{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:2UK56Y6OHLEDKXT6V2C6X2BK53","short_pith_number":"pith:2UK56Y6O","canonical_record":{"source":{"id":"1005.2053","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-05-12T11:26:06Z","cross_cats_sorted":["math.AG","math.MP","nlin.SI"],"title_canon_sha256":"e0828cf65aea8f9336c9b92c2f9d222c2e69bbb8f9f280e7ba88c3b5b63db0a3","abstract_canon_sha256":"334174e5e7d676e102bb2d26be735a5235d0a7eaa1a58b301d0843d8a125325b"},"schema_version":"1.0"},"canonical_sha256":"d515df63ce3ac8355e7eae85ebe82aeec3a24c026caf0a65d8598ce14c39c19a","source":{"kind":"arxiv","id":"1005.2053","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.2053","created_at":"2026-05-18T03:20:35Z"},{"alias_kind":"arxiv_version","alias_value":"1005.2053v3","created_at":"2026-05-18T03:20:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.2053","created_at":"2026-05-18T03:20:35Z"},{"alias_kind":"pith_short_12","alias_value":"2UK56Y6OHLED","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2UK56Y6OHLEDKXT6","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2UK56Y6O","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:2UK56Y6OHLEDKXT6V2C6X2BK53","target":"record","payload":{"canonical_record":{"source":{"id":"1005.2053","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-05-12T11:26:06Z","cross_cats_sorted":["math.AG","math.MP","nlin.SI"],"title_canon_sha256":"e0828cf65aea8f9336c9b92c2f9d222c2e69bbb8f9f280e7ba88c3b5b63db0a3","abstract_canon_sha256":"334174e5e7d676e102bb2d26be735a5235d0a7eaa1a58b301d0843d8a125325b"},"schema_version":"1.0"},"canonical_sha256":"d515df63ce3ac8355e7eae85ebe82aeec3a24c026caf0a65d8598ce14c39c19a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:35.957015Z","signature_b64":"loMi/NqTTY4af//b7lFKbF9QFZu052kkbG8DEcmYde+ExZV8Q0mhyP9IrKy0unJZBjvVGN9m7RBtlvuLvbLmDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d515df63ce3ac8355e7eae85ebe82aeec3a24c026caf0a65d8598ce14c39c19a","last_reissued_at":"2026-05-18T03:20:35.956210Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:35.956210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1005.2053","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":"2026-05-18T03:20:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r7GoLFNS2Cb6v3m52r4yBcOOowlJUpi6sHEI4fcmfbos8DrFFRS1814SbOiMyL7MuCiuvNL/VNpHb22DkDMPDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T10:35:37.885711Z"},"content_sha256":"270aebb05d86e55d988d7c14c5fe08eebc408865c3e5ce952342b42bc623e47e","schema_version":"1.0","event_id":"sha256:270aebb05d86e55d988d7c14c5fe08eebc408865c3e5ce952342b42bc623e47e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:2UK56Y6OHLEDKXT6V2C6X2BK53","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Birkhoff strata of Sato Grassmannian and algebraic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"B.G. Konopelchenko, G. Ortenzi","submitted_at":"2010-05-12T11:26:06Z","abstract_excerpt":"Algebraic and geometric structures associated with Birkhoff strata of Sato Grassmannian are analyzed. It is shown that each Birkhoff stratum $\\Sigma_S$ contains a subset $W_{\\hat{S}}$ of points for which each fiber of the corresponding tautological subbundle $TB_{W_S}$ is closed with respect to multiplication. Algebraically $TB_{W_S}$ is an infinite family of infinite-dimensional commutative associative algebras and geometrically it is an infinite tower of families of algebraic curves. For the big cell the subbundle $TB_{W_\\varnothing}$ represents the tower of families of normal rational (Vero"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2053","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":"2026-05-18T03:20:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GyDBMcaYQiSTPiXtWary4s/OmeC2KzV5PUEY1XQ8admnVlQ/xfMnCetCkuXLZWe1QqyL0idVq/GI8ZxmlaNpDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T10:35:37.886374Z"},"content_sha256":"36266010237f5941cee5829c861a9325eddcae25a06bd3750c3befd99a4a32d9","schema_version":"1.0","event_id":"sha256:36266010237f5941cee5829c861a9325eddcae25a06bd3750c3befd99a4a32d9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2UK56Y6OHLEDKXT6V2C6X2BK53/bundle.json","state_url":"https://pith.science/pith/2UK56Y6OHLEDKXT6V2C