{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:VBN5RLSPWRCJRM35GVI3CWCLIR","short_pith_number":"pith:VBN5RLSP","canonical_record":{"source":{"id":"0706.0433","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.NA","submitted_at":"2007-06-04T13:23:18Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"fa3e1eb91c0d4291349e91bc7f88893967e557f45f886d8b247b3e8242a1d4f6","abstract_canon_sha256":"be242c53747311452c5086fc49d7bc932fc25a8dd864294fdaafb93e6babd80f"},"schema_version":"1.0"},"canonical_sha256":"a85bd8ae4fb44498b37d3551b1584b4458c43c8ca891aad349e0369f76209b0a","source":{"kind":"arxiv","id":"0706.0433","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.0433","created_at":"2026-05-18T04:28:37Z"},{"alias_kind":"arxiv_version","alias_value":"0706.0433v2","created_at":"2026-05-18T04:28:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.0433","created_at":"2026-05-18T04:28:37Z"},{"alias_kind":"pith_short_12","alias_value":"VBN5RLSPWRCJ","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"VBN5RLSPWRCJRM35","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"VBN5RLSP","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:VBN5RLSPWRCJRM35GVI3CWCLIR","target":"record","payload":{"canonical_record":{"source":{"id":"0706.0433","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.NA","submitted_at":"2007-06-04T13:23:18Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"fa3e1eb91c0d4291349e91bc7f88893967e557f45f886d8b247b3e8242a1d4f6","abstract_canon_sha256":"be242c53747311452c5086fc49d7bc932fc25a8dd864294fdaafb93e6babd80f"},"schema_version":"1.0"},"canonical_sha256":"a85bd8ae4fb44498b37d3551b1584b4458c43c8ca891aad349e0369f76209b0a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:28:37.105863Z","signature_b64":"A65VQ3AGmrGD9pqbZfEd7s3MXd2IynAd34uYebZdrlYzCSApL2kmaOUSbGMPO6/zUYgOYzjfmLw8rSnKA0YzCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a85bd8ae4fb44498b37d3551b1584b4458c43c8ca891aad349e0369f76209b0a","last_reissued_at":"2026-05-18T04:28:37.105380Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:28:37.105380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0706.0433","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":"2026-05-18T04:28:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+x2ogAxInF9wOEXE87DSAEpddwCzJ9b44CbycfNNZwiUx24dxm4C0VzeP324X6lMIim+LeOP30hyOsYwz1ckCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T06:00:00.058916Z"},"content_sha256":"cb24c8b6584d3d3abeb80c0709ba521d1c984e588bd0d69480f0a6d6d8ecb03e","schema_version":"1.0","event_id":"sha256:cb24c8b6584d3d3abeb80c0709ba521d1c984e588bd0d69480f0a6d6d8ecb03e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:VBN5RLSPWRCJRM35GVI3CWCLIR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Numerical Clifford Analysis for Nonlinear Schrodinger Problem","license":"","headline":"","cross_cats":["math.CV"],"primary_cat":"math.NA","authors_text":"N. Faustino, N. Vieira, P. Cerejeiras","submitted_at":"2007-06-04T13:23:18Z","abstract_excerpt":"The aim of this work is to study the numerical solution of the nonlinear Schrodinger problem using a combination between Witt basis and finite difference approximations. We construct a discrete fundamental solution for the non-stationary Schrodinger operator and we show the convergence of the numerical scheme. Numerical examples are given at the end of the paper."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.0433","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":"2026-05-18T04:28:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DQfIn+dtrGhGc7223qJcalETfGfyg8qtnLIX4caEqUNFQtRXo1UYS12PJufU9LGjsC1vKpOlSLB+3jtczPdPBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T06:00:00.059290Z"},"content_sha256":"7f1b78f72b0d70189d966c7e5264cd8cb691a5ad248b4318846b7952dc9b5f17","schema_version":"1.0","event_id":"sha256:7f1b78f72b0d70189d966c7e5264cd8cb691a5ad248b4318846b7952dc9b5f17"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VBN5RLSPWRCJRM35GVI3CWCLIR/bundle.json","state_url":"https://pith.science