{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:KHT2JKBE2BJWL6QTLOUWMP5E5B","short_pith_number":"pith:KHT2JKBE","canonical_record":{"source":{"id":"1902.06826","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-02-18T22:43:43Z","cross_cats_sorted":["math.CV","math.OA"],"title_canon_sha256":"b70e09a45f137e19add3aadcf5610b6b6a76aab963142f0a88d1941f8b32dc4b","abstract_canon_sha256":"d1f68497dd93bc451cc82f1558aac153113973902e9dc60dcb3c832768382ec7"},"schema_version":"1.0"},"canonical_sha256":"51e7a4a824d05365fa135ba9663fa4e879f07c2f9978495f695659f69c13b67b","source":{"kind":"arxiv","id":"1902.06826","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.06826","created_at":"2026-05-17T23:53:40Z"},{"alias_kind":"arxiv_version","alias_value":"1902.06826v1","created_at":"2026-05-17T23:53:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.06826","created_at":"2026-05-17T23:53:40Z"},{"alias_kind":"pith_short_12","alias_value":"KHT2JKBE2BJW","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"KHT2JKBE2BJWL6QT","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"KHT2JKBE","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:KHT2JKBE2BJWL6QTLOUWMP5E5B","target":"record","payload":{"canonical_record":{"source":{"id":"1902.06826","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-02-18T22:43:43Z","cross_cats_sorted":["math.CV","math.OA"],"title_canon_sha256":"b70e09a45f137e19add3aadcf5610b6b6a76aab963142f0a88d1941f8b32dc4b","abstract_canon_sha256":"d1f68497dd93bc451cc82f1558aac153113973902e9dc60dcb3c832768382ec7"},"schema_version":"1.0"},"canonical_sha256":"51e7a4a824d05365fa135ba9663fa4e879f07c2f9978495f695659f69c13b67b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:40.677745Z","signature_b64":"JyMT4MpOeJautdgsiFrL1/spIOQ8oNJJKBrHSjIj2hbLW0+X7AfPPVsWIcF3t5WAFroXL1cEQLKDI2h8VrQkAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51e7a4a824d05365fa135ba9663fa4e879f07c2f9978495f695659f69c13b67b","last_reissued_at":"2026-05-17T23:53:40.677165Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:40.677165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.06826","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":"2026-05-17T23:53:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gRf3oehqqkbmMr8FUEyWALFmEfVLZ67fvbG1o+WZRhsgs4EIo8fZbk/beu5BPVoudQG2HY1d26vcjnipPWzsBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T22:45:07.810131Z"},"content_sha256":"dc3d14bd1d3d173a63c19efabec8a4fe9a013a55ff34a174d5aa3eb240a44bde","schema_version":"1.0","event_id":"sha256:dc3d14bd1d3d173a63c19efabec8a4fe9a013a55ff34a174d5aa3eb240a44bde"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:KHT2JKBE2BJWL6QTLOUWMP5E5B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Row contractions annihilated by interpolating vanishing ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.OA"],"primary_cat":"math.FA","authors_text":"Edward J. Timko, Rapha\\\"el Clou\\^atre","submitted_at":"2019-02-18T22:43:43Z","abstract_excerpt":"We study similarity classes of commuting row contractions annihilated by what we call higher order vanishing ideals of interpolating sequences. Our main result exhibits a Jordan-type direct sum decomposition for these row contractions. We illustrate how the family of ideals to which our theorem applies is very rich, especially in several variables. We also give two applications of the main result. First, we obtain a purely operator theoretic characterization of interpolating sequences. Second, we classify certain classes of cyclic commuting row contractions up to quasi-similarity in terms of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.06826","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":""},"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":"2026-05-17T23:53:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"amt5yO1rJp8Rtf+zrRCaNuALhpK8sXZNdoNFcXII5GmyDX2Y64iA0d2kOQo3RLclnyp1dNp3/xMdX0N2T+IQDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T22:45:07.810492Z"},"content_sha256":"9064eb0d91ec8f1f30e0d031a5dd7a7d620974f9676e7466451dce0f1c193118","schema_version":"1.0","event_id":"sha256:9064eb0d91ec8f1f30e0d031a5dd7a7d620974f9676e7466451dce0f1c193118"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KHT2JKBE2BJWL6QTLOUWMP5E5B/bundle.json","