{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:EOZVORH5CLBMS327H2GXHW46CM","short_pith_number":"pith:EOZVORH5","canonical_record":{"source":{"id":"1709.06736","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-20T06:57:50Z","cross_cats_sorted":["math.AG","math.RT"],"title_canon_sha256":"54671c6415726085a81205ce9f8b182cb2b96493174f4ff5f88048aa6f20cf26","abstract_canon_sha256":"a3d7ac36daa3453ae2874fdbe41797afb2cc75c72d2bd730f8797bd379671977"},"schema_version":"1.0"},"canonical_sha256":"23b35744fd12c2c96f5f3e8d73db9e1329e6afe2a4c94268b23cddae9c1af57a","source":{"kind":"arxiv","id":"1709.06736","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.06736","created_at":"2026-05-18T00:27:18Z"},{"alias_kind":"arxiv_version","alias_value":"1709.06736v2","created_at":"2026-05-18T00:27:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.06736","created_at":"2026-05-18T00:27:18Z"},{"alias_kind":"pith_short_12","alias_value":"EOZVORH5CLBM","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EOZVORH5CLBMS327","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EOZVORH5","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:EOZVORH5CLBMS327H2GXHW46CM","target":"record","payload":{"canonical_record":{"source":{"id":"1709.06736","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-20T06:57:50Z","cross_cats_sorted":["math.AG","math.RT"],"title_canon_sha256":"54671c6415726085a81205ce9f8b182cb2b96493174f4ff5f88048aa6f20cf26","abstract_canon_sha256":"a3d7ac36daa3453ae2874fdbe41797afb2cc75c72d2bd730f8797bd379671977"},"schema_version":"1.0"},"canonical_sha256":"23b35744fd12c2c96f5f3e8d73db9e1329e6afe2a4c94268b23cddae9c1af57a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:18.932412Z","signature_b64":"yyblCi0t4Q7h/cpKKiYpiY6r4QZTYUv7tV7gbnoFdiOE4y/mV4U3e6/Z8+tI99eLZAMepFKzmbI8j6YicN4xCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23b35744fd12c2c96f5f3e8d73db9e1329e6afe2a4c94268b23cddae9c1af57a","last_reissued_at":"2026-05-18T00:27:18.931901Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:18.931901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.06736","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":"2026-05-18T00:27:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nGpsuOCenSMSVwDrIOu8Y+ti/nQKmmtZI/ZPp75jWntJIml7wmkvn+spQfPA/qq1BqjafvxaZGhEfPli0UVFDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T01:17:20.485804Z"},"content_sha256":"8970c568fae2cbe9ac40e67d8ede3034bc48fc45ec46000140791c45665071a7","schema_version":"1.0","event_id":"sha256:8970c568fae2cbe9ac40e67d8ede3034bc48fc45ec46000140791c45665071a7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:EOZVORH5CLBMS327H2GXHW46CM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The cohomology of abelian Hessenberg varieties and the Stanley-Stembridge conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RT"],"primary_cat":"math.CO","authors_text":"Martha Precup, Megumi Harada","submitted_at":"2017-09-20T06:57:50Z","abstract_excerpt":"We define a subclass of Hessenberg varieties called abelian Hessenberg varieties, inspired by the theory of abelian ideals in a Lie algebra developed by Kostant and Peterson. We give an inductive formula for the $S_n$-representation on the cohomology of an abelian regular semisimple Hessenberg variety with respect to the action defined by Tymoczko. Our result implies that a graded version of the Stanley-Stembridge conjecture holds in the abelian case, and generalizes results obtained by Shareshian-Wachs and Teff. Our proof uses previous work of Stanley, Gasharov, Shareshian-Wachs, and Brosnan-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.06736","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":"2026-05-18T00:27:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d+ZrMObpwbbcx5lGqIMgdqgBnbJ0SjB0TNKG0hqYv3v/XDikNcOPgBmzLZBfStZKT2VB9IyEM9FMVMoYSV76CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T01:17:20.486162Z"},"content_sha256":"4cd7f0d291078cd6bc91ebd3368555e65e7710571049a5944bba97783b80ff43","schema_version":"1.0","event_id":"sha256:4cd7f0d291078cd6bc91ebd3368555e65e7710571049a5944bba97783b80ff43"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EOZVORH5CLBMS327H2GXHW46CM/bundle.json","state_url":"https://pith.science/pith