{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:OPFPZYDSQYIOU2RWRGMSW4BFJ6","short_pith_number":"pith:OPFPZYDS","canonical_record":{"source":{"id":"1008.0509","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-08-03T10:17:26Z","cross_cats_sorted":["math-ph","math.MP","nlin.SI"],"title_canon_sha256":"f477f0700ef9a90c4b83c9730ad00336018687d140474875f93153496e44aa49","abstract_canon_sha256":"756967912c6ac47bafe3c2bbdd7bd33c42baa8ef1496d598c809aef2384e4d9d"},"schema_version":"1.0"},"canonical_sha256":"73cafce0728610ea6a3689992b70254fbdec7f9bac648f35e651e127258a0bff","source":{"kind":"arxiv","id":"1008.0509","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.0509","created_at":"2026-05-18T03:57:39Z"},{"alias_kind":"arxiv_version","alias_value":"1008.0509v2","created_at":"2026-05-18T03:57:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.0509","created_at":"2026-05-18T03:57:39Z"},{"alias_kind":"pith_short_12","alias_value":"OPFPZYDSQYIO","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OPFPZYDSQYIOU2RW","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OPFPZYDS","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:OPFPZYDSQYIOU2RWRGMSW4BFJ6","target":"record","payload":{"canonical_record":{"source":{"id":"1008.0509","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-08-03T10:17:26Z","cross_cats_sorted":["math-ph","math.MP","nlin.SI"],"title_canon_sha256":"f477f0700ef9a90c4b83c9730ad00336018687d140474875f93153496e44aa49","abstract_canon_sha256":"756967912c6ac47bafe3c2bbdd7bd33c42baa8ef1496d598c809aef2384e4d9d"},"schema_version":"1.0"},"canonical_sha256":"73cafce0728610ea6a3689992b70254fbdec7f9bac648f35e651e127258a0bff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:39.071898Z","signature_b64":"bWQvuaOCGKrUbtf2TGrOcAAbyubg/f9dJEFZ2K/zIyKHiFYfSLGDzwt0TgIUHzDyUvoHhx+Skvhew4Eq2HE7Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73cafce0728610ea6a3689992b70254fbdec7f9bac648f35e651e127258a0bff","last_reissued_at":"2026-05-18T03:57:39.071139Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:39.071139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.0509","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":"2026-05-18T03:57:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oa2hf5zm4g5iMTAjxHO1LU/8J37ACSdg4s1BaHoSgk+sRiqwnxn7fdyjp4dJZC7VVjKW37r7kmSb8hcp3yMgDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:30:10.530124Z"},"content_sha256":"1e09d0e06d12f15613121c94fe14ce90ce0db3bf65503dd1c9dcf561f3be5db7","schema_version":"1.0","event_id":"sha256:1e09d0e06d12f15613121c94fe14ce90ce0db3bf65503dd1c9dcf561f3be5db7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:OPFPZYDSQYIOU2RWRGMSW4BFJ6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quasi-periodic and periodic solutions of the Toda lattice via the hyperelliptic sigma function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.SI"],"primary_cat":"math.AG","authors_text":"Emma Previato, Shigeki Matsutani, Yuji Kodama","submitted_at":"2010-08-03T10:17:26Z","abstract_excerpt":"M. Toda in 1967 (\\textit{J. Phys. Soc. Japan}, \\textbf{22} and \\textbf{23}) considered a lattice model with exponential interaction and proved, as suggested by the Fermi-Pasta-Ulam experiments in the 1950s, that it has exact periodic and soliton solutions. The Toda lattice, as it came to be known, was then extensively studied as one of the completely integrable (differential-difference) non-linear equations which admit exact solutions in terms of theta functions of hyperelliptic curves. In this paper, we extend Toda's original approach to give hyperelliptic solutions of the Toda lattice in ter"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.0509","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":"2026-05-18T03:57:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mga1vgUaS6F2OeAFnzDJgvhiUS9/tlXfGgIAi/ZAuM8cG2HxM+d93OBpD4OP3IAlwphaaIkCCLLTBJ+0qxLWCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:30:10.530559Z"},"content_sha256":"9d5d476e74a6c79e9f091263b1a9804ebc9b7761c2d70aebcf99d1a84cbe6859","schema_version":"1.0","event_id":"sha256:9d5d476e74a6c79e9f091263b1a9804ebc9b7761c2d70aebcf99d1a84cbe6859"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OPFPZYDSQYIOU2RWRGMSW4BFJ6/bundle.json","state_url":"https://pith.science/