2be5e4e5012049b62f26fcc2cd19e7dd968e70c81f33","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:55:59.528539Z","signature_b64":"yqx1DUMC5naw9sjv1dWlWkd0CrHGGSjHfJ+OIk0KGPCp9oXE6Yur8fykWL87eLzB8XAAgz69O+c5wFojJVJqBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"295ceb815ab4d7fa18fa2be5e4e5012049b62f26fcc2cd19e7dd968e70c81f33","last_reissued_at":"2026-05-18T01:55:59.528109Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:55:59.528109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.01520","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:55:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OvCWaKnpcWNQ+5M+QBgMMWJkCOsKEycRqjSWsocgH43VWuWLIN3irxk/tO8Rp8ijNrjZ23QLpQDNlMTy3C1OCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T22:39:06.533220Z"},"content_sha256":"cfac13b89a59b78a551136f8a14e60d95df6200e7cf917d107e0cadec38fd78a","schema_version":"1.0","event_id":"sha256:cfac13b89a59b78a551136f8a14e60d95df6200e7cf917d107e0cadec38fd78a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:FFOOXAK2WTL7UGH2FPS6JZIBEB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Alexander duality for monomial ideals associated with isotone maps between posets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Akihiro Shikama, Ayesha Asloob Qureshi, Juergen Herzog","submitted_at":"2015-04-07T08:43:35Z","abstract_excerpt":"For a pair $(P,Q)$ of finite posets the generators of the ideal $L(P,Q)$ correspond bijectively to the isotone maps from $P$ to $Q$. In this note we determine all pairs $(P,Q)$ for which the Alexander dual of $L(P,Q)$ coincides with $L(Q,P)$, up to a switch of the indices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01520","kind":"arxiv","version":3},"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":"2026-05-18T01:55:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gvyJ0FvnUS6Wz0RBOxU7qZB6eR9DIur3QkgydPWA+SJaN6RctpWTGTS6ppQ4c8jPycXF2uqDSY0DxqsQH0qnDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T22:39:06.533931Z"},"content_sha256":"739b71a9ab1bac1f2b9611a12373c771691a87439c7eefc076ca03f6348001fd","schema_version":"1.0","event_id":"sha256:739b71a9ab1bac1f2b9611a12373c771691a87439c7eefc076ca03f6348001fd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FFOOXAK2WTL7UGH2FPS6JZIBEB/bundle.json","state_url":"https://pith.science/pith/FFOOXAK2WTL7UGH2FPS6JZIBEB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FFOOXAK2WTL7UGH2FPS6JZIBEB/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":"2026-06-05T22:39:06Z","links":{"resolver":"https://pith.science/pith/FFOOXAK2WTL7UGH2FPS6JZIBEB","bundle":"https://pith.science/pith/FFOOXAK2WTL7UGH2FPS6JZIBEB/bundle.json","state":"https://pith.science/pith/FFOOXAK2WTL7UGH2FPS6JZIBEB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FFOOXAK2WTL7UGH2FPS6JZIBEB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FFOOXAK2WTL7UGH2FPS6JZIBEB","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":"99261d965585fb086658fa1efc01e79290dcfaf6303a318efbaa4df8895d3dc1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-04-07T08:43:35Z","title_canon_sha256":"dbdc5b9cd86258087a7a480a07bc75293bb0d40124a4c36fe695a95308fb904b"},"schema_version":"1.0","source":{"id":"1504.01520","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.01520","created_at":"2026-05-18T01:55:59Z"},{"alias_kind":"arxiv_version","alias_value":"1504.01520v3","created_at":"2026-05-18T01:55:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01520","created_at":"2026-05-18T01:55:59Z"},{"alias_kind":"pith_short_12","alias_value":"FFOOXAK2WTL7","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FFOOXAK2WTL7UGH2","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FFOOXAK2","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:739b71a9ab1bac1f2b9611a12373c771691a87439c7eefc076ca03f6348001fd","target":"graph","created_at":"2026-05-18T01:55:59Z","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 a pair $(P,Q)$ of finite posets the generators of the ideal $L(P,Q)$ correspond bijectively to the isotone maps from $P$ to $Q$. In this note we determine all pairs $(P,Q)$ for which the Alexander dual of $L(P,Q)$ coincides with $L(Q,P)$, up to a switch of the indices.","authors_text":"Akihiro Shikama, Ayesha Asloob Qureshi, Juergen Herzog","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-04-07T08:43:35Z","title":"Alexander duality for monomial ideals associated with isotone maps between posets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01520","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:cfac13b89a59b78a551136f8a14e60d95df6200e7cf917d107e0cadec38fd78a","target":"record","created_at":"2026-05-18T01:55:59Z","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":"99261d965585fb086658fa1efc01e79290dcfaf6303a318efbaa4df8895d3dc1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-04-07T08:43:35Z","title_canon_sha256":"dbdc5b9cd86258087a7a480a07bc75293bb0d40124a4c36fe695a95308fb904b"},"schema_version":"1.0","source":{"id":"1504.01520","kind":"arxiv","version":3}},"canonical_sha256":"295ceb815ab4d7fa18fa2be5e4e5012049b62f26fcc2cd19e7dd968e70c81f33","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"295ceb815ab4d7fa18fa2be5e4e5012049b62f26fcc2cd19e7dd968e70c81f33","first_computed_at":"2026-05-18T01:55:59.528109Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:59.528109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yqx1DUMC5naw9sjv1dWlWkd0CrHGGSjHfJ+OIk0KGPCp9oXE6Yur8fykWL87eLzB8XAAgz69O+c5wFojJVJqBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:59.528539Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.01520","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfac13b89a59b78a551136f8a14e60d95df6200e7cf917d107e0cadec38fd78a","sha256:739b71a9ab1bac1f2b9611a12373c771691a87439c7eefc076ca03f6348001fd"],"state_sha256":"acb193d4f5b4a0855c569f2b1f632b53e08f39c9b8330ac7587ce115df3e1331"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3I6w/55wzcCOEI6ginfvt3UvRaZIM+cYTq7A1gNzQ/mirrcWRgu3uaDaHjAfITD/TMAvt/3F9UbA6ulCOD/ACQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T22:39:06.537886Z","bundle_sha256":"6d5b41e1847a573e777948e1ae24df5431cb461d84bd826cdd3db00ac6bf827e"}}