{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:5YCIIT7HS372NTHAPLXK3NLMRA","short_pith_number":"pith:5YCIIT7H","canonical_record":{"source":{"id":"1710.00866","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2017-10-02T18:49:47Z","cross_cats_sorted":[],"title_canon_sha256":"f4ed3f39ca0b07044cbc3e4d31c2a2d2fdb0c7371d4d787fee1cc2cc087d7b43","abstract_canon_sha256":"e868c0ed8fb00bead2f9c8350d6e9a6630d758b059c4a859ea20911a836cedba"},"schema_version":"1.0"},"canonical_sha256":"ee04844fe796ffa6cce07aeeadb56c88154a10b055318b7f470a9cf8c1abd1c1","source":{"kind":"arxiv","id":"1710.00866","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.00866","created_at":"2026-05-18T00:33:47Z"},{"alias_kind":"arxiv_version","alias_value":"1710.00866v1","created_at":"2026-05-18T00:33:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00866","created_at":"2026-05-18T00:33:47Z"},{"alias_kind":"pith_short_12","alias_value":"5YCIIT7HS372","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"5YCIIT7HS372NTHA","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"5YCIIT7H","created_at":"2026-05-18T12:31:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:5YCIIT7HS372NTHAPLXK3NLMRA","target":"record","payload":{"canonical_record":{"source":{"id":"1710.00866","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2017-10-02T18:49:47Z","cross_cats_sorted":[],"title_canon_sha256":"f4ed3f39ca0b07044cbc3e4d31c2a2d2fdb0c7371d4d787fee1cc2cc087d7b43","abstract_canon_sha256":"e868c0ed8fb00bead2f9c8350d6e9a6630d758b059c4a859ea20911a836cedba"},"schema_version":"1.0"},"canonical_sha256":"ee04844fe796ffa6cce07aeeadb56c88154a10b055318b7f470a9cf8c1abd1c1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:47.671887Z","signature_b64":"YUNe/mSe0/gxQYNHyUPQtfZcwEgeqiSa0Lfk2qzb7KB/XXeWHVxaJUFtTboQnW/FUKHwShvGsxuHx+VSoYaqBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee04844fe796ffa6cce07aeeadb56c88154a10b055318b7f470a9cf8c1abd1c1","last_reissued_at":"2026-05-18T00:33:47.671217Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:47.671217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.00866","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":"2026-05-18T00:33:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q3QiWd23FFq7/KYMyJazeG4PLEpW4sdx6i5UNoAZIo9li9cIu9cUI4uSu1+9ecCbxL5rKAWYKR+V1ayFPsZiBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T00:46:09.111727Z"},"content_sha256":"b528725b7d94e8acabe8d98988aa98b6a61ee40c503982b6314ee92455c206fb","schema_version":"1.0","event_id":"sha256:b528725b7d94e8acabe8d98988aa98b6a61ee40c503982b6314ee92455c206fb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:5YCIIT7HS372NTHAPLXK3NLMRA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The space of symmetric squares of hyperelliptic curves and integrable Hamiltonian polynomial systems on $\\bbbR^4$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"A. V. Mikhailov, V. M. Buchstaber","submitted_at":"2017-10-02T18:49:47Z","abstract_excerpt":"We construct Lie algebras of vector fields on universal bundles $\\mathcal{E}^2_{N,0}$ of symmetric squares of hyperelliptic curves of genus $g=1,2,\\dots$, where $g=\\left[\\frac{N-1}{2}\\right], \\ N=3,4,\\ldots$. For each of these Lie algebras, the Lie subalgebra of vertical fields has commuting generators, while the generators of the Lie subalgebra of projectable fields determines the canonical representation of the Lie subalgebra with generators $L_{2q}$, $q=-1, 0, 1, 2, \\dots$, of the Witt algebra. We give explicitly a bi-rational equivalence of the space $\\mathcal{E}^2_{N,0}$ and $\\bbbC^{N+1}$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00866","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":"2026-05-18T00:33:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tV8TL4M2hZ7xywryiiVn1fp+J/D3II7z+H13sD/pGvFrdL+d072VJCE9FxRbj0ThG34Fs7mmgkLMCr8YmNGQCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T00:46:09.112074Z"},"content_sha256":"c2f86ef0ab58dc5def57b9af5e794209c9160d12add15b59a62b2b6c5fc86ba2","schema_version":"1.0","event_id":"sha256:c2f86ef0ab58dc5def57b9af5e794209c9160d12add15b59a62b2b6c5fc86ba2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5YCIIT7HS372NTHAPLXK3NLMRA/bundle.json","state_url":