{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:UWNYK73EDSDSCX7GN44QFS63OY","short_pith_number":"pith:UWNYK73E","canonical_record":{"source":{"id":"1704.03128","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-04-11T03:26:03Z","cross_cats_sorted":[],"title_canon_sha256":"478f20de19a7cf6e54a4f36ac96871338e93c36bb139092d51ef819e85f54ea8","abstract_canon_sha256":"82242372a84817d781ada3b486a26aeaf0cfc44f681d74752ad4d0ba3fe8dd16"},"schema_version":"1.0"},"canonical_sha256":"a59b857f641c87215fe66f3902cbdb761e6bf95e03a451c80053ad0c8067e37b","source":{"kind":"arxiv","id":"1704.03128","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.03128","created_at":"2026-05-18T00:46:33Z"},{"alias_kind":"arxiv_version","alias_value":"1704.03128v1","created_at":"2026-05-18T00:46:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03128","created_at":"2026-05-18T00:46:33Z"},{"alias_kind":"pith_short_12","alias_value":"UWNYK73EDSDS","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"UWNYK73EDSDSCX7G","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"UWNYK73E","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:UWNYK73EDSDSCX7GN44QFS63OY","target":"record","payload":{"canonical_record":{"source":{"id":"1704.03128","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-04-11T03:26:03Z","cross_cats_sorted":[],"title_canon_sha256":"478f20de19a7cf6e54a4f36ac96871338e93c36bb139092d51ef819e85f54ea8","abstract_canon_sha256":"82242372a84817d781ada3b486a26aeaf0cfc44f681d74752ad4d0ba3fe8dd16"},"schema_version":"1.0"},"canonical_sha256":"a59b857f641c87215fe66f3902cbdb761e6bf95e03a451c80053ad0c8067e37b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:33.449116Z","signature_b64":"5KRwFp3SE3OZrngZWmpUHpwGJnmpVXT1DyqPE7fv7vN40rwh1qV1mA8DTeIDMR9dajEQqIJVRvLFowKoOflYDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a59b857f641c87215fe66f3902cbdb761e6bf95e03a451c80053ad0c8067e37b","last_reissued_at":"2026-05-18T00:46:33.448478Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:33.448478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.03128","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":"2026-05-18T00:46:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KDhUIcBJCARKs3wXD4ikWrjoQyI2lnyc7KP9rZ4N2FJxpqGNXUIrgzA+BxjgjmNj911xobP7Xw4ww1tD3kv5CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T20:25:42.052632Z"},"content_sha256":"dc4c0cf657ad182fe84e482eef15807ab37d08e57ad68cfd211c5b12685c97b3","schema_version":"1.0","event_id":"sha256:dc4c0cf657ad182fe84e482eef15807ab37d08e57ad68cfd211c5b12685c97b3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:UWNYK73EDSDSCX7GN44QFS63OY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polynomial interpolation and a priori bootstrap for computer-assisted proofs in nonlinear ODEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jean-Philippe Lessard, Maxime Breden","submitted_at":"2017-04-11T03:26:03Z","abstract_excerpt":"In this work, we introduce a method based on piecewise polynomial interpolation to enclose rigorously solutions of nonlinear ODEs. Using a technique which we call a priori bootstrap, we transform the problem of solving the ODE into one of looking for a fixed point of a high order smoothing Picard-like operator. We then develop a rigorous computational method based on a Newton-Kantorovich type argument (the radii polynomial approach) to prove existence of a fixed point of the Picard-like operator. We present all necessary estimates in full generality and for any nonlinearities. With our approac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03128","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":"2026-05-18T00:46:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iOwLDZnenCRuFlWCDWU0lQAyre7skMyLN+Wsm+O3tW7bCEKV23oj92YmRbDKWgo32sD4jKMl7YDndcTB4F7tCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T20:25:42.052969Z"},"content_sha256":"d86382889ef0de3c922c42a31d036d7594283717d3a3075026783e945dbf9bdc","schema_version":"1.0","event_id":"sha256:d86382889ef0de3c922c42a31d036d7594283717d3a3075026783e945dbf9bdc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UWNYK73EDSDSCX7GN44QFS63OY/bundle.json","state_url":"https://pith.science