/EOZVORH5CLBMS327H2GXHW46CM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EOZVORH5CLBMS327H2GXHW46CM/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":"2026-07-01T01:17:20Z","links":{"resolver":"https://pith.science/pith/EOZVORH5CLBMS327H2GXHW46CM","bundle":"https://pith.science/pith/EOZVORH5CLBMS327H2GXHW46CM/bundle.json","state":"https://pith.science/pith/EOZVORH5CLBMS327H2GXHW46CM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EOZVORH5CLBMS327H2GXHW46CM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:EOZVORH5CLBMS327H2GXHW46CM","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":"a3d7ac36daa3453ae2874fdbe41797afb2cc75c72d2bd730f8797bd379671977","cross_cats_sorted":["math.AG","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-20T06:57:50Z","title_canon_sha256":"54671c6415726085a81205ce9f8b182cb2b96493174f4ff5f88048aa6f20cf26"},"schema_version":"1.0","source":{"id":"1709.06736","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.06736","created_at":"2026-05-18T00:27:18Z"},{"alias_kind":"arxiv_version","alias_value":"1709.06736v2","created_at":"2026-05-18T00:27:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.06736","created_at":"2026-05-18T00:27:18Z"},{"alias_kind":"pith_short_12","alias_value":"EOZVORH5CLBM","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EOZVORH5CLBMS327","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EOZVORH5","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:4cd7f0d291078cd6bc91ebd3368555e65e7710571049a5944bba97783b80ff43","target":"graph","created_at":"2026-05-18T00:27:18Z","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":"We define a subclass of Hessenberg varieties called abelian Hessenberg varieties, inspired by the theory of abelian ideals in a Lie algebra developed by Kostant and Peterson. We give an inductive formula for the $S_n$-representation on the cohomology of an abelian regular semisimple Hessenberg variety with respect to the action defined by Tymoczko. Our result implies that a graded version of the Stanley-Stembridge conjecture holds in the abelian case, and generalizes results obtained by Shareshian-Wachs and Teff. Our proof uses previous work of Stanley, Gasharov, Shareshian-Wachs, and Brosnan-","authors_text":"Martha Precup, Megumi Harada","cross_cats":["math.AG","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-20T06:57:50Z","title":"The cohomology of abelian Hessenberg varieties and the Stanley-Stembridge conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.06736","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":"sha256:8970c568fae2cbe9ac40e67d8ede3034bc48fc45ec46000140791c45665071a7","target":"record","created_at":"2026-05-18T00:27:18Z","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":"a3d7ac36daa3453ae2874fdbe41797afb2cc75c72d2bd730f8797bd379671977","cross_cats_sorted":["math.AG","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-20T06:57:50Z","title_canon_sha256":"54671c6415726085a81205ce9f8b182cb2b96493174f4ff5f88048aa6f20cf26"},"schema_version":"1.0","source":{"id":"1709.06736","kind":"arxiv","version":2}},"canonical_sha256":"23b35744fd12c2c96f5f3e8d73db9e1329e6afe2a4c94268b23cddae9c1af57a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"23b35744fd12c2c96f5f3e8d73db9e1329e6afe2a4c94268b23cddae9c1af57a","first_computed_at":"2026-05-18T00:27:18.931901Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:18.931901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yyblCi0t4Q7h/cpKKiYpiY6r4QZTYUv7tV7gbnoFdiOE4y/mV4U3e6/Z8+tI99eLZAMepFKzmbI8j6YicN4xCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:18.932412Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.06736","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8970c568fae2cbe9ac40e67d8ede3034bc48fc45ec46000140791c45665071a7","sha256:4cd7f0d291078cd6bc91ebd3368555e65e7710571049a5944bba97783b80ff43"],"state_sha256":"25b12b356e9cf0a87c91a8275955caf1463a8c3b31c1a68ca69c119d0a3b42db"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wT0GI98seV81UL7Fvgm5xUgDUn+Qb1BTlyxCEnhAXH2bUGLu6UEgV12V3QZXnVuKy1cJ8sqgcj+6xq7PeAVMDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T01:17:20.488187Z","bundle_sha256":"dc013424d6542cfdadb90f09a4e88846acde7ded2304ebbc3c8087654e8198ca"}}