"https://pith.science/pith/5YCIIT7HS372NTHAPLXK3NLMRA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5YCIIT7HS372NTHAPLXK3NLMRA/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":"2026-06-27T00:46:09Z","links":{"resolver":"https://pith.science/pith/5YCIIT7HS372NTHAPLXK3NLMRA","bundle":"https://pith.science/pith/5YCIIT7HS372NTHAPLXK3NLMRA/bundle.json","state":"https://pith.science/pith/5YCIIT7HS372NTHAPLXK3NLMRA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5YCIIT7HS372NTHAPLXK3NLMRA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:5YCIIT7HS372NTHAPLXK3NLMRA","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":"e868c0ed8fb00bead2f9c8350d6e9a6630d758b059c4a859ea20911a836cedba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2017-10-02T18:49:47Z","title_canon_sha256":"f4ed3f39ca0b07044cbc3e4d31c2a2d2fdb0c7371d4d787fee1cc2cc087d7b43"},"schema_version":"1.0","source":{"id":"1710.00866","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.00866","created_at":"2026-05-18T00:33:47Z"},{"alias_kind":"arxiv_version","alias_value":"1710.00866v1","created_at":"2026-05-18T00:33:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00866","created_at":"2026-05-18T00:33:47Z"},{"alias_kind":"pith_short_12","alias_value":"5YCIIT7HS372","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"5YCIIT7HS372NTHA","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"5YCIIT7H","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:c2f86ef0ab58dc5def57b9af5e794209c9160d12add15b59a62b2b6c5fc86ba2","target":"graph","created_at":"2026-05-18T00:33:47Z","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 construct Lie algebras of vector fields on universal bundles $\\mathcal{E}^2_{N,0}$ of symmetric squares of hyperelliptic curves of genus $g=1,2,\\dots$, where $g=\\left[\\frac{N-1}{2}\\right], \\ N=3,4,\\ldots$. For each of these Lie algebras, the Lie subalgebra of vertical fields has commuting generators, while the generators of the Lie subalgebra of projectable fields determines the canonical representation of the Lie subalgebra with generators $L_{2q}$, $q=-1, 0, 1, 2, \\dots$, of the Witt algebra. We give explicitly a bi-rational equivalence of the space $\\mathcal{E}^2_{N,0}$ and $\\bbbC^{N+1}$","authors_text":"A. V. Mikhailov, V. M. Buchstaber","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2017-10-02T18:49:47Z","title":"The space of symmetric squares of hyperelliptic curves and integrable Hamiltonian polynomial systems on $\\bbbR^4$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00866","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:b528725b7d94e8acabe8d98988aa98b6a61ee40c503982b6314ee92455c206fb","target":"record","created_at":"2026-05-18T00:33:47Z","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":"e868c0ed8fb00bead2f9c8350d6e9a6630d758b059c4a859ea20911a836cedba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2017-10-02T18:49:47Z","title_canon_sha256":"f4ed3f39ca0b07044cbc3e4d31c2a2d2fdb0c7371d4d787fee1cc2cc087d7b43"},"schema_version":"1.0","source":{"id":"1710.00866","kind":"arxiv","version":1}},"canonical_sha256":"ee04844fe796ffa6cce07aeeadb56c88154a10b055318b7f470a9cf8c1abd1c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee04844fe796ffa6cce07aeeadb56c88154a10b055318b7f470a9cf8c1abd1c1","first_computed_at":"2026-05-18T00:33:47.671217Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:47.671217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YUNe/mSe0/gxQYNHyUPQtfZcwEgeqiSa0Lfk2qzb7KB/XXeWHVxaJUFtTboQnW/FUKHwShvGsxuHx+VSoYaqBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:47.671887Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.00866","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b528725b7d94e8acabe8d98988aa98b6a61ee40c503982b6314ee92455c206fb","sha256:c2f86ef0ab58dc5def57b9af5e794209c9160d12add15b59a62b2b6c5fc86ba2"],"state_sha256":"12a733e9fc62b2955dccad41ae340d7bf3e0435d3cac5650483654dbcc319dfc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qk2cZgdlUe7X2cgf21fi/knLwlRNlwAgQLYdEC8go6dBWkCKUhQl/FWDuaQxLrDCgpuBzbN2KeRZaplfQn4ACQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T00:46:09.113970Z","bundle_sha256":"653911a0f878df52c4c2d86d908ef404d818b453fd85c0541de2dab13b99f7ef"}}