{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:SR7UO26624L2XT2QY6VEFJTQ6Z","short_pith_number":"pith:SR7UO266","canonical_record":{"source":{"id":"2607.16781","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-07-18T11:32:04Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"fe6d933fe27930a6e1dadee50fc1f22a335bcaecad54dc60ca45fe9afc70ead2","abstract_canon_sha256":"2735f492619614567c0896d2ba411e731bf3ae7f9f1d70e43a5c86745e3212e7"},"schema_version":"1.0"},"canonical_sha256":"947f476bded717abcf50c7aa42a670f64f5830c4821ab5569ebc18903512b37c","source":{"kind":"arxiv","id":"2607.16781","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.16781","created_at":"2026-07-21T01:20:58Z"},{"alias_kind":"arxiv_version","alias_value":"2607.16781v1","created_at":"2026-07-21T01:20:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.16781","created_at":"2026-07-21T01:20:58Z"},{"alias_kind":"pith_short_12","alias_value":"SR7UO26624L2","created_at":"2026-07-21T01:20:58Z"},{"alias_kind":"pith_short_16","alias_value":"SR7UO26624L2XT2Q","created_at":"2026-07-21T01:20:58Z"},{"alias_kind":"pith_short_8","alias_value":"SR7UO266","created_at":"2026-07-21T01:20:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:SR7UO26624L2XT2QY6VEFJTQ6Z","target":"record","payload":{"canonical_record":{"source":{"id":"2607.16781","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-07-18T11:32:04Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"fe6d933fe27930a6e1dadee50fc1f22a335bcaecad54dc60ca45fe9afc70ead2","abstract_canon_sha256":"2735f492619614567c0896d2ba411e731bf3ae7f9f1d70e43a5c86745e3212e7"},"schema_version":"1.0"},"canonical_sha256":"947f476bded717abcf50c7aa42a670f64f5830c4821ab5569ebc18903512b37c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-21T01:20:58.737964Z","signature_b64":"mcqD5maEWrsxCOIyIcEc4cynnfSNcy/MXlsfC1w/I8tuQM3OABHY8fX5nrSD7J2DlxaifTPrkF1vgkWqXDKECw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"947f476bded717abcf50c7aa42a670f64f5830c4821ab5569ebc18903512b37c","last_reissued_at":"2026-07-21T01:20:58.737143Z","signature_status":"signed_v1","first_computed_at":"2026-07-21T01:20:58.737143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.16781","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":"2026-07-21T01:20:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1wUu6iqjbfjEjjYew5oxogIvXzlVs7ny+bY78E4z7NiGqQIdLcIvQK9yQiwrn0BpdBsMTmm+OHnwS8tHZjtvCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T02:13:58.775073Z"},"content_sha256":"7635af40d24a28035da7998f83ccea6773c3d34fa124fad4067a947f0e5e913c","schema_version":"1.0","event_id":"sha256:7635af40d24a28035da7998f83ccea6773c3d34fa124fad4067a947f0e5e913c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:SR7UO26624L2XT2QY6VEFJTQ6Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analytic regularity for a fourth-order singularly perturbed boundary balue problem with two small parameters","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"C. Xenophontos, I. Sykopetritou","submitted_at":"2026-07-18T11:32:04Z","abstract_excerpt":"We consider a fourth order singularly perturbed boundary value problem with two small parameters, in one dimension, under the assumption of analytic input data. We show that the solution may be decomposed into a smooth part, two different width boundary layers, and a negligible remainder. We provide estimates for arbitrary order derivatives of each term of the decomposition, which are explicit in the differentiation order and the singular perturbation parameters, and are needed for proving the convergence of high order numerical methods, such as the $p/hp$ versions of the Finite Element Method"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16781","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.16781/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-21T01:20:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jJ7iWOnYk4ZqVkZIevGvKcLue6/C+WOISS5Wbi0WYPF0YyaDCSVpv7TXulN7Iv4JvFc7RNb5rP3nZ2nV+JgFDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T02:13:58.775713Z"},"content_sha256":"8bc6895493b4c1b6e8d4e7ad3853732593406d77625f67b044eeacf63e3200ae","schema_version":"1.0","event_id":"sha256:8bc6895493b4c1b6e8d4e7ad3853732593406d77625f67b044eeacf63e3200ae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SR7UO26624L2XT2QY6VEFJTQ6Z/bundle.json","state_url":"https