{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:SLW2CGZIZRA2ALJ3WQ6JJU4U63","short_pith_number":"pith:SLW2CGZI","canonical_record":{"source":{"id":"1703.04198","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-03-12T23:33:32Z","cross_cats_sorted":["math.AG","math.FA"],"title_canon_sha256":"96da32161e6f7e0f451aa6c02bcfc138219a90edd7863a4285340c8c9c36b7ad","abstract_canon_sha256":"c99a47e0a114e30b6beab1a7e33d0137073370ca9ba5f6ef4597d7644124898b"},"schema_version":"1.0"},"canonical_sha256":"92eda11b28cc41a02d3bb43c94d394f6cbc3b5a8c48633b3dad53149965751df","source":{"kind":"arxiv","id":"1703.04198","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.04198","created_at":"2026-05-18T00:23:56Z"},{"alias_kind":"arxiv_version","alias_value":"1703.04198v1","created_at":"2026-05-18T00:23:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.04198","created_at":"2026-05-18T00:23:56Z"},{"alias_kind":"pith_short_12","alias_value":"SLW2CGZIZRA2","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SLW2CGZIZRA2ALJ3","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SLW2CGZI","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:SLW2CGZIZRA2ALJ3WQ6JJU4U63","target":"record","payload":{"canonical_record":{"source":{"id":"1703.04198","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-03-12T23:33:32Z","cross_cats_sorted":["math.AG","math.FA"],"title_canon_sha256":"96da32161e6f7e0f451aa6c02bcfc138219a90edd7863a4285340c8c9c36b7ad","abstract_canon_sha256":"c99a47e0a114e30b6beab1a7e33d0137073370ca9ba5f6ef4597d7644124898b"},"schema_version":"1.0"},"canonical_sha256":"92eda11b28cc41a02d3bb43c94d394f6cbc3b5a8c48633b3dad53149965751df","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:56.740092Z","signature_b64":"NQRnyMuoSwKMGgYsyqc5gm+J1QhOzdA9JEp9pEPw0KwmIxVuUUBd9GwzoV++eft4jKt03Sp1Z8+TPGPibPv/AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92eda11b28cc41a02d3bb43c94d394f6cbc3b5a8c48633b3dad53149965751df","last_reissued_at":"2026-05-18T00:23:56.739512Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:56.739512Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.04198","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":"2026-05-18T00:23:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZBx/E33ityTeny8gBQFH1OygmlRVRECBKgM7X5e+idEqM0crO7vh5QliJa5EoBNlU57u5sBUbK+GPDJw055LAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T03:47:01.671070Z"},"content_sha256":"3e649cd5e41c28615526cafbfe5a3139c2023ec891f52332120225e6b9db5323","schema_version":"1.0","event_id":"sha256:3e649cd5e41c28615526cafbfe5a3139c2023ec891f52332120225e6b9db5323"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:SLW2CGZIZRA2ALJ3WQ6JJU4U63","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Derivatives of rational inner functions: geometry of singularities and integrability at the boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.FA"],"primary_cat":"math.CV","authors_text":"Alan Sola, James Eldred Pascoe, Kelly Bickel","submitted_at":"2017-03-12T23:33:32Z","abstract_excerpt":"We analyze the singularities of rational inner functions on the unit bidisk and study both when these functions belong to Dirichlet-type spaces and when their partial derivatives belong to Hardy spaces. We characterize derivative $H^{\\mathfrak{p}}$ membership purely in terms of contact order, a measure of the rate at which the zero set of a rational inner function approaches the distinguished boundary of the bidisk. We also show that derivatives of rational inner functions with singularities fail to be in $H^{\\mathfrak{p}}$ for $\\mathfrak{p}\\ge\\frac{3}{2}$ and that higher non-tangential regula"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.04198","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":"2026-05-18T00:23:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ANP640EzBDUUdxnsR1/w9JlxDjp962kqCviYhUYKQxznZoC+cIwUuchC1cr+kPLq4rDPC+BIhJYWmveZlW0QDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T03:47:01.671785Z"},"content_sha256":"965c59fcf2889ceb85c851c338668bdfd6483e3a5f60893773defb58012f891b","schema_version":"1.0","event_id":"sha256:965c59fcf2889ceb85c851c338668bdfd6483e3a5f60893773defb58012f891b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SLW2CGZIZRA2ALJ3WQ6JJU4U63/bundle.json","state_url":"https://pith.science