{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:2I3F3REABSRSAPU2DWRXGJJVRG","short_pith_number":"pith:2I3F3REA","canonical_record":{"source":{"id":"1609.08842","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-09-28T09:50:14Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"e60a2523a2c27b64d3bb458b57dce8b7919ba6c0c8c253606c929836646e7f99","abstract_canon_sha256":"fbf118c7da4b94f7447ee73ecd76e0a314cc76676c5931ede1d714fa7c7e5dad"},"schema_version":"1.0"},"canonical_sha256":"d2365dc4800ca3203e9a1da37325358986074808b267706f3d5a5b2332e3f7a9","source":{"kind":"arxiv","id":"1609.08842","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.08842","created_at":"2026-05-18T01:03:41Z"},{"alias_kind":"arxiv_version","alias_value":"1609.08842v1","created_at":"2026-05-18T01:03:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.08842","created_at":"2026-05-18T01:03:41Z"},{"alias_kind":"pith_short_12","alias_value":"2I3F3REABSRS","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2I3F3REABSRSAPU2","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2I3F3REA","created_at":"2026-05-18T12:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:2I3F3REABSRSAPU2DWRXGJJVRG","target":"record","payload":{"canonical_record":{"source":{"id":"1609.08842","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-09-28T09:50:14Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"e60a2523a2c27b64d3bb458b57dce8b7919ba6c0c8c253606c929836646e7f99","abstract_canon_sha256":"fbf118c7da4b94f7447ee73ecd76e0a314cc76676c5931ede1d714fa7c7e5dad"},"schema_version":"1.0"},"canonical_sha256":"d2365dc4800ca3203e9a1da37325358986074808b267706f3d5a5b2332e3f7a9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:41.760164Z","signature_b64":"bqTzqGye9ZqQsSCBsdU4J549+BOC/YJH2gliznktKhJhtfjaL/dRza3i2Nyd6AeI6Obuhw0Mg0/tT1B9WFRRAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2365dc4800ca3203e9a1da37325358986074808b267706f3d5a5b2332e3f7a9","last_reissued_at":"2026-05-18T01:03:41.759693Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:41.759693Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.08842","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":"2026-05-18T01:03:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4/7A1c6ZK8vyEXKWSqcXGARcByiINH44T0qL6WEweANWgch9LgXDS3gHmt6JQKnKjNl0/dHwcn6/o7jaey88Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T18:54:02.053697Z"},"content_sha256":"d1ec54dee31e661be907ad9b12063b06c664016baaf5d9904214b044bb1c5bd2","schema_version":"1.0","event_id":"sha256:d1ec54dee31e661be907ad9b12063b06c664016baaf5d9904214b044bb1c5bd2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:2I3F3REABSRSAPU2DWRXGJJVRG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analysis of Carrier's problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.CA","authors_text":"P. E. Farrell, S. J. Chapman","submitted_at":"2016-09-28T09:50:14Z","abstract_excerpt":"A computational and asymptotic analysis of the solutions of Carrier's problem is presented. The computations reveal a striking and beautiful bifurcation diagram, with an infinite sequence of alternating pitchfork and fold bifurcations as the bifurcation parameter tends to zero. The method of Kuzmak is then applied to construct asymptotic solutions to the problem. This asymptotic approach explains the bifurcation structure identified numerically, and its predictions of the bifurcation points are in excellent agreement with the numerical results. The analysis yields a novel and complete taxonomy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08842","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":"2026-05-18T01:03:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pP49cuDwh71aWLEcrkMWWVGpYSpZNSiVe0g4S6jUSjMz3Q8TXx3Bz9L3Q2Igk4yKTRTY8b4P+fwq/LqI8id7AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T18:54:02.054076Z"},"content_sha256":"01e8d9ff8c71ff069672d2dfee4d464f805b057489bf9b8d63ba214437244f89","schema_version":"1.0","event_id":"sha256:01e8d9ff8c71ff069672d2dfee4d464f805b057489bf9b8d63ba214437244f89"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2I3F3REABSRSAPU2DWRXGJJVRG/bundle.json","