6X2BK53/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2UK56Y6OHLEDKXT6V2C6X2BK53/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":"2026-05-27T10:35:37Z","links":{"resolver":"https://pith.science/pith/2UK56Y6OHLEDKXT6V2C6X2BK53","bundle":"https://pith.science/pith/2UK56Y6OHLEDKXT6V2C6X2BK53/bundle.json","state":"https://pith.science/pith/2UK56Y6OHLEDKXT6V2C6X2BK53/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2UK56Y6OHLEDKXT6V2C6X2BK53/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:2UK56Y6OHLEDKXT6V2C6X2BK53","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":"334174e5e7d676e102bb2d26be735a5235d0a7eaa1a58b301d0843d8a125325b","cross_cats_sorted":["math.AG","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-05-12T11:26:06Z","title_canon_sha256":"e0828cf65aea8f9336c9b92c2f9d222c2e69bbb8f9f280e7ba88c3b5b63db0a3"},"schema_version":"1.0","source":{"id":"1005.2053","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.2053","created_at":"2026-05-18T03:20:35Z"},{"alias_kind":"arxiv_version","alias_value":"1005.2053v3","created_at":"2026-05-18T03:20:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.2053","created_at":"2026-05-18T03:20:35Z"},{"alias_kind":"pith_short_12","alias_value":"2UK56Y6OHLED","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2UK56Y6OHLEDKXT6","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2UK56Y6O","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:36266010237f5941cee5829c861a9325eddcae25a06bd3750c3befd99a4a32d9","target":"graph","created_at":"2026-05-18T03:20:35Z","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":"Algebraic and geometric structures associated with Birkhoff strata of Sato Grassmannian are analyzed. It is shown that each Birkhoff stratum $\\Sigma_S$ contains a subset $W_{\\hat{S}}$ of points for which each fiber of the corresponding tautological subbundle $TB_{W_S}$ is closed with respect to multiplication. Algebraically $TB_{W_S}$ is an infinite family of infinite-dimensional commutative associative algebras and geometrically it is an infinite tower of families of algebraic curves. For the big cell the subbundle $TB_{W_\\varnothing}$ represents the tower of families of normal rational (Vero","authors_text":"B.G. Konopelchenko, G. Ortenzi","cross_cats":["math.AG","math.MP","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-05-12T11:26:06Z","title":"Birkhoff strata of Sato Grassmannian and algebraic curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2053","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":"sha256:270aebb05d86e55d988d7c14c5fe08eebc408865c3e5ce952342b42bc623e47e","target":"record","created_at":"2026-05-18T03:20:35Z","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":"334174e5e7d676e102bb2d26be735a5235d0a7eaa1a58b301d0843d8a125325b","cross_cats_sorted":["math.AG","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-05-12T11:26:06Z","title_canon_sha256":"e0828cf65aea8f9336c9b92c2f9d222c2e69bbb8f9f280e7ba88c3b5b63db0a3"},"schema_version":"1.0","source":{"id":"1005.2053","kind":"arxiv","version":3}},"canonical_sha256":"d515df63ce3ac8355e7eae85ebe82aeec3a24c026caf0a65d8598ce14c39c19a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d515df63ce3ac8355e7eae85ebe82aeec3a24c026caf0a65d8598ce14c39c19a","first_computed_at":"2026-05-18T03:20:35.956210Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:20:35.956210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"loMi/NqTTY4af//b7lFKbF9QFZu052kkbG8DEcmYde+ExZV8Q0mhyP9IrKy0unJZBjvVGN9m7RBtlvuLvbLmDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:20:35.957015Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.2053","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:270aebb05d86e55d988d7c14c5fe08eebc408865c3e5ce952342b42bc623e47e","sha256:36266010237f5941cee5829c861a9325eddcae25a06bd3750c3befd99a4a32d9"],"state_sha256":"98aef26249d65b9095f77235045ded58b3738a89ac4261ea3e5195b333778e25"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uJ76YvxweBIvxBNYPlZFy3PCi7mfnPcJG1uIziSmn1KOzbJBUiI/B0KWQCJBPOZa2vRbnJjI7j68bR52LSFoBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T10:35:37.889717Z","bundle_sha256":"032e2ccd28486be3107380ad80d297c1ee0220c2b3b03a1b3d619317501c13c8"}}