{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:E7OHNKW5NDKFELWVMK3KNP5KYL","short_pith_number":"pith:E7OHNKW5","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"},"canonical_sha256":"27dc76aadd68d4522ed562b6a6bfaac2d955658bb43f2fe40c92153bc7587ab6","source":{"kind":"arxiv","id":"1011.4205","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.4205","created_at":"2026-05-18T02:04:43Z"},{"alias_kind":"arxiv_version","alias_value":"1011.4205v2","created_at":"2026-05-18T02:04:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.4205","created_at":"2026-05-18T02:04:43Z"},{"alias_kind":"pith_short_12","alias_value":"E7OHNKW5NDKF","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"E7OHNKW5NDKFELWV","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"E7OHNKW5","created_at":"2026-05-18T12:26:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:E7OHNKW5NDKFELWVMK3KNP5KYL","target":"record","payload":{"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"},"canonical_sha256":"27dc76aadd68d4522ed562b6a6bfaac2d955658bb43f2fe40c92153bc7587ab6","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"},"source_kind":"arxiv","source_id":"1011.4205","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":"2026-05-18T02:04:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WPVeaJiPqEOV6BQTGbFRjJZuKJG1YiWyDPi3UXmGAxg6WsSa7CRa5r3YOrirP0cp/iTAAq3yKEpewfCF66GPBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T20:46:37.267333Z"},"content_sha256":"c795f3e37eb917a0dec32a923d40695e23ba310b69b9052523a6df1de68d1722","schema_version":"1.0","event_id":"sha256:c795f3e37eb917a0dec32a923d40695e23ba310b69b9052523a6df1de68d1722"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:E7OHNKW5NDKFELWVMK3KNP5KYL","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:04:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V9hvjVxENiWDck6/i6BZKUAkeAF6q6D2vcR/qmUes4BeaehT6hDAkME23mZM0eAXAB+bdf1GRLhHlnHmyRM7Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T20:46:37.267678Z"},"content_sha256":"ab5c93d616cd5bd992d61af6336b6e679f6b369bc39fa14008b267ba030ea84a","schema_version":"1.0","event_id":"sha256:ab5c93d616cd5bd992d61af6336b6e679f6b369bc39fa14008b267ba030ea84a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E7OHNKW5NDKFELWVMK3KNP5KYL/bundle.json","state_url":"https://pith.science/pith/E7OHNKW5NDKFELWVMK3KNP5KYL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E7OHNKW5NDKFELWVMK3KNP5KYL/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":"2026-06-27T20:46:37Z","links":{"resolver":"https://pith.science/pith/E7OHNKW5NDKFELWVMK3KNP5KYL","bundle":"https://pith.science/pith/E7OHNKW5NDKFELWVMK3KNP5KYL/bundle.json","state":"https://pith.science/pith/E7OHNKW5NDKFELWVMK3KNP5KYL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E7OHNKW5NDKFELWVMK3KNP5KYL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:E7OHNKW5NDKFELWVMK3KNP5KYL","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":"1c0dbea40682ff704481cf2c6b21aeb97e69b4ed2000f4354a0f7e34863773c2","cross_cats_sorted":["math.AG","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-11-18T14:54:11Z","title_canon_sha256":"cb7b77286acf9727d16f12dc47eeb1d3ed926ba8d96e2a3ff1f6a303f3fd90aa"},"schema_version":"1.0","source":{"id":"1011.4205","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.4205","created_at":"2026-05-18T02:04:43Z"},{"alias_kind":"arxiv_version","alias_value":"1011.4205v2","created_at":"2026-05-18T02:04:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.4205","created_at":"2026-05-18T02:04:43Z"},{"alias_kind":"pith_short_12","alias_value":"E7OHNKW5NDKF","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"E7OHNKW5NDKFELWV","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"E7OHNKW5","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:ab5c93d616cd5bd992d61af6336b6e679f6b369bc39fa14008b267ba030ea84a","target":"graph","created_at":"2026-05-18T02:04:43Z","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 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.","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":"2010-11-18T14:54:11Z","title":"Birkhoff strata of the Grassmannian Gr$\\mathrm{^{(2)}}$: Algebraic curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.4205","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:c795f3e37eb917a0dec32a923d40695e23ba310b69b9052523a6df1de68d1722","target":"record","created_at":"2026-05-18T02:04:43Z","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":"1c0dbea40682ff704481cf2c6b21aeb97e69b4ed2000f4354a0f7e34863773c2","cross_cats_sorted":["math.AG","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-11-18T14:54:11Z","title_canon_sha256":"cb7b77286acf9727d16f12dc47eeb1d3ed926ba8d96e2a3ff1f6a303f3fd90aa"},"schema_version":"1.0","source":{"id":"1011.4205","kind":"arxiv","version":2}},"canonical_sha256":"27dc76aadd68d4522ed562b6a6bfaac2d955658bb43f2fe40c92153bc7587ab6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27dc76aadd68d4522ed562b6a6bfaac2d955658bb43f2fe40c92153bc7587ab6","first_computed_at":"2026-05-18T02:04:43.980275Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:04:43.980275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ob2rELysCcQGxvuEh2oBmLvjx7HcY1cqZO0crYVtvPgJISOZ1QmKX2Lb82Kdaett38cU/wDptsOuoqsVwyW+Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:04:43.981170Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.4205","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c795f3e37eb917a0dec32a923d40695e23ba310b69b9052523a6df1de68d1722","sha256:ab5c93d616cd5bd992d61af6336b6e679f6b369bc39fa14008b267ba030ea84a"],"state_sha256":"b286c00d4f69afbc4ee6bdb309483331c30b4a54cbeaa6edf4ccfd723e192161"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3TIEQBemv71c9WsJRdXWXEEpFBOy6hXUzmzMO8K+80YWtju/0vETlMHOscsBbjk7S0AHNgmeyWHPhLlHjTjQBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T20:46:37.269553Z","bundle_sha256":"38d3f42db37dc6e60abfcc1457f18d00f3829048286d265bd79e6067f8457a84"}}