/pith/VBN5RLSPWRCJRM35GVI3CWCLIR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VBN5RLSPWRCJRM35GVI3CWCLIR/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":"2026-06-02T06:00:00Z","links":{"resolver":"https://pith.science/pith/VBN5RLSPWRCJRM35GVI3CWCLIR","bundle":"https://pith.science/pith/VBN5RLSPWRCJRM35GVI3CWCLIR/bundle.json","state":"https://pith.science/pith/VBN5RLSPWRCJRM35GVI3CWCLIR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VBN5RLSPWRCJRM35GVI3CWCLIR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:VBN5RLSPWRCJRM35GVI3CWCLIR","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":"be242c53747311452c5086fc49d7bc932fc25a8dd864294fdaafb93e6babd80f","cross_cats_sorted":["math.CV"],"license":"","primary_cat":"math.NA","submitted_at":"2007-06-04T13:23:18Z","title_canon_sha256":"fa3e1eb91c0d4291349e91bc7f88893967e557f45f886d8b247b3e8242a1d4f6"},"schema_version":"1.0","source":{"id":"0706.0433","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.0433","created_at":"2026-05-18T04:28:37Z"},{"alias_kind":"arxiv_version","alias_value":"0706.0433v2","created_at":"2026-05-18T04:28:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.0433","created_at":"2026-05-18T04:28:37Z"},{"alias_kind":"pith_short_12","alias_value":"VBN5RLSPWRCJ","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"VBN5RLSPWRCJRM35","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"VBN5RLSP","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:7f1b78f72b0d70189d966c7e5264cd8cb691a5ad248b4318846b7952dc9b5f17","target":"graph","created_at":"2026-05-18T04:28:37Z","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":"The aim of this work is to study the numerical solution of the nonlinear Schrodinger problem using a combination between Witt basis and finite difference approximations. We construct a discrete fundamental solution for the non-stationary Schrodinger operator and we show the convergence of the numerical scheme. Numerical examples are given at the end of the paper.","authors_text":"N. Faustino, N. Vieira, P. Cerejeiras","cross_cats":["math.CV"],"headline":"","license":"","primary_cat":"math.NA","submitted_at":"2007-06-04T13:23:18Z","title":"Numerical Clifford Analysis for Nonlinear Schrodinger Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.0433","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:cb24c8b6584d3d3abeb80c0709ba521d1c984e588bd0d69480f0a6d6d8ecb03e","target":"record","created_at":"2026-05-18T04:28:37Z","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":"be242c53747311452c5086fc49d7bc932fc25a8dd864294fdaafb93e6babd80f","cross_cats_sorted":["math.CV"],"license":"","primary_cat":"math.NA","submitted_at":"2007-06-04T13:23:18Z","title_canon_sha256":"fa3e1eb91c0d4291349e91bc7f88893967e557f45f886d8b247b3e8242a1d4f6"},"schema_version":"1.0","source":{"id":"0706.0433","kind":"arxiv","version":2}},"canonical_sha256":"a85bd8ae4fb44498b37d3551b1584b4458c43c8ca891aad349e0369f76209b0a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a85bd8ae4fb44498b37d3551b1584b4458c43c8ca891aad349e0369f76209b0a","first_computed_at":"2026-05-18T04:28:37.105380Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:28:37.105380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A65VQ3AGmrGD9pqbZfEd7s3MXd2IynAd34uYebZdrlYzCSApL2kmaOUSbGMPO6/zUYgOYzjfmLw8rSnKA0YzCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:28:37.105863Z","signed_message":"canonical_sha256_bytes"},"source_id":"0706.0433","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb24c8b6584d3d3abeb80c0709ba521d1c984e588bd0d69480f0a6d6d8ecb03e","sha256:7f1b78f72b0d70189d966c7e5264cd8cb691a5ad248b4318846b7952dc9b5f17"],"state_sha256":"3acab230c88540018e2a67e6596b5ac296f017157edea2f3ade84bc839cf13a1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Opn/GDP6cNN2T3bgKZZznBs5NbvJNysfkNFl69qtvmHHZ13mv8pW+5N3tNFSdsez4NO6SypBIztFZb9AIYMaAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T06:00:00.062158Z","bundle_sha256":"8729a213281ec1bffd0527e719bea7d6a17ca85a94218fbafa515b6e9eaf6472"}}