/pith/SLW2CGZIZRA2ALJ3WQ6JJU4U63/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SLW2CGZIZRA2ALJ3WQ6JJU4U63/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":"2026-06-11T03:47:01Z","links":{"resolver":"https://pith.science/pith/SLW2CGZIZRA2ALJ3WQ6JJU4U63","bundle":"https://pith.science/pith/SLW2CGZIZRA2ALJ3WQ6JJU4U63/bundle.json","state":"https://pith.science/pith/SLW2CGZIZRA2ALJ3WQ6JJU4U63/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SLW2CGZIZRA2ALJ3WQ6JJU4U63/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SLW2CGZIZRA2ALJ3WQ6JJU4U63","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":"c99a47e0a114e30b6beab1a7e33d0137073370ca9ba5f6ef4597d7644124898b","cross_cats_sorted":["math.AG","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-03-12T23:33:32Z","title_canon_sha256":"96da32161e6f7e0f451aa6c02bcfc138219a90edd7863a4285340c8c9c36b7ad"},"schema_version":"1.0","source":{"id":"1703.04198","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.04198","created_at":"2026-05-18T00:23:56Z"},{"alias_kind":"arxiv_version","alias_value":"1703.04198v1","created_at":"2026-05-18T00:23:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.04198","created_at":"2026-05-18T00:23:56Z"},{"alias_kind":"pith_short_12","alias_value":"SLW2CGZIZRA2","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SLW2CGZIZRA2ALJ3","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SLW2CGZI","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:965c59fcf2889ceb85c851c338668bdfd6483e3a5f60893773defb58012f891b","target":"graph","created_at":"2026-05-18T00:23:56Z","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 analyze the singularities of rational inner functions on the unit bidisk and study both when these functions belong to Dirichlet-type spaces and when their partial derivatives belong to Hardy spaces. We characterize derivative $H^{\\mathfrak{p}}$ membership purely in terms of contact order, a measure of the rate at which the zero set of a rational inner function approaches the distinguished boundary of the bidisk. We also show that derivatives of rational inner functions with singularities fail to be in $H^{\\mathfrak{p}}$ for $\\mathfrak{p}\\ge\\frac{3}{2}$ and that higher non-tangential regula","authors_text":"Alan Sola, James Eldred Pascoe, Kelly Bickel","cross_cats":["math.AG","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-03-12T23:33:32Z","title":"Derivatives of rational inner functions: geometry of singularities and integrability at the boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.04198","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":"sha256:3e649cd5e41c28615526cafbfe5a3139c2023ec891f52332120225e6b9db5323","target":"record","created_at":"2026-05-18T00:23:56Z","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":"c99a47e0a114e30b6beab1a7e33d0137073370ca9ba5f6ef4597d7644124898b","cross_cats_sorted":["math.AG","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-03-12T23:33:32Z","title_canon_sha256":"96da32161e6f7e0f451aa6c02bcfc138219a90edd7863a4285340c8c9c36b7ad"},"schema_version":"1.0","source":{"id":"1703.04198","kind":"arxiv","version":1}},"canonical_sha256":"92eda11b28cc41a02d3bb43c94d394f6cbc3b5a8c48633b3dad53149965751df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92eda11b28cc41a02d3bb43c94d394f6cbc3b5a8c48633b3dad53149965751df","first_computed_at":"2026-05-18T00:23:56.739512Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:56.739512Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NQRnyMuoSwKMGgYsyqc5gm+J1QhOzdA9JEp9pEPw0KwmIxVuUUBd9GwzoV++eft4jKt03Sp1Z8+TPGPibPv/AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:56.740092Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.04198","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e649cd5e41c28615526cafbfe5a3139c2023ec891f52332120225e6b9db5323","sha256:965c59fcf2889ceb85c851c338668bdfd6483e3a5f60893773defb58012f891b"],"state_sha256":"73377c23b0bc47fbe4007ce6648ba7067d602b112776639832f246a1478b8a32"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xc4HumPrxJyOXOO/d/ayCUdubQv9u3pag2e9RZsim8X88aVFrCPcSXFvlYc+/QjuHtRCFscI3kLLhFAMpiusBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T03:47:01.675703Z","bundle_sha256":"3259ac0572cf93c54b590030756097eecc6d20fc14f8e8936c9bd560262e62db"}}