{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:RKNCEDRXFGLFOTLYH77BCJJTEK","short_pith_number":"pith:RKNCEDRX","canonical_record":{"source":{"id":"math/0312156","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.RT","submitted_at":"2003-12-08T11:18:49Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"c6254159a9c438691047ac37b67acd2416e6cae28c1f2eed63e1c1122df27919","abstract_canon_sha256":"82b67e550fe8a9f653c495b8783eb5620aa768a08f6ef98e4a5e693f7eae853d"},"schema_version":"1.0"},"canonical_sha256":"8a9a220e372996574d783ffe11253322a7dcd44343cfe68dcb2406c295b62deb","source":{"kind":"arxiv","id":"math/0312156","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0312156","created_at":"2026-07-04T14:38:04Z"},{"alias_kind":"arxiv_version","alias_value":"math/0312156v1","created_at":"2026-07-04T14:38:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0312156","created_at":"2026-07-04T14:38:04Z"},{"alias_kind":"pith_short_12","alias_value":"RKNCEDRXFGLF","created_at":"2026-07-04T14:38:04Z"},{"alias_kind":"pith_short_16","alias_value":"RKNCEDRXFGLFOTLY","created_at":"2026-07-04T14:38:04Z"},{"alias_kind":"pith_short_8","alias_value":"RKNCEDRX","created_at":"2026-07-04T14:38:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:RKNCEDRXFGLFOTLYH77BCJJTEK","target":"record","payload":{"canonical_record":{"source":{"id":"math/0312156","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.RT","submitted_at":"2003-12-08T11:18:49Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"c6254159a9c438691047ac37b67acd2416e6cae28c1f2eed63e1c1122df27919","abstract_canon_sha256":"82b67e550fe8a9f653c495b8783eb5620aa768a08f6ef98e4a5e693f7eae853d"},"schema_version":"1.0"},"canonical_sha256":"8a9a220e372996574d783ffe11253322a7dcd44343cfe68dcb2406c295b62deb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:38:04.261502Z","signature_b64":"eokQ8XxXWGdqh0Cf9aM+FI/2Qp/+3oFf7f5HCBw9gwsogmovlOqv8HqXGjI7JdcrkWErQXvFXpbXnkuRTVL5Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a9a220e372996574d783ffe11253322a7dcd44343cfe68dcb2406c295b62deb","last_reissued_at":"2026-07-04T14:38:04.261113Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:38:04.261113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0312156","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:38:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"unQVXSId+DO6iBy5GsHrLBa3pSIYbeWTZSJKm8heRQRTDsvuaBvka3Kj/P59LeR6+tt9TPLDoD3etTm5ajsHCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T06:09:17.078640Z"},"content_sha256":"e4ccf4991b6f9bd134c3fd07e55b334a83ef63f1868d5e48f55840f06046647a","schema_version":"1.0","event_id":"sha256:e4ccf4991b6f9bd134c3fd07e55b334a83ef63f1868d5e48f55840f06046647a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:RKNCEDRXFGLFOTLYH77BCJJTEK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some Hodge theory from Lie algebras","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Constantin Teleman","submitted_at":"2003-12-08T11:18:49Z","abstract_excerpt":"We discuss Hodge-theoretic aspects, related to the loop Grassmannian, of the strong Macdonald conjecture (whose proof is joint work with Fishel and Grojnowski)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0312156","kind":"arxiv","version":1},"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/math/0312156/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":"2026-07-04T14:38:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"go8ukEenEYj35gYR5ooDRyQf9N1UeUcJ8a6nsP6teOLx6pA26SGxhkGZh+w/duwDxELS1k8pabCFmufGp8urDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T06:09:17.079106Z"},"content_sha256":"6b24962893d07de882a535a7767923606c83c3809a1335dbe967f8049103c68c","schema_version":"1.0","event_id":"sha256:6b24962893d07de882a535a7767923606c83c3809a1335dbe967f8049103c68c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RKNCEDRXFGLFOTLYH77BCJJTEK/bundle.json","state_url":"https://pith.science/pith