{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:VEKPHBLCX3OSTLDWEM5TYMYJJQ","short_pith_number":"pith:VEKPHBLC","canonical_record":{"source":{"id":"1208.4314","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-08-21T17:34:12Z","cross_cats_sorted":["math.AC","math.AG"],"title_canon_sha256":"1c9eb1d4453486d0ee301fbc42fa1eed3a0d593d2e8db11396eeac0c1d457177","abstract_canon_sha256":"57751c7338344157a749f2b43841114bc63cf72b79897cd0fa509a3e802f3ccf"},"schema_version":"1.0"},"canonical_sha256":"a914f38562bedd29ac76233b3c33094c1dee7b2b630041605d0b4470597d9467","source":{"kind":"arxiv","id":"1208.4314","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.4314","created_at":"2026-05-18T03:38:23Z"},{"alias_kind":"arxiv_version","alias_value":"1208.4314v2","created_at":"2026-05-18T03:38:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.4314","created_at":"2026-05-18T03:38:23Z"},{"alias_kind":"pith_short_12","alias_value":"VEKPHBLCX3OS","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VEKPHBLCX3OSTLDW","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VEKPHBLC","created_at":"2026-05-18T12:27:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:VEKPHBLCX3OSTLDWEM5TYMYJJQ","target":"record","payload":{"canonical_record":{"source":{"id":"1208.4314","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-08-21T17:34:12Z","cross_cats_sorted":["math.AC","math.AG"],"title_canon_sha256":"1c9eb1d4453486d0ee301fbc42fa1eed3a0d593d2e8db11396eeac0c1d457177","abstract_canon_sha256":"57751c7338344157a749f2b43841114bc63cf72b79897cd0fa509a3e802f3ccf"},"schema_version":"1.0"},"canonical_sha256":"a914f38562bedd29ac76233b3c33094c1dee7b2b630041605d0b4470597d9467","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:23.209901Z","signature_b64":"i+f3JrCY4DytB3HWEd+TJzldwOq53qsVPZDGkY7z5W+Y5/ByiDffPGJ528tKL+Y+UFftsMzC8Ppj5cWBfWMlBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a914f38562bedd29ac76233b3c33094c1dee7b2b630041605d0b4470597d9467","last_reissued_at":"2026-05-18T03:38:23.209361Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:23.209361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.4314","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":"2026-05-18T03:38:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zb+87lGaPahTxwMujjx93DGJxXODtYMzX+KjXA7egQoO52kYsCZlOA3XjRibfL8dJNI4NTGj3RFBY7syuCL7BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T13:13:24.123376Z"},"content_sha256":"e4d7c5bc426948625d0de708c04d80a3fb8cff8d74470d6de8deeba7de51709d","schema_version":"1.0","event_id":"sha256:e4d7c5bc426948625d0de708c04d80a3fb8cff8d74470d6de8deeba7de51709d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:VEKPHBLCX3OSTLDWEM5TYMYJJQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algebraic Frobenius Splitting of Cotangent Bundles of Flag Varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.AG"],"primary_cat":"math.RT","authors_text":"Chuck Hague","submitted_at":"2012-08-21T17:34:12Z","abstract_excerpt":"Following the program of algebraic Frobenius splitting begun by Kumar and Littelmann, we use representation-theoretic techniques to construct a Frobenius splitting of the cotangent bundle of the flag variety of a semisimple algebraic group over an algebraically closed field of positive characteristic. We also show that this splitting is the same as one of the splittings constructed by Kumar, Lauritzen, and Thomsen."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.4314","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":"2026-05-18T03:38:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WL550/Kx3OD7UkTNFKNiLG6nlp+SflFQPSzIgDiyuPevPOn9DALkNydaI+M57+I3DKRzjTSBAH41Pid0TLC9BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T13:13:24.123725Z"},"content_sha256":"655aa8166650491a05d307c96925a38ce912dfa8c28dc4727588b3563bd88507","schema_version":"1.0","event_id":"sha256:655aa8166650491a05d307c96925a38ce912dfa8c28dc4727588b3563bd88507"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VEKPHBLCX3OSTLDWEM5TYMYJJQ/bundle.json","state_url":"https://