{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:4ET44X3OSDQX6N7JY5YPCI74TR","short_pith_number":"pith:4ET44X3O","canonical_record":{"source":{"id":"math/0408429","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AC","submitted_at":"2004-08-31T10:11:45Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"7eec8e3fcbbda6d2d5f26e40ee1e0c9bddb25c7a815be3332c82888aa44bfb29","abstract_canon_sha256":"fbeb4b45ca677594df9866081c00e1f240a1228c2d13474e83ac5dfa1c2e7bf4"},"schema_version":"1.0"},"canonical_sha256":"e127ce5f6e90e17f37e9c770f123fc9c5267dc5809858a928f3c39ded99828d3","source":{"kind":"arxiv","id":"math/0408429","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0408429","created_at":"2026-05-18T04:34:28Z"},{"alias_kind":"arxiv_version","alias_value":"math/0408429v1","created_at":"2026-05-18T04:34:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0408429","created_at":"2026-05-18T04:34:28Z"},{"alias_kind":"pith_short_12","alias_value":"4ET44X3OSDQX","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"4ET44X3OSDQX6N7J","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"4ET44X3O","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:4ET44X3OSDQX6N7JY5YPCI74TR","target":"record","payload":{"canonical_record":{"source":{"id":"math/0408429","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AC","submitted_at":"2004-08-31T10:11:45Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"7eec8e3fcbbda6d2d5f26e40ee1e0c9bddb25c7a815be3332c82888aa44bfb29","abstract_canon_sha256":"fbeb4b45ca677594df9866081c00e1f240a1228c2d13474e83ac5dfa1c2e7bf4"},"schema_version":"1.0"},"canonical_sha256":"e127ce5f6e90e17f37e9c770f123fc9c5267dc5809858a928f3c39ded99828d3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:28.228602Z","signature_b64":"LaqyugNRWj8Z+GhLZr5044hVC8bOaOmN+86LwXjFXSyYHahjBYAcowqtQP9S2IrQlB0jATMLS+y+1nps8MlUBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e127ce5f6e90e17f37e9c770f123fc9c5267dc5809858a928f3c39ded99828d3","last_reissued_at":"2026-05-18T04:34:28.228094Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:28.228094Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0408429","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":"2026-05-18T04:34:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HGp6QYHy/67kb7Gjhw8e2Rb7nEgU1nvZOMsk8PYCTTZqqdTpXr3CpJ0v9V2zELdluW+e9j1vqk05acTpX5PpDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T23:47:41.908608Z"},"content_sha256":"34dabffb13995d23b9a96a94f9c191ba4c16a52fd1144859ef91b7893264d7c7","schema_version":"1.0","event_id":"sha256:34dabffb13995d23b9a96a94f9c191ba4c16a52fd1144859ef91b7893264d7c7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:4ET44X3OSDQX6N7JY5YPCI74TR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Another proof of theorems of De Concini and Procesi","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Mitsuyasu Hashimoto","submitted_at":"2004-08-31T10:11:45Z","abstract_excerpt":"We give a new proof of some characteristic-free fundamental theorems in invariant theory first proved in C. De Concini and C. Procesi, A characteristic free approach to invariant theory, Adv. Math. 21 (1976), 330--354. We treat the action of the general linear group and the symplectic group. Our approach is geometric, and utilizes the fact that the categorical quotients are principal fiber bundles off codimension two or more."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0408429","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":""},"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":"2026-05-18T04:34:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b1r6qagt+CQHw40byBNzQqTt/+8+fZVfeGrPA96xa3zY7FYYIHuQWy3byHMhUVY0p5vWw95rp1pBJCAoz+jODg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T23:47:41.908942Z"},"content_sha256":"552f7b42033678787766d018c7ef3094e42a66fb3e32361bde4a15e201c19616","schema_version":"1.0","event_id":"sha256:552f7b42033678787766d018c7ef3094e42a66fb3e32361bde4a15e201c19616"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4ET44X3OSDQX6N7JY5YPCI74TR/bundle.json","state_url