{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:HAAW4LJFLR5KCPSQ237VSIDVN6","short_pith_number":"pith:HAAW4LJF","canonical_record":{"source":{"id":"1706.03871","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-06-12T23:50:26Z","cross_cats_sorted":[],"title_canon_sha256":"9f536b383eb8af7d4c943b3f13d1de48fea935fb3e0a75e57b4e1c0844998de6","abstract_canon_sha256":"23c5d7eae44f94d18085bbc8ac48fb62edd6c6955075e8a128f4e364c48c9b38"},"schema_version":"1.0"},"canonical_sha256":"38016e2d255c7aa13e50d6ff5920756fbd6acff9852dedb81a9dadb1c617721f","source":{"kind":"arxiv","id":"1706.03871","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.03871","created_at":"2026-05-18T00:42:28Z"},{"alias_kind":"arxiv_version","alias_value":"1706.03871v1","created_at":"2026-05-18T00:42:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.03871","created_at":"2026-05-18T00:42:28Z"},{"alias_kind":"pith_short_12","alias_value":"HAAW4LJFLR5K","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HAAW4LJFLR5KCPSQ","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HAAW4LJF","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:HAAW4LJFLR5KCPSQ237VSIDVN6","target":"record","payload":{"canonical_record":{"source":{"id":"1706.03871","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-06-12T23:50:26Z","cross_cats_sorted":[],"title_canon_sha256":"9f536b383eb8af7d4c943b3f13d1de48fea935fb3e0a75e57b4e1c0844998de6","abstract_canon_sha256":"23c5d7eae44f94d18085bbc8ac48fb62edd6c6955075e8a128f4e364c48c9b38"},"schema_version":"1.0"},"canonical_sha256":"38016e2d255c7aa13e50d6ff5920756fbd6acff9852dedb81a9dadb1c617721f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:28.155524Z","signature_b64":"MlkmfcP/Mj/1H1bBTGSRuWiDNnQmWxfhF8K+EJiMCGE+hpMKFMNG9s8pO2Nqy1jz8h95JQzV7dluPdT4lV2QAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38016e2d255c7aa13e50d6ff5920756fbd6acff9852dedb81a9dadb1c617721f","last_reissued_at":"2026-05-18T00:42:28.154813Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:28.154813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.03871","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":"2026-05-18T00:42:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cDAN75GQFeRGcYb5jUDC7JoAsAiBKGK4pKlPeRAOlC70nN5qk9qcAs9+JW4Sc/NaBv7eYb22hjs9zVTSTOHGCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:08:15.516403Z"},"content_sha256":"a4f80c209b9c1bb3cafb26462afa9c4dd5da7cb817ebec4886b401f54f6f3fdc","schema_version":"1.0","event_id":"sha256:a4f80c209b9c1bb3cafb26462afa9c4dd5da7cb817ebec4886b401f54f6f3fdc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:HAAW4LJFLR5KCPSQ237VSIDVN6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A linear implicit finite difference discretization of the Schrodinger-Hirota Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Georgios E. Zouraris","submitted_at":"2017-06-12T23:50:26Z","abstract_excerpt":"A linear implicit finite difference method is proposed for the approximation of the solution to a periodic, initial value problem for a Schrodinger-Hirota equation. Optimal, second order convergence in the discrete $H^1-$norm is proved, assuming that $\\tau$, $h$ and $\\tau^4/h$ are sufficiently small, where $\\tau$ is the time-step and $h$ is the space mesh-size. The efficiency of the proposed method is verified by results from numerical experiments."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.03871","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":"2026-05-18T00:42:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/kfTnxVofvHlWOAoyF79gH03GFNRIxKq6ru6OhOdEmI0Nefea9248yjtWNSWYSEahUKS7Wp1WRVBfU9xAa1MDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:08:15.517091Z"},"content_sha256":"5cd91182d955bff064748dd913b9c1b5861321bdd4550b15642b42c2c9e0b144","schema_version":"1.0","event_id":"sha256:5cd91182d955bff064748dd913b9c1b5861321bdd4550b15642b42c2c9e0b144"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HAAW4LJFLR5KCPSQ237VSIDVN6/bundle.json","state_url":"https://pith.science