{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:F6BBBIOYZM5ZLXFVRR2LXSTFF2","short_pith_number":"pith:F6BBBIOY","canonical_record":{"source":{"id":"0904.2602","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-04-16T22:54:24Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"ff793d75f57e70be101ee928da2525cee8b5475625eef5dd7c9369af3eaf50a8","abstract_canon_sha256":"78f65d544983116e878244212bd70352ca35fe95ffd945d8e4b44b4ebab40b86"},"schema_version":"1.0"},"canonical_sha256":"2f8210a1d8cb3b95dcb58c74bbca652ebb784d2884d36cd9fdd9012116553d9a","source":{"kind":"arxiv","id":"0904.2602","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.2602","created_at":"2026-07-04T15:41:23Z"},{"alias_kind":"arxiv_version","alias_value":"0904.2602v1","created_at":"2026-07-04T15:41:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.2602","created_at":"2026-07-04T15:41:23Z"},{"alias_kind":"pith_short_12","alias_value":"F6BBBIOYZM5Z","created_at":"2026-07-04T15:41:23Z"},{"alias_kind":"pith_short_16","alias_value":"F6BBBIOYZM5ZLXFV","created_at":"2026-07-04T15:41:23Z"},{"alias_kind":"pith_short_8","alias_value":"F6BBBIOY","created_at":"2026-07-04T15:41:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:F6BBBIOYZM5ZLXFVRR2LXSTFF2","target":"record","payload":{"canonical_record":{"source":{"id":"0904.2602","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-04-16T22:54:24Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"ff793d75f57e70be101ee928da2525cee8b5475625eef5dd7c9369af3eaf50a8","abstract_canon_sha256":"78f65d544983116e878244212bd70352ca35fe95ffd945d8e4b44b4ebab40b86"},"schema_version":"1.0"},"canonical_sha256":"2f8210a1d8cb3b95dcb58c74bbca652ebb784d2884d36cd9fdd9012116553d9a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:41:23.090697Z","signature_b64":"KV0839EMOpYpt4InomwnMfGp5m3nuJvAKopzZ8UtM6g+Gr4LwwcpPUYF4Yxy6LZL+c0pi7Ot+lob44Wgye+hAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f8210a1d8cb3b95dcb58c74bbca652ebb784d2884d36cd9fdd9012116553d9a","last_reissued_at":"2026-07-04T15:41:23.090266Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:41:23.090266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0904.2602","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":"2026-07-04T15:41:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P8oVD8d1iMIyowafVIiQt61OkIX9O290KmJQp9YlZZraVpwCO7Q/hU1k3Yrbv106+HNaRUFyXr7mxGslgG3XCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T06:13:20.558269Z"},"content_sha256":"7fb754ba0ffd6ec30ecaa0bb16553e85010b111bc7b8192dd67a18a5bcba0f17","schema_version":"1.0","event_id":"sha256:7fb754ba0ffd6ec30ecaa0bb16553e85010b111bc7b8192dd67a18a5bcba0f17"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:F6BBBIOYZM5ZLXFVRR2LXSTFF2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cauchy Biorthogonal Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"J. Szmigielski, M. Bertola, M. Gekhtman","submitted_at":"2009-04-16T22:54:24Z","abstract_excerpt":"The paper investigates the properties of certain biorthogonal polynomials appearing in a specific simultaneous Hermite-Pade' approximation scheme. Associated to any totally positive kernel and a pair of positive measures on the positive axis we define biorthogonal polynomials and prove that their zeroes are simple and positive. We then specialize the kernel to the Cauchy kernel 1/{x+y} and show that the ensuing biorthogonal polynomials solve a four-term recurrence relation, have relevant Christoffel-Darboux generalized formulae, and their zeroes are interlaced. In addition, these polynomial so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.2602","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/0904.2602/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":"2026-07-04T15:41:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Su+W67tBcVhin6FkcG7/1zRRDXGvK/A10Gb8HVXf1lOhddzp29iuAJ42tVkTP9lUsOpMa6lFHoEIx67KZrizCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T06:13:20.558661Z"},"content_sha256":"ee3eac80157edba153318e08aae7de4d0e59868ed50ef5af119d1c211cc33426","schema_version":"1.0","event_id":"sha256:ee3eac80157edba153318e08aae7de4d0e59868ed50ef5af119d1c211cc33426"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F6BBBIOYZM5ZLXFVRR2LXSTFF2/bundle.json","state_url":"https://pith.science