{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:PPUYVZFXDFRM3DLTCUVB5Z5CC4","short_pith_number":"pith:PPUYVZFX","canonical_record":{"source":{"id":"1610.06844","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-21T16:27:29Z","cross_cats_sorted":[],"title_canon_sha256":"53b031b383758a3ba25718f90e256064d2248f90712f7ed596c550f274680b76","abstract_canon_sha256":"07745e5e11b48b3e5ab9a1a6d309cc4d19c36ae75eb4cd94d44f1a8f9469e979"},"schema_version":"1.0"},"canonical_sha256":"7be98ae4b71962cd8d73152a1ee7a2173647ff25f6e577b0cc33f37076ee9787","source":{"kind":"arxiv","id":"1610.06844","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06844","created_at":"2026-05-18T00:06:51Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06844v1","created_at":"2026-05-18T00:06:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06844","created_at":"2026-05-18T00:06:51Z"},{"alias_kind":"pith_short_12","alias_value":"PPUYVZFXDFRM","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PPUYVZFXDFRM3DLT","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PPUYVZFX","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:PPUYVZFXDFRM3DLTCUVB5Z5CC4","target":"record","payload":{"canonical_record":{"source":{"id":"1610.06844","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-21T16:27:29Z","cross_cats_sorted":[],"title_canon_sha256":"53b031b383758a3ba25718f90e256064d2248f90712f7ed596c550f274680b76","abstract_canon_sha256":"07745e5e11b48b3e5ab9a1a6d309cc4d19c36ae75eb4cd94d44f1a8f9469e979"},"schema_version":"1.0"},"canonical_sha256":"7be98ae4b71962cd8d73152a1ee7a2173647ff25f6e577b0cc33f37076ee9787","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:51.505809Z","signature_b64":"I9f6y3Ruxk8MXcbdwCnqQpBJ7DQvqFywfJpRZWSLlcAqOKifcsDpktB6qA2+IpVJiHgAc3D+p7lvN/YPyR9lAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7be98ae4b71962cd8d73152a1ee7a2173647ff25f6e577b0cc33f37076ee9787","last_reissued_at":"2026-05-18T00:06:51.504890Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:51.504890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.06844","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":"2026-05-18T00:06:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"25oTrX7GtcpEKm07KDZxNHQElngFw3gSbFGCMdj4C97w3d7OMiTCfafH+rT8OpjUGp5REXm25kninLtNBS5pAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T13:50:46.236399Z"},"content_sha256":"c7f9ffc0750b506a4eb31eb38838c402aa393305a09888da8eddee89b4bb8c46","schema_version":"1.0","event_id":"sha256:c7f9ffc0750b506a4eb31eb38838c402aa393305a09888da8eddee89b4bb8c46"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:PPUYVZFXDFRM3DLTCUVB5Z5CC4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An optimal approximation formula for functions with singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Ken'ichiro Tanaka, Masaaki Sugihara, Tomoaki Okayama","submitted_at":"2016-10-21T16:27:29Z","abstract_excerpt":"We propose an optimal approximation formula for analytic functions that are defined on a complex region containing the real interval $(-1,1)$ and possibly have algebraic singularities at the endpoints of the interval. As a space of such functions,we consider a Hardy space with the weight given by $w_{\\mu}(z) = (1-z^{2})^{\\mu/2}$ for $\\mu > 0$, and formulate the optimality of an approximation formula for the functions in the space. Then, we propose an optimal approximation formula for the space for any $\\mu > 0$ as opposed to existing results with the restriction $0 < \\mu < \\mu_{\\ast}$ for a ce"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06844","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":"2026-05-18T00:06:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NZ0Np6i4c/6hhgrbDjTxG6HgLGTrHgAdHwWN7kI38G7svZOqiRDfOSyqh+/Scw5mX9dtObpXAXBzrnu0tUB7BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T13:50:46.236741Z"},"content_sha256":"04c1804c6fdda31a11d3f628e37ea64f33a884e6519500b713f7652bd6b22e4d","schema_version":"1.0","event_id":"sha256:04c1804c6fdda31a11d3f628e37ea64f33a884e6519500b713f7652bd6b22e4d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PPUYVZFXDFRM3DLTCUVB5Z5CC4/bundle.json","state_url":"https://pith