{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:N3GJZ553TSAP6OQJBKUMIK7X2G","short_pith_number":"pith:N3GJZ553","canonical_record":{"source":{"id":"1904.12379","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-04-28T20:06:33Z","cross_cats_sorted":[],"title_canon_sha256":"10d8db88d417ec2c037eff94b469338f350e527881c40a4b4a1ad59ae146fbef","abstract_canon_sha256":"f7606844dbaa267f70aa8f6beb333a0dd702e4b504275e4843baa7aaf6725a70"},"schema_version":"1.0"},"canonical_sha256":"6ecc9cf7bb9c80ff3a090aa8c42bf7d1ad0f588c641353781fd71e11165ebd45","source":{"kind":"arxiv","id":"1904.12379","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.12379","created_at":"2026-05-17T23:46:52Z"},{"alias_kind":"arxiv_version","alias_value":"1904.12379v2","created_at":"2026-05-17T23:46:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.12379","created_at":"2026-05-17T23:46:52Z"},{"alias_kind":"pith_short_12","alias_value":"N3GJZ553TSAP","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"N3GJZ553TSAP6OQJ","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"N3GJZ553","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:N3GJZ553TSAP6OQJBKUMIK7X2G","target":"record","payload":{"canonical_record":{"source":{"id":"1904.12379","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-04-28T20:06:33Z","cross_cats_sorted":[],"title_canon_sha256":"10d8db88d417ec2c037eff94b469338f350e527881c40a4b4a1ad59ae146fbef","abstract_canon_sha256":"f7606844dbaa267f70aa8f6beb333a0dd702e4b504275e4843baa7aaf6725a70"},"schema_version":"1.0"},"canonical_sha256":"6ecc9cf7bb9c80ff3a090aa8c42bf7d1ad0f588c641353781fd71e11165ebd45","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:52.293619Z","signature_b64":"Tog6wOhl8CrSvnPuDjLdKlMAGSdDcw5SSuO7ONsUQpmMB4/CnhISQww3tBSWdDLDex6kmIp8bBejyEs+RcgJAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ecc9cf7bb9c80ff3a090aa8c42bf7d1ad0f588c641353781fd71e11165ebd45","last_reissued_at":"2026-05-17T23:46:52.292930Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:52.292930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.12379","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:46:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eDb5iIdEG6YFemcj2K1wmgwzQjaGIlnWhk2xM480GlJQu2jHW6SZhNYl56PdOTO+hmA+Kk8t/Fz1tF3Qr5aeCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T07:43:58.845182Z"},"content_sha256":"1ecfe2928d0fdb9b48db2594aad8e20918a525ecc1b9fe6911e920019be16c98","schema_version":"1.0","event_id":"sha256:1ecfe2928d0fdb9b48db2594aad8e20918a525ecc1b9fe6911e920019be16c98"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:N3GJZ553TSAP6OQJBKUMIK7X2G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the generalized method of lines and its proximal explicit and hyper-finite difference approaches","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Fabio Botelho","submitted_at":"2019-04-28T20:06:33Z","abstract_excerpt":"This article firstly develops a proximal explicit approach for the generalized method of lines. In such a method, the domain of the PDE in question is discretized in lines and the equation solution is written on these lines as functions of the boundary conditions and domain shape. The main objective of introducing a proximal formulation is to minimize the solution error as a typical parameter $\\varepsilon>0$ is too small. In a second step we present another procedure to minimize this same error, namely, the hyper-finite differences approach. In this last method the domain is divided in sub-dom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.12379","kind":"arxiv","version":2},"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":"2026-05-17T23:46:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aJlLmO/S3ILXppnW4J5SVrMjQ98TvJ5XJuRgSiMArf6u7L3HaNNzXQmbuCZY6hTgom6FatCokKf9Yes8aIljBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T07:43:58.846193Z"},"content_sha256":"794e7e34e8344069f11463aa1ba52a4b014e9ac9c177feab28a90880ce00b354","schema_version":"1.0","event_id":"sha256:794e7e34e8344069f11463aa1ba52a4b014e9ac9c177feab28a90880ce00b354"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N3GJZ553TSAP6OQJBKUMIK7X2G/bundle.json","state_url":"https://pith.science/pith/N3GJZ553TSAP6OQJBKUMIK7X2G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N3GJZ553TSAP6OQJBKUMIK7X2G/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":"2026-08-16T07:43:58Z","links":{"resolver":"https://pith.science/pith/N3GJZ553TSAP6OQJBKUMIK7X2G","bundle":"https://pith.science/pith/N3GJZ553TSAP6OQJBKUMIK7X2G/bundle.json","state":"https://pith.science/pith/N3GJZ553TSAP6OQJBKUMIK7X2G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N3GJZ553TSAP6OQJBKUMIK7X2G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:N3GJZ553TSAP6OQJBKUMIK7X2G","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":"f7606844dbaa267f70aa8f6beb333a0dd702e4b504275e4843baa7aaf6725a70","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-04-28T20:06:33Z","title_canon_sha256":"10d8db88d417ec2c037eff94b469338f350e527881c40a4b4a1ad59ae146fbef"},"schema_version":"1.0","source":{"id":"1904.12379","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.12379","created_at":"2026-05-17T23:46:52Z"},{"alias_kind":"arxiv_version","alias_value":"1904.12379v2","created_at":"2026-05-17T23:46:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.12379","created_at":"2026-05-17T23:46:52Z"},{"alias_kind":"pith_short_12","alias_value":"N3GJZ553TSAP","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"N3GJZ553TSAP6OQJ","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"N3GJZ553","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:794e7e34e8344069f11463aa1ba52a4b014e9ac9c177feab28a90880ce00b354","target":"graph","created_at":"2026-05-17T23:46:52Z","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":"This article firstly develops a proximal explicit approach for the generalized method of lines. In such a method, the domain of the PDE in question is discretized in lines and the equation solution is written on these lines as functions of the boundary conditions and domain shape. The main objective of introducing a proximal formulation is to minimize the solution error as a typical parameter $\\varepsilon>0$ is too small. In a second step we present another procedure to minimize this same error, namely, the hyper-finite differences approach. In this last method the domain is divided in sub-dom","authors_text":"Fabio Botelho","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-04-28T20:06:33Z","title":"On the generalized method of lines and its proximal explicit and hyper-finite difference approaches"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.12379","kind":"arxiv","version":2},"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":"sha256:1ecfe2928d0fdb9b48db2594aad8e20918a525ecc1b9fe6911e920019be16c98","target":"record","created_at":"2026-05-17T23:46:52Z","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":"f7606844dbaa267f70aa8f6beb333a0dd702e4b504275e4843baa7aaf6725a70","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-04-28T20:06:33Z","title_canon_sha256":"10d8db88d417ec2c037eff94b469338f350e527881c40a4b4a1ad59ae146fbef"},"schema_version":"1.0","source":{"id":"1904.12379","kind":"arxiv","version":2}},"canonical_sha256":"6ecc9cf7bb9c80ff3a090aa8c42bf7d1ad0f588c641353781fd71e11165ebd45","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ecc9cf7bb9c80ff3a090aa8c42bf7d1ad0f588c641353781fd71e11165ebd45","first_computed_at":"2026-05-17T23:46:52.292930Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:52.292930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Tog6wOhl8CrSvnPuDjLdKlMAGSdDcw5SSuO7ONsUQpmMB4/CnhISQww3tBSWdDLDex6kmIp8bBejyEs+RcgJAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:52.293619Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.12379","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ecfe2928d0fdb9b48db2594aad8e20918a525ecc1b9fe6911e920019be16c98","sha256:794e7e34e8344069f11463aa1ba52a4b014e9ac9c177feab28a90880ce00b354"],"state_sha256":"2290489bcac3b75c2a51400249e38b40cbbc1ee2eb54fa33efddadca0a4602ef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Wf342etCgNeoOuPmjb4ibg5s13DUB8GsE4KcywES61vh1xdSQCSKBl/+xVeaZn9cs6YNVVQ5XYcrKIh6iMSCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T07:43:58.852141Z","bundle_sha256":"fb70176e323146e89387c8a5bb5da6890e069556eb9eff03d21634173e16c7e5"}}