pith.science/pith/VEKPHBLCX3OSTLDWEM5TYMYJJQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VEKPHBLCX3OSTLDWEM5TYMYJJQ/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":"2026-07-03T13:13:24Z","links":{"resolver":"https://pith.science/pith/VEKPHBLCX3OSTLDWEM5TYMYJJQ","bundle":"https://pith.science/pith/VEKPHBLCX3OSTLDWEM5TYMYJJQ/bundle.json","state":"https://pith.science/pith/VEKPHBLCX3OSTLDWEM5TYMYJJQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VEKPHBLCX3OSTLDWEM5TYMYJJQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VEKPHBLCX3OSTLDWEM5TYMYJJQ","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":"57751c7338344157a749f2b43841114bc63cf72b79897cd0fa509a3e802f3ccf","cross_cats_sorted":["math.AC","math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-08-21T17:34:12Z","title_canon_sha256":"1c9eb1d4453486d0ee301fbc42fa1eed3a0d593d2e8db11396eeac0c1d457177"},"schema_version":"1.0","source":{"id":"1208.4314","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.4314","created_at":"2026-05-18T03:38:23Z"},{"alias_kind":"arxiv_version","alias_value":"1208.4314v2","created_at":"2026-05-18T03:38:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.4314","created_at":"2026-05-18T03:38:23Z"},{"alias_kind":"pith_short_12","alias_value":"VEKPHBLCX3OS","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VEKPHBLCX3OSTLDW","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VEKPHBLC","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:655aa8166650491a05d307c96925a38ce912dfa8c28dc4727588b3563bd88507","target":"graph","created_at":"2026-05-18T03:38:23Z","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":"Following the program of algebraic Frobenius splitting begun by Kumar and Littelmann, we use representation-theoretic techniques to construct a Frobenius splitting of the cotangent bundle of the flag variety of a semisimple algebraic group over an algebraically closed field of positive characteristic. We also show that this splitting is the same as one of the splittings constructed by Kumar, Lauritzen, and Thomsen.","authors_text":"Chuck Hague","cross_cats":["math.AC","math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-08-21T17:34:12Z","title":"Algebraic Frobenius Splitting of Cotangent Bundles of Flag Varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.4314","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:e4d7c5bc426948625d0de708c04d80a3fb8cff8d74470d6de8deeba7de51709d","target":"record","created_at":"2026-05-18T03:38:23Z","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":"57751c7338344157a749f2b43841114bc63cf72b79897cd0fa509a3e802f3ccf","cross_cats_sorted":["math.AC","math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-08-21T17:34:12Z","title_canon_sha256":"1c9eb1d4453486d0ee301fbc42fa1eed3a0d593d2e8db11396eeac0c1d457177"},"schema_version":"1.0","source":{"id":"1208.4314","kind":"arxiv","version":2}},"canonical_sha256":"a914f38562bedd29ac76233b3c33094c1dee7b2b630041605d0b4470597d9467","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a914f38562bedd29ac76233b3c33094c1dee7b2b630041605d0b4470597d9467","first_computed_at":"2026-05-18T03:38:23.209361Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:23.209361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i+f3JrCY4DytB3HWEd+TJzldwOq53qsVPZDGkY7z5W+Y5/ByiDffPGJ528tKL+Y+UFftsMzC8Ppj5cWBfWMlBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:23.209901Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.4314","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4d7c5bc426948625d0de708c04d80a3fb8cff8d74470d6de8deeba7de51709d","sha256:655aa8166650491a05d307c96925a38ce912dfa8c28dc4727588b3563bd88507"],"state_sha256":"ee027641479d869bd74e31f142d2d1337b267f716ac3ab004c15bf163febbcff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nbRLOxdImUoRb5r2U2gWuEiPBpx0QzYTE6erTINO67iXb7uSz7gxOHgL67hZyH1CUuvOr07K/kUpAJp6f6xtBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T13:13:24.125594Z","bundle_sha256":"3640fb757416d8557f707379c607bde4042e0868ea65abbbcaf902283ef17212"}}