{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:VX5OOP2WQVJA33ZYQFBW3ROLOG","short_pith_number":"pith:VX5OOP2W","canonical_record":{"source":{"id":"1012.1630","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-12-07T22:14:34Z","cross_cats_sorted":["math.AC","math.AG"],"title_canon_sha256":"bc73c08ebb782b49d871124b922072743de6451729eac47e69695923167d02a7","abstract_canon_sha256":"9304bc26c824dbb5911a72cb7ff798130edb57a988ba5115abf59aff7a5db845"},"schema_version":"1.0"},"canonical_sha256":"adfae73f5685520def3881436dc5cb719713d1b6025106bb2c564f581f3a1be1","source":{"kind":"arxiv","id":"1012.1630","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.1630","created_at":"2026-05-18T01:23:21Z"},{"alias_kind":"arxiv_version","alias_value":"1012.1630v3","created_at":"2026-05-18T01:23:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.1630","created_at":"2026-05-18T01:23:21Z"},{"alias_kind":"pith_short_12","alias_value":"VX5OOP2WQVJA","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VX5OOP2WQVJA33ZY","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VX5OOP2W","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:VX5OOP2WQVJA33ZYQFBW3ROLOG","target":"record","payload":{"canonical_record":{"source":{"id":"1012.1630","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-12-07T22:14:34Z","cross_cats_sorted":["math.AC","math.AG"],"title_canon_sha256":"bc73c08ebb782b49d871124b922072743de6451729eac47e69695923167d02a7","abstract_canon_sha256":"9304bc26c824dbb5911a72cb7ff798130edb57a988ba5115abf59aff7a5db845"},"schema_version":"1.0"},"canonical_sha256":"adfae73f5685520def3881436dc5cb719713d1b6025106bb2c564f581f3a1be1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:21.135700Z","signature_b64":"dO+jSPxObxQyZzI/qa4b8DKOcx2IZU9FYpl4N/+/Hf8IDvJZznoTqfwLnanDySaYyMBX4LyRBj7LwvFlUSW5CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"adfae73f5685520def3881436dc5cb719713d1b6025106bb2c564f581f3a1be1","last_reissued_at":"2026-05-18T01:23:21.134991Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:21.134991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.1630","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":"2026-05-18T01:23:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WSnoFHCmo/9J0hDn2KuDABInzWhIkXU5y0bh05thu+ebvOUbBF3TsUQ3iBdqGYAukLob9vNWfFpEsSqii5PeBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T19:35:48.734867Z"},"content_sha256":"9d12b30e44409f89f9c5badd08613aaa191af1755f47ad9f8a10ff21761ea10f","schema_version":"1.0","event_id":"sha256:9d12b30e44409f89f9c5badd08613aaa191af1755f47ad9f8a10ff21761ea10f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:VX5OOP2WQVJA33ZYQFBW3ROLOG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalizing Tanisaki's ideal via ideals of truncated symmetric functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.AG"],"primary_cat":"math.CO","authors_text":"Aba Mbirika, Julianna Tymoczko","submitted_at":"2010-12-07T22:14:34Z","abstract_excerpt":"We define a family of ideals $I_h$ in the polynomial ring $\\mathbb{Z}[x_1,...,x_n]$ that are parametrized by Hessenberg functions $h$ (equivalently Dyck paths or ample partitions). The ideals $I_h$ generalize algebraically a family of ideals called the Tanisaki ideal, which is used in a geometric construction of permutation representations called Springer theory. To define $I_h$, we use polynomials in a proper subset of the variables ${x_1,...,x_n}$ that are symmetric under the corresponding permutation subgroup. We call these polynomials {\\em truncated symmetric functions} and show combinator"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.1630","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":"2026-05-18T01:23:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mXuPfgJ1TWZDY6ICBTKnp2hteadGUN3q2WIsToybPnGom4zpC0SNrR7dxKykr5BRCfDPRAWqjLa6n80jkVSKCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T19:35:48.735491Z"},"content_sha256":"20d882ec997af2f107ca88de87de11216045767b437f9313a5f379c2e3d6be22","schema_version":"1.0","event_id":"sha256:20d882ec997af2f107ca88de87de11216045767b437f9313a5f379c2e3d6be22"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VX5OOP2WQVJA33ZYQFBW3ROLOG/bundle.json","state_url":"https://pith.science/pith