.science/pith/PPUYVZFXDFRM3DLTCUVB5Z5CC4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PPUYVZFXDFRM3DLTCUVB5Z5CC4/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":"2026-06-26T13:50:46Z","links":{"resolver":"https://pith.science/pith/PPUYVZFXDFRM3DLTCUVB5Z5CC4","bundle":"https://pith.science/pith/PPUYVZFXDFRM3DLTCUVB5Z5CC4/bundle.json","state":"https://pith.science/pith/PPUYVZFXDFRM3DLTCUVB5Z5CC4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PPUYVZFXDFRM3DLTCUVB5Z5CC4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PPUYVZFXDFRM3DLTCUVB5Z5CC4","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":"07745e5e11b48b3e5ab9a1a6d309cc4d19c36ae75eb4cd94d44f1a8f9469e979","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-21T16:27:29Z","title_canon_sha256":"53b031b383758a3ba25718f90e256064d2248f90712f7ed596c550f274680b76"},"schema_version":"1.0","source":{"id":"1610.06844","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06844","created_at":"2026-05-18T00:06:51Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06844v1","created_at":"2026-05-18T00:06:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06844","created_at":"2026-05-18T00:06:51Z"},{"alias_kind":"pith_short_12","alias_value":"PPUYVZFXDFRM","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PPUYVZFXDFRM3DLT","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PPUYVZFX","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:04c1804c6fdda31a11d3f628e37ea64f33a884e6519500b713f7652bd6b22e4d","target":"graph","created_at":"2026-05-18T00:06:51Z","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 propose an optimal approximation formula for analytic functions that are defined on a complex region containing the real interval $(-1,1)$ and possibly have algebraic singularities at the endpoints of the interval. As a space of such functions,we consider a Hardy space with the weight given by $w_{\\mu}(z) = (1-z^{2})^{\\mu/2}$ for $\\mu > 0$, and formulate the optimality of an approximation formula for the functions in the space. Then, we propose an optimal approximation formula for the space for any $\\mu > 0$ as opposed to existing results with the restriction $0 < \\mu < \\mu_{\\ast}$ for a ce","authors_text":"Ken'ichiro Tanaka, Masaaki Sugihara, Tomoaki Okayama","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-21T16:27:29Z","title":"An optimal approximation formula for functions with singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06844","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:c7f9ffc0750b506a4eb31eb38838c402aa393305a09888da8eddee89b4bb8c46","target":"record","created_at":"2026-05-18T00:06:51Z","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":"07745e5e11b48b3e5ab9a1a6d309cc4d19c36ae75eb4cd94d44f1a8f9469e979","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-21T16:27:29Z","title_canon_sha256":"53b031b383758a3ba25718f90e256064d2248f90712f7ed596c550f274680b76"},"schema_version":"1.0","source":{"id":"1610.06844","kind":"arxiv","version":1}},"canonical_sha256":"7be98ae4b71962cd8d73152a1ee7a2173647ff25f6e577b0cc33f37076ee9787","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7be98ae4b71962cd8d73152a1ee7a2173647ff25f6e577b0cc33f37076ee9787","first_computed_at":"2026-05-18T00:06:51.504890Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:51.504890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I9f6y3Ruxk8MXcbdwCnqQpBJ7DQvqFywfJpRZWSLlcAqOKifcsDpktB6qA2+IpVJiHgAc3D+p7lvN/YPyR9lAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:51.505809Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.06844","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7f9ffc0750b506a4eb31eb38838c402aa393305a09888da8eddee89b4bb8c46","sha256:04c1804c6fdda31a11d3f628e37ea64f33a884e6519500b713f7652bd6b22e4d"],"state_sha256":"b11227727b3dd526b431979f878199cc7f6ef9c2947dfd29080f88bca6b7d0b4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K/UVOlqsFPACbrT14ydRHp3lx8Rlt6gWi3xeOVhbAGt/EtwW2Q4sPCcAnKvycLKhMgQ3SRkyD00j0WPsplp6CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T13:50:46.238835Z","bundle_sha256":"8ad196410f46d15bb03c928bb328327692ef8e661f975d41b3aa7d3d8787525b"}}