/pith/HAAW4LJFLR5KCPSQ237VSIDVN6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HAAW4LJFLR5KCPSQ237VSIDVN6/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":"2026-05-28T22:08:15Z","links":{"resolver":"https://pith.science/pith/HAAW4LJFLR5KCPSQ237VSIDVN6","bundle":"https://pith.science/pith/HAAW4LJFLR5KCPSQ237VSIDVN6/bundle.json","state":"https://pith.science/pith/HAAW4LJFLR5KCPSQ237VSIDVN6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HAAW4LJFLR5KCPSQ237VSIDVN6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:HAAW4LJFLR5KCPSQ237VSIDVN6","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":"23c5d7eae44f94d18085bbc8ac48fb62edd6c6955075e8a128f4e364c48c9b38","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-06-12T23:50:26Z","title_canon_sha256":"9f536b383eb8af7d4c943b3f13d1de48fea935fb3e0a75e57b4e1c0844998de6"},"schema_version":"1.0","source":{"id":"1706.03871","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.03871","created_at":"2026-05-18T00:42:28Z"},{"alias_kind":"arxiv_version","alias_value":"1706.03871v1","created_at":"2026-05-18T00:42:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.03871","created_at":"2026-05-18T00:42:28Z"},{"alias_kind":"pith_short_12","alias_value":"HAAW4LJFLR5K","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HAAW4LJFLR5KCPSQ","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HAAW4LJF","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:5cd91182d955bff064748dd913b9c1b5861321bdd4550b15642b42c2c9e0b144","target":"graph","created_at":"2026-05-18T00:42:28Z","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 linear implicit finite difference method is proposed for the approximation of the solution to a periodic, initial value problem for a Schrodinger-Hirota equation. Optimal, second order convergence in the discrete $H^1-$norm is proved, assuming that $\\tau$, $h$ and $\\tau^4/h$ are sufficiently small, where $\\tau$ is the time-step and $h$ is the space mesh-size. The efficiency of the proposed method is verified by results from numerical experiments.","authors_text":"Georgios E. Zouraris","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-06-12T23:50:26Z","title":"A linear implicit finite difference discretization of the Schrodinger-Hirota Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.03871","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:a4f80c209b9c1bb3cafb26462afa9c4dd5da7cb817ebec4886b401f54f6f3fdc","target":"record","created_at":"2026-05-18T00:42:28Z","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":"23c5d7eae44f94d18085bbc8ac48fb62edd6c6955075e8a128f4e364c48c9b38","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-06-12T23:50:26Z","title_canon_sha256":"9f536b383eb8af7d4c943b3f13d1de48fea935fb3e0a75e57b4e1c0844998de6"},"schema_version":"1.0","source":{"id":"1706.03871","kind":"arxiv","version":1}},"canonical_sha256":"38016e2d255c7aa13e50d6ff5920756fbd6acff9852dedb81a9dadb1c617721f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"38016e2d255c7aa13e50d6ff5920756fbd6acff9852dedb81a9dadb1c617721f","first_computed_at":"2026-05-18T00:42:28.154813Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:28.154813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MlkmfcP/Mj/1H1bBTGSRuWiDNnQmWxfhF8K+EJiMCGE+hpMKFMNG9s8pO2Nqy1jz8h95JQzV7dluPdT4lV2QAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:28.155524Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.03871","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4f80c209b9c1bb3cafb26462afa9c4dd5da7cb817ebec4886b401f54f6f3fdc","sha256:5cd91182d955bff064748dd913b9c1b5861321bdd4550b15642b42c2c9e0b144"],"state_sha256":"1a00208dd42b43332379c2f904d82ff33939de0af4467920c3abfd957abeefcd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"midFuGGsNkVTlQQKZ05LkEUKU0eq/PCYtbOhNVawSaueU+zIuMfUZq1xCAlvjiYku6zryUJ2nVA2f1B4byfgBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T22:08:15.521683Z","bundle_sha256":"5e25c44a2a4264abafb28709fcee16744ae5234462863d3205b4e65b631f7a2d"}}