{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2000:HIGDH4UQZ4I4IMGIQYBLI722FD","short_pith_number":"pith:HIGDH4UQ","canonical_record":{"source":{"id":"nlin/0010048","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"nlin.SI","submitted_at":"2000-10-27T14:34:50Z","cross_cats_sorted":["math-ph","math.CA","math.MP"],"title_canon_sha256":"88a5268651076c20237cc1a3434249182496d09f2387ed4f54ad33dc5f6cfd54","abstract_canon_sha256":"bebfeab5dabbf0858e379888987a4a2f85ee62c2eff95de23d42ddf1a8c0b3ad"},"schema_version":"1.0"},"canonical_sha256":"3a0c33f290cf11c430c88602b47f5a28deae5ba98c5ca7a5f756615f6721907a","source":{"kind":"arxiv","id":"nlin/0010048","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0010048","created_at":"2026-07-04T14:41:36Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0010048v2","created_at":"2026-07-04T14:41:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0010048","created_at":"2026-07-04T14:41:36Z"},{"alias_kind":"pith_short_12","alias_value":"HIGDH4UQZ4I4","created_at":"2026-07-04T14:41:36Z"},{"alias_kind":"pith_short_16","alias_value":"HIGDH4UQZ4I4IMGI","created_at":"2026-07-04T14:41:36Z"},{"alias_kind":"pith_short_8","alias_value":"HIGDH4UQ","created_at":"2026-07-04T14:41:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2000:HIGDH4UQZ4I4IMGIQYBLI722FD","target":"record","payload":{"canonical_record":{"source":{"id":"nlin/0010048","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"nlin.SI","submitted_at":"2000-10-27T14:34:50Z","cross_cats_sorted":["math-ph","math.CA","math.MP"],"title_canon_sha256":"88a5268651076c20237cc1a3434249182496d09f2387ed4f54ad33dc5f6cfd54","abstract_canon_sha256":"bebfeab5dabbf0858e379888987a4a2f85ee62c2eff95de23d42ddf1a8c0b3ad"},"schema_version":"1.0"},"canonical_sha256":"3a0c33f290cf11c430c88602b47f5a28deae5ba98c5ca7a5f756615f6721907a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:41:36.818470Z","signature_b64":"UeaO0dKuHGcMlDw1F6NP6n1Zk6VLbKbMWMe+jg18N2bjoP+zMLf4gDK51WBY7ZhhuOJFCui+f36v+uu7tnHLBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a0c33f290cf11c430c88602b47f5a28deae5ba98c5ca7a5f756615f6721907a","last_reissued_at":"2026-07-04T14:41:36.818090Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:41:36.818090Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"nlin/0010048","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":"2026-07-04T14:41:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mAaNy205+YrZBGk7Q1GZ6aiyrRygIBQydVkoObWnCXAoP+yd0JWP/w5+CFeeJ0ofRWiKzSPkHfyyZuO+DvhWDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-25T08:01:04.269659Z"},"content_sha256":"4e037596bae5cc37d1895902130ffa568aa8d5ab6c67e3d8be8d43dbf1e2bff1","schema_version":"1.0","event_id":"sha256:4e037596bae5cc37d1895902130ffa568aa8d5ab6c67e3d8be8d43dbf1e2bff1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2000:HIGDH4UQZ4I4IMGIQYBLI722FD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Darboux transforms on Band Matrices, Weights and associated Polynomials","license":"","headline":"","cross_cats":["math-ph","math.CA","math.MP"],"primary_cat":"nlin.SI","authors_text":"Mark Adler, Pierre van Moerbeke","submitted_at":"2000-10-27T14:34:50Z","abstract_excerpt":"Classically, it is well known that a single weight on a real interval leads to orthogonal polynomials. In \"Generalized orthogonal polynomials, discrete KP and Riemann-Hilbert problems\", Comm. Math. Phys.\n  207, pp. 589-620 (1999), we have shown that $m$-periodic sequences of weights lead to \"moments\", polynomials defined by determinants of matrices involving these moments and $2m+1$-step relations between them, thus leading to $2m+1$-band matrices $L$. Given a Darboux transformations on $L$, which effect does it have on the $m$-periodic sequence of weights and on the associated polynomials ? T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0010048","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/nlin/0010048/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":"2026-07-04T14:41:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"twQRNm0YhDJ9f9WwXNm+fNzMkT81uVxo4QMhDPDmE4fEdKBGiigA3of42ab5XnOuiBXNFW6WHH+kNEX96XeMDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-25T08:01:04.270048Z"},"content_sha256":"f0001a55acd096ac082554a236f55aa7c84dfda29d2bbb0067ca2afb705d5a55","schema_version":"1.0","event_id":"sha256:f0001a55acd096ac082554a236f55aa7c84dfda29d2bbb0067ca2afb705d5a55"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HIGDH4UQZ4I4IMGIQYBLI722FD/bundle.json","state_url":"https