/pith/F6BBBIOYZM5ZLXFVRR2LXSTFF2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F6BBBIOYZM5ZLXFVRR2LXSTFF2/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":"2026-08-06T06:13:20Z","links":{"resolver":"https://pith.science/pith/F6BBBIOYZM5ZLXFVRR2LXSTFF2","bundle":"https://pith.science/pith/F6BBBIOYZM5ZLXFVRR2LXSTFF2/bundle.json","state":"https://pith.science/pith/F6BBBIOYZM5ZLXFVRR2LXSTFF2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F6BBBIOYZM5ZLXFVRR2LXSTFF2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:F6BBBIOYZM5ZLXFVRR2LXSTFF2","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":"78f65d544983116e878244212bd70352ca35fe95ffd945d8e4b44b4ebab40b86","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-04-16T22:54:24Z","title_canon_sha256":"ff793d75f57e70be101ee928da2525cee8b5475625eef5dd7c9369af3eaf50a8"},"schema_version":"1.0","source":{"id":"0904.2602","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.2602","created_at":"2026-07-04T15:41:23Z"},{"alias_kind":"arxiv_version","alias_value":"0904.2602v1","created_at":"2026-07-04T15:41:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.2602","created_at":"2026-07-04T15:41:23Z"},{"alias_kind":"pith_short_12","alias_value":"F6BBBIOYZM5Z","created_at":"2026-07-04T15:41:23Z"},{"alias_kind":"pith_short_16","alias_value":"F6BBBIOYZM5ZLXFV","created_at":"2026-07-04T15:41:23Z"},{"alias_kind":"pith_short_8","alias_value":"F6BBBIOY","created_at":"2026-07-04T15:41:23Z"}],"graph_snapshots":[{"event_id":"sha256:ee3eac80157edba153318e08aae7de4d0e59868ed50ef5af119d1c211cc33426","target":"graph","created_at":"2026-07-04T15:41:23Z","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/0904.2602/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The paper investigates the properties of certain biorthogonal polynomials appearing in a specific simultaneous Hermite-Pade' approximation scheme. Associated to any totally positive kernel and a pair of positive measures on the positive axis we define biorthogonal polynomials and prove that their zeroes are simple and positive. We then specialize the kernel to the Cauchy kernel 1/{x+y} and show that the ensuing biorthogonal polynomials solve a four-term recurrence relation, have relevant Christoffel-Darboux generalized formulae, and their zeroes are interlaced. In addition, these polynomial so","authors_text":"J. Szmigielski, M. Bertola, M. Gekhtman","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-04-16T22:54:24Z","title":"Cauchy Biorthogonal Polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.2602","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":"sha256:7fb754ba0ffd6ec30ecaa0bb16553e85010b111bc7b8192dd67a18a5bcba0f17","target":"record","created_at":"2026-07-04T15:41:23Z","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":"78f65d544983116e878244212bd70352ca35fe95ffd945d8e4b44b4ebab40b86","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-04-16T22:54:24Z","title_canon_sha256":"ff793d75f57e70be101ee928da2525cee8b5475625eef5dd7c9369af3eaf50a8"},"schema_version":"1.0","source":{"id":"0904.2602","kind":"arxiv","version":1}},"canonical_sha256":"2f8210a1d8cb3b95dcb58c74bbca652ebb784d2884d36cd9fdd9012116553d9a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f8210a1d8cb3b95dcb58c74bbca652ebb784d2884d36cd9fdd9012116553d9a","first_computed_at":"2026-07-04T15:41:23.090266Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:41:23.090266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KV0839EMOpYpt4InomwnMfGp5m3nuJvAKopzZ8UtM6g+Gr4LwwcpPUYF4Yxy6LZL+c0pi7Ot+lob44Wgye+hAw==","signature_status":"signed_v1","signed_at":"2026-07-04T15:41:23.090697Z","signed_message":"canonical_sha256_bytes"},"source_id":"0904.2602","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7fb754ba0ffd6ec30ecaa0bb16553e85010b111bc7b8192dd67a18a5bcba0f17","sha256:ee3eac80157edba153318e08aae7de4d0e59868ed50ef5af119d1c211cc33426"],"state_sha256":"f3be6607b72cf5297f1389786bc5f8e3dbd4f1ad408809b1f96acec93df5622f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NcpgOjQ0rI2MiWJ4MXy9M4gbcqcA0mTPgIZx+7uuLTqvJPQUHyx4Wu6G94rEUxRp1h1cRGH7sAZG1g6rWSp3AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T06:13:20.562378Z","bundle_sha256":"bd1967ca1ef77d667169c34c8e5674f53c3a3ad57cc7183974f75bcaee3fcb1d"}}