/VX5OOP2WQVJA33ZYQFBW3ROLOG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VX5OOP2WQVJA33ZYQFBW3ROLOG/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":"2026-06-04T19:35:48Z","links":{"resolver":"https://pith.science/pith/VX5OOP2WQVJA33ZYQFBW3ROLOG","bundle":"https://pith.science/pith/VX5OOP2WQVJA33ZYQFBW3ROLOG/bundle.json","state":"https://pith.science/pith/VX5OOP2WQVJA33ZYQFBW3ROLOG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VX5OOP2WQVJA33ZYQFBW3ROLOG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:VX5OOP2WQVJA33ZYQFBW3ROLOG","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":"9304bc26c824dbb5911a72cb7ff798130edb57a988ba5115abf59aff7a5db845","cross_cats_sorted":["math.AC","math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-12-07T22:14:34Z","title_canon_sha256":"bc73c08ebb782b49d871124b922072743de6451729eac47e69695923167d02a7"},"schema_version":"1.0","source":{"id":"1012.1630","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.1630","created_at":"2026-05-18T01:23:21Z"},{"alias_kind":"arxiv_version","alias_value":"1012.1630v3","created_at":"2026-05-18T01:23:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.1630","created_at":"2026-05-18T01:23:21Z"},{"alias_kind":"pith_short_12","alias_value":"VX5OOP2WQVJA","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VX5OOP2WQVJA33ZY","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VX5OOP2W","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:20d882ec997af2f107ca88de87de11216045767b437f9313a5f379c2e3d6be22","target":"graph","created_at":"2026-05-18T01:23:21Z","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 family of ideals $I_h$ in the polynomial ring $\\mathbb{Z}[x_1,...,x_n]$ that are parametrized by Hessenberg functions $h$ (equivalently Dyck paths or ample partitions). The ideals $I_h$ generalize algebraically a family of ideals called the Tanisaki ideal, which is used in a geometric construction of permutation representations called Springer theory. To define $I_h$, we use polynomials in a proper subset of the variables ${x_1,...,x_n}$ that are symmetric under the corresponding permutation subgroup. We call these polynomials {\\em truncated symmetric functions} and show combinator","authors_text":"Aba Mbirika, Julianna Tymoczko","cross_cats":["math.AC","math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-12-07T22:14:34Z","title":"Generalizing Tanisaki's ideal via ideals of truncated symmetric functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.1630","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":"sha256:9d12b30e44409f89f9c5badd08613aaa191af1755f47ad9f8a10ff21761ea10f","target":"record","created_at":"2026-05-18T01:23:21Z","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":"9304bc26c824dbb5911a72cb7ff798130edb57a988ba5115abf59aff7a5db845","cross_cats_sorted":["math.AC","math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-12-07T22:14:34Z","title_canon_sha256":"bc73c08ebb782b49d871124b922072743de6451729eac47e69695923167d02a7"},"schema_version":"1.0","source":{"id":"1012.1630","kind":"arxiv","version":3}},"canonical_sha256":"adfae73f5685520def3881436dc5cb719713d1b6025106bb2c564f581f3a1be1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"adfae73f5685520def3881436dc5cb719713d1b6025106bb2c564f581f3a1be1","first_computed_at":"2026-05-18T01:23:21.134991Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:21.134991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dO+jSPxObxQyZzI/qa4b8DKOcx2IZU9FYpl4N/+/Hf8IDvJZznoTqfwLnanDySaYyMBX4LyRBj7LwvFlUSW5CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:21.135700Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.1630","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d12b30e44409f89f9c5badd08613aaa191af1755f47ad9f8a10ff21761ea10f","sha256:20d882ec997af2f107ca88de87de11216045767b437f9313a5f379c2e3d6be22"],"state_sha256":"a441f0fdf0b36ae21bd4a20df082c245f79fd73265c8f1d03b896b93cb22f8bd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F+1z5xLEBWqW5jfua75LHBQbh2rheIzwf1ct5+zzyEt8yEAVhtzMszhb9TvQkiFyC2IVgXCI9hxhlQyL3volBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T19:35:48.738806Z","bundle_sha256":"324c79029191f95dc90126d82f65fba0bdeb39b3a41e56caf6c9cccab1014e96"}}