{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:K5FVL2TBDDBXLM3T6GCFTCR5JJ","short_pith_number":"pith:K5FVL2TB","canonical_record":{"source":{"id":"1901.05210","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-01-16T10:21:01Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"0a089f70ae374addc715f2a47f75ef3682e89a09fe6b291d06fbdf226c6bef2c","abstract_canon_sha256":"d56b2cd9d72648253780215380f33647c504b46ed09c73c3f82a1e970eda30ba"},"schema_version":"1.0"},"canonical_sha256":"574b55ea6118c375b373f184598a3d4a4ddbd559de2e5d07f28b0419d5e28a17","source":{"kind":"arxiv","id":"1901.05210","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.05210","created_at":"2026-05-17T23:56:11Z"},{"alias_kind":"arxiv_version","alias_value":"1901.05210v1","created_at":"2026-05-17T23:56:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.05210","created_at":"2026-05-17T23:56:11Z"},{"alias_kind":"pith_short_12","alias_value":"K5FVL2TBDDBX","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"K5FVL2TBDDBXLM3T","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"K5FVL2TB","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:K5FVL2TBDDBXLM3T6GCFTCR5JJ","target":"record","payload":{"canonical_record":{"source":{"id":"1901.05210","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-01-16T10:21:01Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"0a089f70ae374addc715f2a47f75ef3682e89a09fe6b291d06fbdf226c6bef2c","abstract_canon_sha256":"d56b2cd9d72648253780215380f33647c504b46ed09c73c3f82a1e970eda30ba"},"schema_version":"1.0"},"canonical_sha256":"574b55ea6118c375b373f184598a3d4a4ddbd559de2e5d07f28b0419d5e28a17","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:11.513588Z","signature_b64":"/XRO9B48JCgNEBcKZ1n9T915cxul1+aYzKBI0yuVdyiAhtn4aqDH4oTjWWJvNQ0tUEiZk8nSFJw2Omm5wmwUBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"574b55ea6118c375b373f184598a3d4a4ddbd559de2e5d07f28b0419d5e28a17","last_reissued_at":"2026-05-17T23:56:11.512859Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:11.512859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1901.05210","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":"2026-05-17T23:56:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x/Rd0Vs1iLKnfWxsnNkhYaf907WDy+JJdJrJk18lHNiqgYb+2cUX6RozbpRQ8I6BFVTBwiEaq5Z2XPeV5B3HDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:09:24.400946Z"},"content_sha256":"fab85e9e858360c1ac18f1434af513007bff10f93d132b68c859a6915623d5a4","schema_version":"1.0","event_id":"sha256:fab85e9e858360c1ac18f1434af513007bff10f93d132b68c859a6915623d5a4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:K5FVL2TBDDBXLM3T6GCFTCR5JJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On singularly perturbed linear initial value problems with mixed irregular and Fuchsian time singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CV","authors_text":"Alberto Lastra, Stephane Malek","submitted_at":"2019-01-16T10:21:01Z","abstract_excerpt":"We consider a family of linear singularly perturbed PDE relying on a complex perturbation parameter $\\epsilon$. As in a former study of the authors (A. Lastra, S. Malek, Parametric Gevrey asymptotics for some nonlinear initial value Cauchy problems, J. Differential Equations 259 (2015), no. 10, 5220--5270), our problem possesses an irregular singularity in time located at the origin but, in the present work, it entangles also differential operators of Fuchsian type acting on the time variable. As a new feature, a set of sectorial holomorphic solutions are built up through iterated Laplace tran"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.05210","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":"2026-05-17T23:56:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XoiiYpU/PnBXk1sI7+JaetlrLYTxT/gO67wDAbDr/K8wKlH4izFVWwXYXNRAQPzswjKoqM0AARb7R+ep7Kq9Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:09:24.401614Z"},"content_sha256":"ab178a5ceaf21b65bc7f823e7a783b5d08f0d02221007be5b81e4caba7c03a13","schema_version":"1.0","event_id":"sha256:ab178a5ceaf21b65bc7f823e7a783b5d08f0d02221007be5b81e4caba7c03a13"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K5FVL2TBDDBXLM3T6GCFTCR5JJ/bundle.json","state_url":"