":"https://pith.science/pith/4ET44X3OSDQX6N7JY5YPCI74TR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4ET44X3OSDQX6N7JY5YPCI74TR/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":"2026-06-26T23:47:41Z","links":{"resolver":"https://pith.science/pith/4ET44X3OSDQX6N7JY5YPCI74TR","bundle":"https://pith.science/pith/4ET44X3OSDQX6N7JY5YPCI74TR/bundle.json","state":"https://pith.science/pith/4ET44X3OSDQX6N7JY5YPCI74TR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4ET44X3OSDQX6N7JY5YPCI74TR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:4ET44X3OSDQX6N7JY5YPCI74TR","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":"fbeb4b45ca677594df9866081c00e1f240a1228c2d13474e83ac5dfa1c2e7bf4","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.AC","submitted_at":"2004-08-31T10:11:45Z","title_canon_sha256":"7eec8e3fcbbda6d2d5f26e40ee1e0c9bddb25c7a815be3332c82888aa44bfb29"},"schema_version":"1.0","source":{"id":"math/0408429","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0408429","created_at":"2026-05-18T04:34:28Z"},{"alias_kind":"arxiv_version","alias_value":"math/0408429v1","created_at":"2026-05-18T04:34:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0408429","created_at":"2026-05-18T04:34:28Z"},{"alias_kind":"pith_short_12","alias_value":"4ET44X3OSDQX","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"4ET44X3OSDQX6N7J","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"4ET44X3O","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:552f7b42033678787766d018c7ef3094e42a66fb3e32361bde4a15e201c19616","target":"graph","created_at":"2026-05-18T04:34:28Z","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 give a new proof of some characteristic-free fundamental theorems in invariant theory first proved in C. De Concini and C. Procesi, A characteristic free approach to invariant theory, Adv. Math. 21 (1976), 330--354. We treat the action of the general linear group and the symplectic group. Our approach is geometric, and utilizes the fact that the categorical quotients are principal fiber bundles off codimension two or more.","authors_text":"Mitsuyasu Hashimoto","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"math.AC","submitted_at":"2004-08-31T10:11:45Z","title":"Another proof of theorems of De Concini and Procesi"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0408429","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":"sha256:34dabffb13995d23b9a96a94f9c191ba4c16a52fd1144859ef91b7893264d7c7","target":"record","created_at":"2026-05-18T04:34:28Z","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":"fbeb4b45ca677594df9866081c00e1f240a1228c2d13474e83ac5dfa1c2e7bf4","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.AC","submitted_at":"2004-08-31T10:11:45Z","title_canon_sha256":"7eec8e3fcbbda6d2d5f26e40ee1e0c9bddb25c7a815be3332c82888aa44bfb29"},"schema_version":"1.0","source":{"id":"math/0408429","kind":"arxiv","version":1}},"canonical_sha256":"e127ce5f6e90e17f37e9c770f123fc9c5267dc5809858a928f3c39ded99828d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e127ce5f6e90e17f37e9c770f123fc9c5267dc5809858a928f3c39ded99828d3","first_computed_at":"2026-05-18T04:34:28.228094Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:28.228094Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LaqyugNRWj8Z+GhLZr5044hVC8bOaOmN+86LwXjFXSyYHahjBYAcowqtQP9S2IrQlB0jATMLS+y+1nps8MlUBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:28.228602Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0408429","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34dabffb13995d23b9a96a94f9c191ba4c16a52fd1144859ef91b7893264d7c7","sha256:552f7b42033678787766d018c7ef3094e42a66fb3e32361bde4a15e201c19616"],"state_sha256":"074871bea98d75048fd43dd334ba045ed4f2d5e4c111b56369a33c2a487df195"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"obqqMiuRryFCG5paMyPbMi0/bhYeJrFeY9xmsHgS/2lXUhAincjK8pnXSUhtG8XczmKnWfD5Gn/pdhm64NHGAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T23:47:41.910827Z","bundle_sha256":"2bb637d4e950c84e3cbdae99bb0de40d57be6875d03e2843bc89c50fa65f7138"}}