state_url":"https://pith.science/pith/2I3F3REABSRSAPU2DWRXGJJVRG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2I3F3REABSRSAPU2DWRXGJJVRG/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":"2026-05-26T18:54:02Z","links":{"resolver":"https://pith.science/pith/2I3F3REABSRSAPU2DWRXGJJVRG","bundle":"https://pith.science/pith/2I3F3REABSRSAPU2DWRXGJJVRG/bundle.json","state":"https://pith.science/pith/2I3F3REABSRSAPU2DWRXGJJVRG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2I3F3REABSRSAPU2DWRXGJJVRG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2I3F3REABSRSAPU2DWRXGJJVRG","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":"fbf118c7da4b94f7447ee73ecd76e0a314cc76676c5931ede1d714fa7c7e5dad","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-09-28T09:50:14Z","title_canon_sha256":"e60a2523a2c27b64d3bb458b57dce8b7919ba6c0c8c253606c929836646e7f99"},"schema_version":"1.0","source":{"id":"1609.08842","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.08842","created_at":"2026-05-18T01:03:41Z"},{"alias_kind":"arxiv_version","alias_value":"1609.08842v1","created_at":"2026-05-18T01:03:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.08842","created_at":"2026-05-18T01:03:41Z"},{"alias_kind":"pith_short_12","alias_value":"2I3F3REABSRS","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2I3F3REABSRSAPU2","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2I3F3REA","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:01e8d9ff8c71ff069672d2dfee4d464f805b057489bf9b8d63ba214437244f89","target":"graph","created_at":"2026-05-18T01:03:41Z","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":"A computational and asymptotic analysis of the solutions of Carrier's problem is presented. The computations reveal a striking and beautiful bifurcation diagram, with an infinite sequence of alternating pitchfork and fold bifurcations as the bifurcation parameter tends to zero. The method of Kuzmak is then applied to construct asymptotic solutions to the problem. This asymptotic approach explains the bifurcation structure identified numerically, and its predictions of the bifurcation points are in excellent agreement with the numerical results. The analysis yields a novel and complete taxonomy","authors_text":"P. E. Farrell, S. J. Chapman","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-09-28T09:50:14Z","title":"Analysis of Carrier's problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08842","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:d1ec54dee31e661be907ad9b12063b06c664016baaf5d9904214b044bb1c5bd2","target":"record","created_at":"2026-05-18T01:03:41Z","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":"fbf118c7da4b94f7447ee73ecd76e0a314cc76676c5931ede1d714fa7c7e5dad","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-09-28T09:50:14Z","title_canon_sha256":"e60a2523a2c27b64d3bb458b57dce8b7919ba6c0c8c253606c929836646e7f99"},"schema_version":"1.0","source":{"id":"1609.08842","kind":"arxiv","version":1}},"canonical_sha256":"d2365dc4800ca3203e9a1da37325358986074808b267706f3d5a5b2332e3f7a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d2365dc4800ca3203e9a1da37325358986074808b267706f3d5a5b2332e3f7a9","first_computed_at":"2026-05-18T01:03:41.759693Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:41.759693Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bqTzqGye9ZqQsSCBsdU4J549+BOC/YJH2gliznktKhJhtfjaL/dRza3i2Nyd6AeI6Obuhw0Mg0/tT1B9WFRRAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:41.760164Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.08842","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1ec54dee31e661be907ad9b12063b06c664016baaf5d9904214b044bb1c5bd2","sha256:01e8d9ff8c71ff069672d2dfee4d464f805b057489bf9b8d63ba214437244f89"],"state_sha256":"fd5d87c28a1d2d6dcbbb487a34b1804bf9c7b00d231471bc9d24da17e9480785"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PuXbm+hWiO3oPF8eZ+SxHns6Fhk1aMO4Iy3WZGfdj5KINVBs11xjhjyWRUVoUFkzZP+Cdg5cMqwQyYdv3Fi1Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T18:54:02.056400Z","bundle_sha256":"197b2031cbbdf69789c7b7622f92c21eee6873f3da9ef62304045cc24d5a72be"}}