://pith.science/pith/SR7UO26624L2XT2QY6VEFJTQ6Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SR7UO26624L2XT2QY6VEFJTQ6Z/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":"2026-08-15T02:13:58Z","links":{"resolver":"https://pith.science/pith/SR7UO26624L2XT2QY6VEFJTQ6Z","bundle":"https://pith.science/pith/SR7UO26624L2XT2QY6VEFJTQ6Z/bundle.json","state":"https://pith.science/pith/SR7UO26624L2XT2QY6VEFJTQ6Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SR7UO26624L2XT2QY6VEFJTQ6Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SR7UO26624L2XT2QY6VEFJTQ6Z","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":"2735f492619614567c0896d2ba411e731bf3ae7f9f1d70e43a5c86745e3212e7","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-07-18T11:32:04Z","title_canon_sha256":"fe6d933fe27930a6e1dadee50fc1f22a335bcaecad54dc60ca45fe9afc70ead2"},"schema_version":"1.0","source":{"id":"2607.16781","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.16781","created_at":"2026-07-21T01:20:58Z"},{"alias_kind":"arxiv_version","alias_value":"2607.16781v1","created_at":"2026-07-21T01:20:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.16781","created_at":"2026-07-21T01:20:58Z"},{"alias_kind":"pith_short_12","alias_value":"SR7UO26624L2","created_at":"2026-07-21T01:20:58Z"},{"alias_kind":"pith_short_16","alias_value":"SR7UO26624L2XT2Q","created_at":"2026-07-21T01:20:58Z"},{"alias_kind":"pith_short_8","alias_value":"SR7UO266","created_at":"2026-07-21T01:20:58Z"}],"graph_snapshots":[{"event_id":"sha256:8bc6895493b4c1b6e8d4e7ad3853732593406d77625f67b044eeacf63e3200ae","target":"graph","created_at":"2026-07-21T01:20:58Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.16781/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a fourth order singularly perturbed boundary value problem with two small parameters, in one dimension, under the assumption of analytic input data. We show that the solution may be decomposed into a smooth part, two different width boundary layers, and a negligible remainder. We provide estimates for arbitrary order derivatives of each term of the decomposition, which are explicit in the differentiation order and the singular perturbation parameters, and are needed for proving the convergence of high order numerical methods, such as the $p/hp$ versions of the Finite Element Method","authors_text":"C. Xenophontos, I. Sykopetritou","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-07-18T11:32:04Z","title":"Analytic regularity for a fourth-order singularly perturbed boundary balue problem with two small parameters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16781","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":"sha256:7635af40d24a28035da7998f83ccea6773c3d34fa124fad4067a947f0e5e913c","target":"record","created_at":"2026-07-21T01:20:58Z","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":"2735f492619614567c0896d2ba411e731bf3ae7f9f1d70e43a5c86745e3212e7","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-07-18T11:32:04Z","title_canon_sha256":"fe6d933fe27930a6e1dadee50fc1f22a335bcaecad54dc60ca45fe9afc70ead2"},"schema_version":"1.0","source":{"id":"2607.16781","kind":"arxiv","version":1}},"canonical_sha256":"947f476bded717abcf50c7aa42a670f64f5830c4821ab5569ebc18903512b37c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"947f476bded717abcf50c7aa42a670f64f5830c4821ab5569ebc18903512b37c","first_computed_at":"2026-07-21T01:20:58.737143Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-21T01:20:58.737143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mcqD5maEWrsxCOIyIcEc4cynnfSNcy/MXlsfC1w/I8tuQM3OABHY8fX5nrSD7J2DlxaifTPrkF1vgkWqXDKECw==","signature_status":"signed_v1","signed_at":"2026-07-21T01:20:58.737964Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.16781","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7635af40d24a28035da7998f83ccea6773c3d34fa124fad4067a947f0e5e913c","sha256:8bc6895493b4c1b6e8d4e7ad3853732593406d77625f67b044eeacf63e3200ae"],"state_sha256":"eafb1c059e213c184b592695661f0b1456a502a225ce12c0afc790211fdf2068"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dF1UJY3NGrSKpAiPKvW6pHWwM9mylRPYH5yZZbqHu50GrXDeoB8irEY58D1+zVCkF5j300G9kuVXhUMhU9CXCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T02:13:58.780932Z","bundle_sha256":"5b9a99cf53c212974c6d0f0d17b4f1494da3c6e3b0e31670e5866cf9ff9b780b"}}