/pith/UWNYK73EDSDSCX7GN44QFS63OY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UWNYK73EDSDSCX7GN44QFS63OY/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":"2026-06-20T20:25:42Z","links":{"resolver":"https://pith.science/pith/UWNYK73EDSDSCX7GN44QFS63OY","bundle":"https://pith.science/pith/UWNYK73EDSDSCX7GN44QFS63OY/bundle.json","state":"https://pith.science/pith/UWNYK73EDSDSCX7GN44QFS63OY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UWNYK73EDSDSCX7GN44QFS63OY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:UWNYK73EDSDSCX7GN44QFS63OY","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":"82242372a84817d781ada3b486a26aeaf0cfc44f681d74752ad4d0ba3fe8dd16","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-04-11T03:26:03Z","title_canon_sha256":"478f20de19a7cf6e54a4f36ac96871338e93c36bb139092d51ef819e85f54ea8"},"schema_version":"1.0","source":{"id":"1704.03128","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.03128","created_at":"2026-05-18T00:46:33Z"},{"alias_kind":"arxiv_version","alias_value":"1704.03128v1","created_at":"2026-05-18T00:46:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03128","created_at":"2026-05-18T00:46:33Z"},{"alias_kind":"pith_short_12","alias_value":"UWNYK73EDSDS","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"UWNYK73EDSDSCX7G","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"UWNYK73E","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:d86382889ef0de3c922c42a31d036d7594283717d3a3075026783e945dbf9bdc","target":"graph","created_at":"2026-05-18T00:46:33Z","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":"In this work, we introduce a method based on piecewise polynomial interpolation to enclose rigorously solutions of nonlinear ODEs. Using a technique which we call a priori bootstrap, we transform the problem of solving the ODE into one of looking for a fixed point of a high order smoothing Picard-like operator. We then develop a rigorous computational method based on a Newton-Kantorovich type argument (the radii polynomial approach) to prove existence of a fixed point of the Picard-like operator. We present all necessary estimates in full generality and for any nonlinearities. With our approac","authors_text":"Jean-Philippe Lessard, Maxime Breden","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-04-11T03:26:03Z","title":"Polynomial interpolation and a priori bootstrap for computer-assisted proofs in nonlinear ODEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03128","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:dc4c0cf657ad182fe84e482eef15807ab37d08e57ad68cfd211c5b12685c97b3","target":"record","created_at":"2026-05-18T00:46:33Z","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":"82242372a84817d781ada3b486a26aeaf0cfc44f681d74752ad4d0ba3fe8dd16","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-04-11T03:26:03Z","title_canon_sha256":"478f20de19a7cf6e54a4f36ac96871338e93c36bb139092d51ef819e85f54ea8"},"schema_version":"1.0","source":{"id":"1704.03128","kind":"arxiv","version":1}},"canonical_sha256":"a59b857f641c87215fe66f3902cbdb761e6bf95e03a451c80053ad0c8067e37b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a59b857f641c87215fe66f3902cbdb761e6bf95e03a451c80053ad0c8067e37b","first_computed_at":"2026-05-18T00:46:33.448478Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:33.448478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5KRwFp3SE3OZrngZWmpUHpwGJnmpVXT1DyqPE7fv7vN40rwh1qV1mA8DTeIDMR9dajEQqIJVRvLFowKoOflYDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:33.449116Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.03128","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc4c0cf657ad182fe84e482eef15807ab37d08e57ad68cfd211c5b12685c97b3","sha256:d86382889ef0de3c922c42a31d036d7594283717d3a3075026783e945dbf9bdc"],"state_sha256":"9a961f9dc3d1e44941535d649ccfa4fa4a22955da7ce907854189513a9e04292"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1PgUMr2QgmQr/KxXRHwNdtio5tR93FaHGxMDsQ/qciff/GXWQTZRlbyVnNxddKOytk0lCAoPQothKq/u5RgXAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T20:25:42.054887Z","bundle_sha256":"50ba7d1dc6cf9d5ecbacda970fd510868e4a33bff042289568ad0fd17edce13d"}}