{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:E7OHNKW5NDKFELWVMK3KNP5KYL","short_pith_number":"pith:E7OHNKW5","schema_version":"1.0","canonical_sha256":"27dc76aadd68d4522ed562b6a6bfaac2d955658bb43f2fe40c92153bc7587ab6","source":{"kind":"arxiv","id":"1011.4205","version":2},"attestation_state":"computed","paper":{"title":"Birkhoff strata of the Grassmannian Gr$\\mathrm{^{(2)}}$: 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":"2010-11-18T14:54:11Z","abstract_excerpt":"Algebraic varieties and curves arising in Birkhoff strata of the Sato Grassmannian Gr${^{(2)}}$ are studied. It is shown that the big cell $\\Sigma_0$ contains the tower of families of the normal rational curves of all odd orders. Strata $\\Sigma_{2n}$, $n=1,2,3,...$ contain hyperelliptic curves of genus $n$ and their coordinate rings. Strata $\\Sigma_{2n+1}$, $n=0,1,2,3,...$ contain $(2m+1,2m+3)-$plane curves for $n=2m,2m-1$ $(m \\geq 2)$ and $(3,4)$ and $(3,5)$ curves in $\\Sigma_3$, $\\Sigma_5$ respectively. Curves in the strata $\\Sigma_{2n+1}$ have zero genus."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1011.4205","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-11-18T14:54:11Z","cross_cats_sorted":["math.AG","math.MP","nlin.SI"],"title_canon_sha256":"cb7b77286acf9727d16f12dc47eeb1d3ed926ba8d96e2a3ff1f6a303f3fd90aa","abstract_canon_sha256":"1c0dbea40682ff704481cf2c6b21aeb97e69b4ed2000f4354a0f7e34863773c2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:04:43.981170Z","signature_b64":"ob2rELysCcQGxvuEh2oBmLvjx7HcY1cqZO0crYVtvPgJISOZ1QmKX2Lb82Kdaett38cU/wDptsOuoqsVwyW+Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27dc76aadd68d4522ed562b6a6bfaac2d955658bb43f2fe40c92153bc7587ab6","last_reissued_at":"2026-05-18T02:04:43.980275Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:04:43.980275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Birkhoff strata of the Grassmannian Gr$\\mathrm{^{(2)}}$: 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":"2010-11-18T14:54:11Z","abstract_excerpt":"Algebraic varieties and curves arising in Birkhoff strata of the Sato Grassmannian Gr${^{(2)}}$ are studied. It is shown that the big cell $\\Sigma_0$ contains the tower of families of the normal rational curves of all odd orders. Strata $\\Sigma_{2n}$, $n=1,2,3,...$ contain hyperelliptic curves of genus $n$ and their coordinate rings. Strata $\\Sigma_{2n+1}$, $n=0,1,2,3,...$ contain $(2m+1,2m+3)-$plane curves for $n=2m,2m-1$ $(m \\geq 2)$ and $(3,4)$ and $(3,5)$ curves in $\\Sigma_3$, $\\Sigma_5$ respectively. Curves in the strata $\\Sigma_{2n+1}$ have zero genus."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.4205","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1011.4205","created_at":"2026-05-18T02:04:43.980423+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.4205v2","created_at":"2026-05-18T02:04:43.980423+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.4205","created_at":"2026-05-18T02:04:43.980423+00:00"},{"alias_kind":"pith_short_12","alias_value":"E7OHNKW5NDKF","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_16","alias_value":"E7OHNKW5NDKFELWV","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_8","alias_value":"E7OHNKW5","created_at":"2026-05-18T12:26:06.534383+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/E7OHNKW5NDKFELWVMK3KNP5KYL","json":"https://pith.science/pith/E7OHNKW5NDKFELWVMK3KNP5KYL.json","graph_json":"https://pith.science/api/pith-number/E7OHNKW5NDKFELWVMK3KNP5KYL/graph.json","events_json":"https://pith.science/api/pith-number/E7OHNKW5NDKFELWVMK3KNP5KYL/events.json","paper":"https://pith.science/paper/E7OHNKW5"},"agent_actions":{"view_html":"https://pith.science/pith/E7OHNKW5NDKFELWVMK3KNP5KYL","download_json":"https://pith.science/pith/E7OHNKW5NDKFELWVMK3KNP5KYL.json","view_paper":"https://pith.science/paper/E7OHNKW5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.4205&json=true","fetch_graph":"https://pith.science/api/pith-number/E7OHNKW5NDKFELWVMK3KNP5KYL/graph.json","fetch_events":"https://pith.science/api/pith-number/E7OHNKW5NDKFELWVMK3KNP5KYL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E7OHNKW5NDKFELWVMK3KNP5KYL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E7OHNKW5NDKFELWVMK3KNP5KYL/action/storage_attestation","attest_author":"https://pith.science/pith/E7OHNKW5NDKFELWVMK3KNP5KYL/action/author_attestation","sign_citation":"https://pith.science/pith/E7OHNKW5NDKFELWVMK3KNP5KYL/action/citation_signature","submit_replication":"https://pith.science/pith/E7OHNKW5NDKFELWVMK3KNP5KYL/action/replication_record"}},"created_at":"2026-05-18T02:04:43.980423+00:00","updated_at":"2026-05-18T02:04:43.980423+00:00"}