{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:QIFBI2Z4CTNR6SPEFLQEWGYUUC","short_pith_number":"pith:QIFBI2Z4","canonical_record":{"source":{"id":"2108.06560","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2021-08-14T15:19:52Z","cross_cats_sorted":[],"title_canon_sha256":"e670de36d23f38d18e4b8f741f0c272783d1f30577608482a581d4c7d930342e","abstract_canon_sha256":"dad98b485367e0e4a5192e5f7086f2ecf4ae8b72ba59000741fba47626083177"},"schema_version":"1.0"},"canonical_sha256":"820a146b3c14db1f49e42ae04b1b14a0860eef50aeac0b795b6640b33d29b93e","source":{"kind":"arxiv","id":"2108.06560","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2108.06560","created_at":"2026-07-05T03:05:55Z"},{"alias_kind":"arxiv_version","alias_value":"2108.06560v1","created_at":"2026-07-05T03:05:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.06560","created_at":"2026-07-05T03:05:55Z"},{"alias_kind":"pith_short_12","alias_value":"QIFBI2Z4CTNR","created_at":"2026-07-05T03:05:55Z"},{"alias_kind":"pith_short_16","alias_value":"QIFBI2Z4CTNR6SPE","created_at":"2026-07-05T03:05:55Z"},{"alias_kind":"pith_short_8","alias_value":"QIFBI2Z4","created_at":"2026-07-05T03:05:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:QIFBI2Z4CTNR6SPEFLQEWGYUUC","target":"record","payload":{"canonical_record":{"source":{"id":"2108.06560","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2021-08-14T15:19:52Z","cross_cats_sorted":[],"title_canon_sha256":"e670de36d23f38d18e4b8f741f0c272783d1f30577608482a581d4c7d930342e","abstract_canon_sha256":"dad98b485367e0e4a5192e5f7086f2ecf4ae8b72ba59000741fba47626083177"},"schema_version":"1.0"},"canonical_sha256":"820a146b3c14db1f49e42ae04b1b14a0860eef50aeac0b795b6640b33d29b93e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:05:55.791969Z","signature_b64":"qlZ2pfeI+JtDyMl46QH1pkrGwCwFDANE/O2ZePb3XPOoSFU2Iy+/VIOngqiDq4weVYCDgfcPHTmEwoTQ6NCFCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"820a146b3c14db1f49e42ae04b1b14a0860eef50aeac0b795b6640b33d29b93e","last_reissued_at":"2026-07-05T03:05:55.791625Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:05:55.791625Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2108.06560","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":"2026-07-05T03:05:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uuxcrXt0r5OGjFfU5UNlLbCd+4vaRGIOO52KtMaA+Hglx7Kw73QsMv9fuP3XEAVfAmbb00Jp5zqTkzuqp0EJDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T20:18:25.884003Z"},"content_sha256":"745de6e884ede98cc7fe120e9db5aaae84c8a9f70b6b14413fde0e4eee820984","schema_version":"1.0","event_id":"sha256:745de6e884ede98cc7fe120e9db5aaae84c8a9f70b6b14413fde0e4eee820984"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:QIFBI2Z4CTNR6SPEFLQEWGYUUC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hyperelliptic continued fractions in the singular case of genus zero","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Francesco Ballini, Francesco Veneziano","submitted_at":"2021-08-14T15:19:52Z","abstract_excerpt":"It is possible to define a continued fraction expansion of elements in a function field of a curve by expanding as a Laurent series in a local parameter. Considering the square root of a polynomial $\\sqrt{D(t)}$ leads to an interesting theory related to polynomial Pell equations. Unlike the classical Pell equation, the corresponding polynomial equation is not always solvable and its solvability is related to arithmetic conditions on the Jacobian (or generalized Jacobian) of the curve defined by $y^2=D(t)$. In this setting, it has been shown by Zannier in \\cite{zannier} that the sequence of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.06560","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2108.06560/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T03:05:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iV9D7uNFMCq+IrcQZb3KbWGe5Kn+Y+Felmx22rt3CyKG/0YAq8PS7uloU4kYNULp5TMPwN8983kxBQj2O7cpAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T20:18:25.884501Z"},"content_sha256":"d5c87c20e4b62e65d2eac0b519a674a5c6cd57dd641574a7619cb11d79b1f5cf","schema_version":"1.0","event_id":"sha256:d5c87c20e4b62e65d2eac0b519a674a5c6cd57dd641574a7619cb11d79b1f5cf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QIFBI2Z4CTNR6SPEFLQEWGYUUC/bundle.json","state_url":"https://pith.science/pith/QIFBI2Z4CTNR6SPEFLQEWGYUUC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QIFBI2Z4CTNR6SPEFLQEWGYUUC/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":"2026-08-03T20:18:25Z","links":{"resolver":"https://pith.science/pith/QIFBI2Z4CTNR6SPEFLQEWGYUUC","bundle":"https://pith.science/pith/QIFBI2Z4CTNR6SPEFLQEWGYUUC/bundle.json","state":"https://pith.science/pith/QIFBI2Z4CTNR6SPEFLQEWGYUUC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QIFBI2Z4CTNR6SPEFLQEWGYUUC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:QIFBI2Z4CTNR6SPEFLQEWGYUUC","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":"dad98b485367e0e4a5192e5f7086f2ecf4ae8b72ba59000741fba47626083177","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2021-08-14T15:19:52Z","title_canon_sha256":"e670de36d23f38d18e4b8f741f0c272783d1f30577608482a581d4c7d930342e"},"schema_version":"1.0","source":{"id":"2108.06560","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2108.06560","created_at":"2026-07-05T03:05:55Z"},{"alias_kind":"arxiv_version","alias_value":"2108.06560v1","created_at":"2026-07-05T03:05:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.06560","created_at":"2026-07-05T03:05:55Z"},{"alias_kind":"pith_short_12","alias_value":"QIFBI2Z4CTNR","created_at":"2026-07-05T03:05:55Z"},{"alias_kind":"pith_short_16","alias_value":"QIFBI2Z4CTNR6SPE","created_at":"2026-07-05T03:05:55Z"},{"alias_kind":"pith_short_8","alias_value":"QIFBI2Z4","created_at":"2026-07-05T03:05:55Z"}],"graph_snapshots":[{"event_id":"sha256:d5c87c20e4b62e65d2eac0b519a674a5c6cd57dd641574a7619cb11d79b1f5cf","target":"graph","created_at":"2026-07-05T03:05:55Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2108.06560/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It is possible to define a continued fraction expansion of elements in a function field of a curve by expanding as a Laurent series in a local parameter. Considering the square root of a polynomial $\\sqrt{D(t)}$ leads to an interesting theory related to polynomial Pell equations. Unlike the classical Pell equation, the corresponding polynomial equation is not always solvable and its solvability is related to arithmetic conditions on the Jacobian (or generalized Jacobian) of the curve defined by $y^2=D(t)$. In this setting, it has been shown by Zannier in \\cite{zannier} that the sequence of the","authors_text":"Francesco Ballini, Francesco Veneziano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2021-08-14T15:19:52Z","title":"Hyperelliptic continued fractions in the singular case of genus zero"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.06560","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":"sha256:745de6e884ede98cc7fe120e9db5aaae84c8a9f70b6b14413fde0e4eee820984","target":"record","created_at":"2026-07-05T03:05:55Z","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":"dad98b485367e0e4a5192e5f7086f2ecf4ae8b72ba59000741fba47626083177","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2021-08-14T15:19:52Z","title_canon_sha256":"e670de36d23f38d18e4b8f741f0c272783d1f30577608482a581d4c7d930342e"},"schema_version":"1.0","source":{"id":"2108.06560","kind":"arxiv","version":1}},"canonical_sha256":"820a146b3c14db1f49e42ae04b1b14a0860eef50aeac0b795b6640b33d29b93e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"820a146b3c14db1f49e42ae04b1b14a0860eef50aeac0b795b6640b33d29b93e","first_computed_at":"2026-07-05T03:05:55.791625Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:05:55.791625Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qlZ2pfeI+JtDyMl46QH1pkrGwCwFDANE/O2ZePb3XPOoSFU2Iy+/VIOngqiDq4weVYCDgfcPHTmEwoTQ6NCFCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:05:55.791969Z","signed_message":"canonical_sha256_bytes"},"source_id":"2108.06560","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:745de6e884ede98cc7fe120e9db5aaae84c8a9f70b6b14413fde0e4eee820984","sha256:d5c87c20e4b62e65d2eac0b519a674a5c6cd57dd641574a7619cb11d79b1f5cf"],"state_sha256":"875bb8b7a75b0da55208a000e3a81ae1869f53fc2c35bc327cdbde3cdd942a25"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WrDzkj0phNMspS+GR6ViedOPSf/thnxI8ot5EmO+GP/YWny3vYj2kf+jFqvb3qNFpJnSSAiEDPuDLVFOiO6kCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T20:18:25.889320Z","bundle_sha256":"d96723e32725e6f03a9f70e181a7b7181bd4b7addc2b474d04dc9841c100252f"}}