pith/OPFPZYDSQYIOU2RWRGMSW4BFJ6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OPFPZYDSQYIOU2RWRGMSW4BFJ6/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":"2026-05-26T22:30:10Z","links":{"resolver":"https://pith.science/pith/OPFPZYDSQYIOU2RWRGMSW4BFJ6","bundle":"https://pith.science/pith/OPFPZYDSQYIOU2RWRGMSW4BFJ6/bundle.json","state":"https://pith.science/pith/OPFPZYDSQYIOU2RWRGMSW4BFJ6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OPFPZYDSQYIOU2RWRGMSW4BFJ6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:OPFPZYDSQYIOU2RWRGMSW4BFJ6","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":"756967912c6ac47bafe3c2bbdd7bd33c42baa8ef1496d598c809aef2384e4d9d","cross_cats_sorted":["math-ph","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-08-03T10:17:26Z","title_canon_sha256":"f477f0700ef9a90c4b83c9730ad00336018687d140474875f93153496e44aa49"},"schema_version":"1.0","source":{"id":"1008.0509","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.0509","created_at":"2026-05-18T03:57:39Z"},{"alias_kind":"arxiv_version","alias_value":"1008.0509v2","created_at":"2026-05-18T03:57:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.0509","created_at":"2026-05-18T03:57:39Z"},{"alias_kind":"pith_short_12","alias_value":"OPFPZYDSQYIO","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OPFPZYDSQYIOU2RW","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OPFPZYDS","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:9d5d476e74a6c79e9f091263b1a9804ebc9b7761c2d70aebcf99d1a84cbe6859","target":"graph","created_at":"2026-05-18T03:57:39Z","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":"M. Toda in 1967 (\\textit{J. Phys. Soc. Japan}, \\textbf{22} and \\textbf{23}) considered a lattice model with exponential interaction and proved, as suggested by the Fermi-Pasta-Ulam experiments in the 1950s, that it has exact periodic and soliton solutions. The Toda lattice, as it came to be known, was then extensively studied as one of the completely integrable (differential-difference) non-linear equations which admit exact solutions in terms of theta functions of hyperelliptic curves. In this paper, we extend Toda's original approach to give hyperelliptic solutions of the Toda lattice in ter","authors_text":"Emma Previato, Shigeki Matsutani, Yuji Kodama","cross_cats":["math-ph","math.MP","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-08-03T10:17:26Z","title":"Quasi-periodic and periodic solutions of the Toda lattice via the hyperelliptic sigma function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.0509","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":"sha256:1e09d0e06d12f15613121c94fe14ce90ce0db3bf65503dd1c9dcf561f3be5db7","target":"record","created_at":"2026-05-18T03:57:39Z","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":"756967912c6ac47bafe3c2bbdd7bd33c42baa8ef1496d598c809aef2384e4d9d","cross_cats_sorted":["math-ph","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-08-03T10:17:26Z","title_canon_sha256":"f477f0700ef9a90c4b83c9730ad00336018687d140474875f93153496e44aa49"},"schema_version":"1.0","source":{"id":"1008.0509","kind":"arxiv","version":2}},"canonical_sha256":"73cafce0728610ea6a3689992b70254fbdec7f9bac648f35e651e127258a0bff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73cafce0728610ea6a3689992b70254fbdec7f9bac648f35e651e127258a0bff","first_computed_at":"2026-05-18T03:57:39.071139Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:39.071139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bWQvuaOCGKrUbtf2TGrOcAAbyubg/f9dJEFZ2K/zIyKHiFYfSLGDzwt0TgIUHzDyUvoHhx+Skvhew4Eq2HE7Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:39.071898Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.0509","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e09d0e06d12f15613121c94fe14ce90ce0db3bf65503dd1c9dcf561f3be5db7","sha256:9d5d476e74a6c79e9f091263b1a9804ebc9b7761c2d70aebcf99d1a84cbe6859"],"state_sha256":"38ad92503c7c3c02a0c9bafe948e8337bf8a081217a53c6dc29654ed146afd3f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ns6QWSBBqMPxuMUGp5DdsYh2F4tnNyrM3tlF2difgRizzwlsuvxsSKlh1pdjuNThsKOkBeGKG9S3LD62x+VUBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T22:30:10.532880Z","bundle_sha256":"de2efdfa16290dfa9c0b2cd739f290e550354cfd6a99d3f332979d1e165ac24a"}}