{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RWXDEM5VIC2XPB3MISI74ULGTL","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":"957fecb0d3297e68e4f03a8719ea0ec4bfd383a0dfc41ffe8f8128aa4d3218ea","cross_cats_sorted":["math-ph","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-12-15T18:39:10Z","title_canon_sha256":"376755ca04d4dbb58d069d797373381e6193d7b20ee05d7a7fadfbc6e74ca9fb"},"schema_version":"1.0","source":{"id":"1612.07229","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.07229","created_at":"2026-05-18T00:54:14Z"},{"alias_kind":"arxiv_version","alias_value":"1612.07229v1","created_at":"2026-05-18T00:54:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.07229","created_at":"2026-05-18T00:54:14Z"},{"alias_kind":"pith_short_12","alias_value":"RWXDEM5VIC2X","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RWXDEM5VIC2XPB3M","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RWXDEM5V","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:8e33da85e5040d7ec82ac5207d55044657e24df92b20a4311429be178b267cba","target":"graph","created_at":"2026-05-18T00:54:14Z","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 introduce a large class of Sobolev bi-orthogonal polynomial sequences arising from a $LU$-factorizable moment matrix and associated with a suitable measure matrix that characterizes the Sobolev bilinear form. A theory of deformations of Sobolev bilinear forms is also proposed. We consider both polynomial deformations and a class of transformations related to the action of linear operators on the entries of a given bilinear form. Transformation formulae among new and old polynomial sequences are determined. Finally, integrable hierarchies of evolution equations arising from the factorization","authors_text":"Gerardo Ariznabarreta, Manuel Ma\\~nas, Piergiulio Tempesta","cross_cats":["math-ph","math.MP","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-12-15T18:39:10Z","title":"Generalized Sobolev orthogonal polynomials, matrix moment problems and integrable systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07229","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:b311e64d141cf5124e042cec397a581fef6195dcffbf0d28fff494cb32e22b57","target":"record","created_at":"2026-05-18T00:54:14Z","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":"957fecb0d3297e68e4f03a8719ea0ec4bfd383a0dfc41ffe8f8128aa4d3218ea","cross_cats_sorted":["math-ph","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-12-15T18:39:10Z","title_canon_sha256":"376755ca04d4dbb58d069d797373381e6193d7b20ee05d7a7fadfbc6e74ca9fb"},"schema_version":"1.0","source":{"id":"1612.07229","kind":"arxiv","version":1}},"canonical_sha256":"8dae3233b540b577876c4491fe51669afdb88859d5b32a7e04c8b7e8e0989399","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8dae3233b540b577876c4491fe51669afdb88859d5b32a7e04c8b7e8e0989399","first_computed_at":"2026-05-18T00:54:14.412438Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:14.412438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PY8oh1/e9sRlaec0PqDIqRIDluqnd5MHbCskX4uNDkYisCUkJn1Bbt652jkcZWx/iPXUfk1UwdjqlQlz6Kd5AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:14.412975Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.07229","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b311e64d141cf5124e042cec397a581fef6195dcffbf0d28fff494cb32e22b57","sha256:8e33da85e5040d7ec82ac5207d55044657e24df92b20a4311429be178b267cba"],"state_sha256":"56e56d00c906c024965bd35851817db01c0f1632b177bf88fe777f0a7b947f56"}