state_url":"https://pith.science/pith/KHT2JKBE2BJWL6QTLOUWMP5E5B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KHT2JKBE2BJWL6QTLOUWMP5E5B/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":"2026-06-25T22:45:07Z","links":{"resolver":"https://pith.science/pith/KHT2JKBE2BJWL6QTLOUWMP5E5B","bundle":"https://pith.science/pith/KHT2JKBE2BJWL6QTLOUWMP5E5B/bundle.json","state":"https://pith.science/pith/KHT2JKBE2BJWL6QTLOUWMP5E5B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KHT2JKBE2BJWL6QTLOUWMP5E5B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:KHT2JKBE2BJWL6QTLOUWMP5E5B","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":"d1f68497dd93bc451cc82f1558aac153113973902e9dc60dcb3c832768382ec7","cross_cats_sorted":["math.CV","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-02-18T22:43:43Z","title_canon_sha256":"b70e09a45f137e19add3aadcf5610b6b6a76aab963142f0a88d1941f8b32dc4b"},"schema_version":"1.0","source":{"id":"1902.06826","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.06826","created_at":"2026-05-17T23:53:40Z"},{"alias_kind":"arxiv_version","alias_value":"1902.06826v1","created_at":"2026-05-17T23:53:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.06826","created_at":"2026-05-17T23:53:40Z"},{"alias_kind":"pith_short_12","alias_value":"KHT2JKBE2BJW","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"KHT2JKBE2BJWL6QT","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"KHT2JKBE","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:9064eb0d91ec8f1f30e0d031a5dd7a7d620974f9676e7466451dce0f1c193118","target":"graph","created_at":"2026-05-17T23:53:40Z","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 study similarity classes of commuting row contractions annihilated by what we call higher order vanishing ideals of interpolating sequences. Our main result exhibits a Jordan-type direct sum decomposition for these row contractions. We illustrate how the family of ideals to which our theorem applies is very rich, especially in several variables. We also give two applications of the main result. First, we obtain a purely operator theoretic characterization of interpolating sequences. Second, we classify certain classes of cyclic commuting row contractions up to quasi-similarity in terms of t","authors_text":"Edward J. Timko, Rapha\\\"el Clou\\^atre","cross_cats":["math.CV","math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-02-18T22:43:43Z","title":"Row contractions annihilated by interpolating vanishing ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.06826","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:dc3d14bd1d3d173a63c19efabec8a4fe9a013a55ff34a174d5aa3eb240a44bde","target":"record","created_at":"2026-05-17T23:53:40Z","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":"d1f68497dd93bc451cc82f1558aac153113973902e9dc60dcb3c832768382ec7","cross_cats_sorted":["math.CV","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-02-18T22:43:43Z","title_canon_sha256":"b70e09a45f137e19add3aadcf5610b6b6a76aab963142f0a88d1941f8b32dc4b"},"schema_version":"1.0","source":{"id":"1902.06826","kind":"arxiv","version":1}},"canonical_sha256":"51e7a4a824d05365fa135ba9663fa4e879f07c2f9978495f695659f69c13b67b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"51e7a4a824d05365fa135ba9663fa4e879f07c2f9978495f695659f69c13b67b","first_computed_at":"2026-05-17T23:53:40.677165Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:40.677165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JyMT4MpOeJautdgsiFrL1/spIOQ8oNJJKBrHSjIj2hbLW0+X7AfPPVsWIcF3t5WAFroXL1cEQLKDI2h8VrQkAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:40.677745Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.06826","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc3d14bd1d3d173a63c19efabec8a4fe9a013a55ff34a174d5aa3eb240a44bde","sha256:9064eb0d91ec8f1f30e0d031a5dd7a7d620974f9676e7466451dce0f1c193118"],"state_sha256":"f6bd04b82b0c433222f5ed82dec8a5b502ab526623d3e98cd7c6b2ee0451c9ff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YlG6HrPdkgMowNrTg0yE2vYmowld16KVDYFyUbqCCXCZg5VQRI6m7jceouqNRKJBQkrWnsXiD4u1HTqAofR1Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T22:45:07.812442Z","bundle_sha256":"5c6c92ea08c085f1a8fe1d77a3cf7ad11017e5b5390963aa546213c1df42713f"}}