{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:WTVTSKFYW5UQQBNZBNLE5S3R2X","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":"1e2cc39e14a49b2e1fc1ac133151e62b76f2136d1473b68425b8aa487efd3d38","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-01-03T08:07:34Z","title_canon_sha256":"5ca32f93d8acd6eb058e4c62e1c87880460b5baad92681a43c81a41f94acdf3e"},"schema_version":"1.0","source":{"id":"1401.0602","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0602","created_at":"2026-05-18T03:03:22Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0602v1","created_at":"2026-05-18T03:03:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0602","created_at":"2026-05-18T03:03:22Z"},{"alias_kind":"pith_short_12","alias_value":"WTVTSKFYW5UQ","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WTVTSKFYW5UQQBNZ","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WTVTSKFY","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:8876840295c37626f2bdf34bd039415a99afdfb5806a14615d123076190368fb","target":"graph","created_at":"2026-05-18T03:03:22Z","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":"Let $f\\in\\Q[x]$ be a square-free polynomial of degree $\\geq 3$ and $m\\geq 3$ be an odd positive integer. Based on our earlier investigations we prove that there exists a function $D_{1}\\in\\Q(u,v,w)$ such that the Jacobians of the curves \\begin{equation*} C_{1}:\\;D_{1}y^2=f(x),\\quad C_{2}:\\;y^2=D_{1}x^m+b,\\quad C_{3}:\\;y^2=D_{1}x^m+c, \\end{equation*} have all positive ranks over $\\Q(u,v,w)$. Similarly, we prove that there exists a function $D_{2}\\in\\Q(u,v,w)$ such that the Jacobians of the curves \\begin{equation*} C_{1}:\\;D_{2}y^2=h(x),\\quad C_{2}:\\;y^2=D_{2}x^m+b,\\quad C_{3}:\\;y^2=x^m+cD_{2}, ","authors_text":"Maciej Ulas, Tomasz J\\k{e}drzejak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-01-03T08:07:34Z","title":"Variations on twists of tuples of hyperelliptic curves and related results"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0602","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":"sha256:5a04c3ab4126ee42170a8ac3d757f1e564428e6efd1b422f1dfa65b440d6f68a","target":"record","created_at":"2026-05-18T03:03:22Z","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":"1e2cc39e14a49b2e1fc1ac133151e62b76f2136d1473b68425b8aa487efd3d38","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-01-03T08:07:34Z","title_canon_sha256":"5ca32f93d8acd6eb058e4c62e1c87880460b5baad92681a43c81a41f94acdf3e"},"schema_version":"1.0","source":{"id":"1401.0602","kind":"arxiv","version":1}},"canonical_sha256":"b4eb3928b8b7690805b90b564ecb71d5ec0ec8b281dc827f7b434749ce3fa967","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4eb3928b8b7690805b90b564ecb71d5ec0ec8b281dc827f7b434749ce3fa967","first_computed_at":"2026-05-18T03:03:22.351339Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:22.351339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D7klSJXygBUJuCvMtHe6NzPGLjN/32gAqOeICQO3EZGTqzt8vrvb+K+eOC9qagN9xsM9ORtALujqS00zrRFfDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:22.351958Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.0602","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a04c3ab4126ee42170a8ac3d757f1e564428e6efd1b422f1dfa65b440d6f68a","sha256:8876840295c37626f2bdf34bd039415a99afdfb5806a14615d123076190368fb"],"state_sha256":"9ffffaeec3d9291bf407082c255c89f41fcd5ae3cb6a4f36761ff921b095d0c2"}