/RKNCEDRXFGLFOTLYH77BCJJTEK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RKNCEDRXFGLFOTLYH77BCJJTEK/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":"2026-08-04T06:09:17Z","links":{"resolver":"https://pith.science/pith/RKNCEDRXFGLFOTLYH77BCJJTEK","bundle":"https://pith.science/pith/RKNCEDRXFGLFOTLYH77BCJJTEK/bundle.json","state":"https://pith.science/pith/RKNCEDRXFGLFOTLYH77BCJJTEK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RKNCEDRXFGLFOTLYH77BCJJTEK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:RKNCEDRXFGLFOTLYH77BCJJTEK","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":"82b67e550fe8a9f653c495b8783eb5620aa768a08f6ef98e4a5e693f7eae853d","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.RT","submitted_at":"2003-12-08T11:18:49Z","title_canon_sha256":"c6254159a9c438691047ac37b67acd2416e6cae28c1f2eed63e1c1122df27919"},"schema_version":"1.0","source":{"id":"math/0312156","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0312156","created_at":"2026-07-04T14:38:04Z"},{"alias_kind":"arxiv_version","alias_value":"math/0312156v1","created_at":"2026-07-04T14:38:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0312156","created_at":"2026-07-04T14:38:04Z"},{"alias_kind":"pith_short_12","alias_value":"RKNCEDRXFGLF","created_at":"2026-07-04T14:38:04Z"},{"alias_kind":"pith_short_16","alias_value":"RKNCEDRXFGLFOTLY","created_at":"2026-07-04T14:38:04Z"},{"alias_kind":"pith_short_8","alias_value":"RKNCEDRX","created_at":"2026-07-04T14:38:04Z"}],"graph_snapshots":[{"event_id":"sha256:6b24962893d07de882a535a7767923606c83c3809a1335dbe967f8049103c68c","target":"graph","created_at":"2026-07-04T14:38:04Z","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/math/0312156/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We discuss Hodge-theoretic aspects, related to the loop Grassmannian, of the strong Macdonald conjecture (whose proof is joint work with Fishel and Grojnowski).","authors_text":"Constantin Teleman","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"math.RT","submitted_at":"2003-12-08T11:18:49Z","title":"Some Hodge theory from Lie algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0312156","kind":"arxiv","version":1},"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:e4ccf4991b6f9bd134c3fd07e55b334a83ef63f1868d5e48f55840f06046647a","target":"record","created_at":"2026-07-04T14:38:04Z","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":"82b67e550fe8a9f653c495b8783eb5620aa768a08f6ef98e4a5e693f7eae853d","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.RT","submitted_at":"2003-12-08T11:18:49Z","title_canon_sha256":"c6254159a9c438691047ac37b67acd2416e6cae28c1f2eed63e1c1122df27919"},"schema_version":"1.0","source":{"id":"math/0312156","kind":"arxiv","version":1}},"canonical_sha256":"8a9a220e372996574d783ffe11253322a7dcd44343cfe68dcb2406c295b62deb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a9a220e372996574d783ffe11253322a7dcd44343cfe68dcb2406c295b62deb","first_computed_at":"2026-07-04T14:38:04.261113Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:38:04.261113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eokQ8XxXWGdqh0Cf9aM+FI/2Qp/+3oFf7f5HCBw9gwsogmovlOqv8HqXGjI7JdcrkWErQXvFXpbXnkuRTVL5Dw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:38:04.261502Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0312156","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4ccf4991b6f9bd134c3fd07e55b334a83ef63f1868d5e48f55840f06046647a","sha256:6b24962893d07de882a535a7767923606c83c3809a1335dbe967f8049103c68c"],"state_sha256":"870610d6ab15ac406556ba9e6cf3308a8725eda087e9dc4caa78a991ef4021c8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+I1izUBckkJ4QxNxxYIxDpG6LEJrMnB4e2VbJTgLs/yWhb8kKwTJTOqspjon2LMXgfgddnjMrX/hbfnvPs3iAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T06:09:17.082507Z","bundle_sha256":"f240d4afc1ed576730959aa6893f04e96981bf068ad1bd48fcd0d48024de4710"}}