{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6QA6ARRRB5EAFMLOJ2ELOZ3P5K","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":"79f60ebbe4a799a782b45d369f496e3007ee5ccf8c8af6394f8de9510f9d0a42","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-07-05T21:22:06Z","title_canon_sha256":"f1880bbbc933bb31b7bc2a24062d93e226ebfe99d9e7e26d5cbd2e6d2a57cac4"},"schema_version":"1.0","source":{"id":"1607.01421","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.01421","created_at":"2026-05-18T01:11:26Z"},{"alias_kind":"arxiv_version","alias_value":"1607.01421v1","created_at":"2026-05-18T01:11:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.01421","created_at":"2026-05-18T01:11:26Z"},{"alias_kind":"pith_short_12","alias_value":"6QA6ARRRB5EA","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6QA6ARRRB5EAFMLO","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6QA6ARRR","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:0c62336f1f247e9c731c032e5bf1308a45b08bdcbaf56efa447f3235281a839e","target":"graph","created_at":"2026-05-18T01:11:26Z","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 paper we investigate the application of pseudo-transient-continuation (PTC) schemes for the numerical solution of semilinear elliptic partial differential equations, with possible singular perturbations. We will outline a residual reduction analysis within the framework of general Hilbert spaces, and, subsequently, employ the PTC-methodology in the context of finite element discretizations of semilinear boundary value problems. Our approach combines both a prediction-type PTC-method (for infinite dimensional problems) and an adaptive finite element discretization (based on a robust a p","authors_text":"Mario Amrein, Thomas P. Wihler","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-07-05T21:22:06Z","title":"Adaptive Pseudo-Transient-Continuation-Galerkin Methods for Semilinear Elliptic Partial Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01421","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:ccfc39bbce74315708e8d06bafc7fbed80b39e4bc8b72390a2c44e82e4e6ec32","target":"record","created_at":"2026-05-18T01:11:26Z","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":"79f60ebbe4a799a782b45d369f496e3007ee5ccf8c8af6394f8de9510f9d0a42","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-07-05T21:22:06Z","title_canon_sha256":"f1880bbbc933bb31b7bc2a24062d93e226ebfe99d9e7e26d5cbd2e6d2a57cac4"},"schema_version":"1.0","source":{"id":"1607.01421","kind":"arxiv","version":1}},"canonical_sha256":"f401e046310f4802b16e4e88b7676fea9ff15d942b8c3b1f38a8dc965d6e0037","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f401e046310f4802b16e4e88b7676fea9ff15d942b8c3b1f38a8dc965d6e0037","first_computed_at":"2026-05-18T01:11:26.450663Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:26.450663Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k615gr8+rureBEObx2K0XFQl5ljatYr37RBP5JV16T08qbz6h95mTpgy28uKdLr+SUIKVsP+Qdg5Vnm1sBj7AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:26.451239Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.01421","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ccfc39bbce74315708e8d06bafc7fbed80b39e4bc8b72390a2c44e82e4e6ec32","sha256:0c62336f1f247e9c731c032e5bf1308a45b08bdcbaf56efa447f3235281a839e"],"state_sha256":"5a97b1f00b2a727ac212a2dc3e9a792a0febcd44548d26956b4549eb301716a2"}