://pith.science/pith/HIGDH4UQZ4I4IMGIQYBLI722FD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HIGDH4UQZ4I4IMGIQYBLI722FD/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":"2026-07-25T08:01:04Z","links":{"resolver":"https://pith.science/pith/HIGDH4UQZ4I4IMGIQYBLI722FD","bundle":"https://pith.science/pith/HIGDH4UQZ4I4IMGIQYBLI722FD/bundle.json","state":"https://pith.science/pith/HIGDH4UQZ4I4IMGIQYBLI722FD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HIGDH4UQZ4I4IMGIQYBLI722FD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:HIGDH4UQZ4I4IMGIQYBLI722FD","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":"bebfeab5dabbf0858e379888987a4a2f85ee62c2eff95de23d42ddf1a8c0b3ad","cross_cats_sorted":["math-ph","math.CA","math.MP"],"license":"","primary_cat":"nlin.SI","submitted_at":"2000-10-27T14:34:50Z","title_canon_sha256":"88a5268651076c20237cc1a3434249182496d09f2387ed4f54ad33dc5f6cfd54"},"schema_version":"1.0","source":{"id":"nlin/0010048","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0010048","created_at":"2026-07-04T14:41:36Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0010048v2","created_at":"2026-07-04T14:41:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0010048","created_at":"2026-07-04T14:41:36Z"},{"alias_kind":"pith_short_12","alias_value":"HIGDH4UQZ4I4","created_at":"2026-07-04T14:41:36Z"},{"alias_kind":"pith_short_16","alias_value":"HIGDH4UQZ4I4IMGI","created_at":"2026-07-04T14:41:36Z"},{"alias_kind":"pith_short_8","alias_value":"HIGDH4UQ","created_at":"2026-07-04T14:41:36Z"}],"graph_snapshots":[{"event_id":"sha256:f0001a55acd096ac082554a236f55aa7c84dfda29d2bbb0067ca2afb705d5a55","target":"graph","created_at":"2026-07-04T14:41:36Z","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/nlin/0010048/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Classically, it is well known that a single weight on a real interval leads to orthogonal polynomials. In \"Generalized orthogonal polynomials, discrete KP and Riemann-Hilbert problems\", Comm. Math. Phys.\n  207, pp. 589-620 (1999), we have shown that $m$-periodic sequences of weights lead to \"moments\", polynomials defined by determinants of matrices involving these moments and $2m+1$-step relations between them, thus leading to $2m+1$-band matrices $L$. Given a Darboux transformations on $L$, which effect does it have on the $m$-periodic sequence of weights and on the associated polynomials ? T","authors_text":"Mark Adler, Pierre van Moerbeke","cross_cats":["math-ph","math.CA","math.MP"],"headline":"","license":"","primary_cat":"nlin.SI","submitted_at":"2000-10-27T14:34:50Z","title":"Darboux transforms on Band Matrices, Weights and associated Polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0010048","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":"sha256:4e037596bae5cc37d1895902130ffa568aa8d5ab6c67e3d8be8d43dbf1e2bff1","target":"record","created_at":"2026-07-04T14:41:36Z","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":"bebfeab5dabbf0858e379888987a4a2f85ee62c2eff95de23d42ddf1a8c0b3ad","cross_cats_sorted":["math-ph","math.CA","math.MP"],"license":"","primary_cat":"nlin.SI","submitted_at":"2000-10-27T14:34:50Z","title_canon_sha256":"88a5268651076c20237cc1a3434249182496d09f2387ed4f54ad33dc5f6cfd54"},"schema_version":"1.0","source":{"id":"nlin/0010048","kind":"arxiv","version":2}},"canonical_sha256":"3a0c33f290cf11c430c88602b47f5a28deae5ba98c5ca7a5f756615f6721907a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a0c33f290cf11c430c88602b47f5a28deae5ba98c5ca7a5f756615f6721907a","first_computed_at":"2026-07-04T14:41:36.818090Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:41:36.818090Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UeaO0dKuHGcMlDw1F6NP6n1Zk6VLbKbMWMe+jg18N2bjoP+zMLf4gDK51WBY7ZhhuOJFCui+f36v+uu7tnHLBg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:41:36.818470Z","signed_message":"canonical_sha256_bytes"},"source_id":"nlin/0010048","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e037596bae5cc37d1895902130ffa568aa8d5ab6c67e3d8be8d43dbf1e2bff1","sha256:f0001a55acd096ac082554a236f55aa7c84dfda29d2bbb0067ca2afb705d5a55"],"state_sha256":"f1fab522ff77c2225467711a870b80fb61255a53dca971ecda10a782199e9f56"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iPkA0qbYenC8LZc+ipCzATJIKEMy9ViEotS0dlzPg+uoRD4CmFTr5Jt/8litZ1PPg4TuEfIIYH6fCxKqbEo5Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-25T08:01:04.272583Z","bundle_sha256":"7c7fbc5d1e93c7619e8c43d2489f30355b007fe6524c1d1dc3d3a66f5ead9a13"}}