https://pith.science/pith/K5FVL2TBDDBXLM3T6GCFTCR5JJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K5FVL2TBDDBXLM3T6GCFTCR5JJ/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":"2026-06-06T20:09:24Z","links":{"resolver":"https://pith.science/pith/K5FVL2TBDDBXLM3T6GCFTCR5JJ","bundle":"https://pith.science/pith/K5FVL2TBDDBXLM3T6GCFTCR5JJ/bundle.json","state":"https://pith.science/pith/K5FVL2TBDDBXLM3T6GCFTCR5JJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K5FVL2TBDDBXLM3T6GCFTCR5JJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:K5FVL2TBDDBXLM3T6GCFTCR5JJ","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":"d56b2cd9d72648253780215380f33647c504b46ed09c73c3f82a1e970eda30ba","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-01-16T10:21:01Z","title_canon_sha256":"0a089f70ae374addc715f2a47f75ef3682e89a09fe6b291d06fbdf226c6bef2c"},"schema_version":"1.0","source":{"id":"1901.05210","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.05210","created_at":"2026-05-17T23:56:11Z"},{"alias_kind":"arxiv_version","alias_value":"1901.05210v1","created_at":"2026-05-17T23:56:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.05210","created_at":"2026-05-17T23:56:11Z"},{"alias_kind":"pith_short_12","alias_value":"K5FVL2TBDDBX","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"K5FVL2TBDDBXLM3T","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"K5FVL2TB","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:ab178a5ceaf21b65bc7f823e7a783b5d08f0d02221007be5b81e4caba7c03a13","target":"graph","created_at":"2026-05-17T23:56:11Z","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 consider a family of linear singularly perturbed PDE relying on a complex perturbation parameter $\\epsilon$. As in a former study of the authors (A. Lastra, S. Malek, Parametric Gevrey asymptotics for some nonlinear initial value Cauchy problems, J. Differential Equations 259 (2015), no. 10, 5220--5270), our problem possesses an irregular singularity in time located at the origin but, in the present work, it entangles also differential operators of Fuchsian type acting on the time variable. As a new feature, a set of sectorial holomorphic solutions are built up through iterated Laplace tran","authors_text":"Alberto Lastra, Stephane Malek","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-01-16T10:21:01Z","title":"On singularly perturbed linear initial value problems with mixed irregular and Fuchsian time singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.05210","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:fab85e9e858360c1ac18f1434af513007bff10f93d132b68c859a6915623d5a4","target":"record","created_at":"2026-05-17T23:56:11Z","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":"d56b2cd9d72648253780215380f33647c504b46ed09c73c3f82a1e970eda30ba","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-01-16T10:21:01Z","title_canon_sha256":"0a089f70ae374addc715f2a47f75ef3682e89a09fe6b291d06fbdf226c6bef2c"},"schema_version":"1.0","source":{"id":"1901.05210","kind":"arxiv","version":1}},"canonical_sha256":"574b55ea6118c375b373f184598a3d4a4ddbd559de2e5d07f28b0419d5e28a17","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"574b55ea6118c375b373f184598a3d4a4ddbd559de2e5d07f28b0419d5e28a17","first_computed_at":"2026-05-17T23:56:11.512859Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:11.512859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/XRO9B48JCgNEBcKZ1n9T915cxul1+aYzKBI0yuVdyiAhtn4aqDH4oTjWWJvNQ0tUEiZk8nSFJw2Omm5wmwUBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:11.513588Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.05210","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fab85e9e858360c1ac18f1434af513007bff10f93d132b68c859a6915623d5a4","sha256:ab178a5ceaf21b65bc7f823e7a783b5d08f0d02221007be5b81e4caba7c03a13"],"state_sha256":"46ed138612326c19572d2c77800d359b4cdf9bb6bdfd2cbba73711eb2927430f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A/s9fZt7B157nKP47/LDsxAMZmmHTPQADnMoWT6QNKRWV0fRS1YseB8Rd2sZ7Ifq0wTZrqo9STDlvGqK5/AXBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T20:09:24.404863Z","bundle_sha256":"80d299e965a4bbf8766d53a8221a899509efaa99dd2c2abc53cb87179cdaf88c"}}