{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:AF3JI4JWJVBV5RX3AMKIUDXETR","short_pith_number":"pith:AF3JI4JW","canonical_record":{"source":{"id":"2306.15901","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-06-28T03:48:20Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"da4307a5f5f9c4feec83c5aa3be0f815ebab993de14b010979825ca6e6c53536","abstract_canon_sha256":"c5528c098d36a5eb0a8c3f6633ffecab994990cc3b50327497c2f87c4dc1833f"},"schema_version":"1.0"},"canonical_sha256":"01769471364d435ec6fb03148a0ee49c45eb9a5708499fb88b760b841f921fbd","source":{"kind":"arxiv","id":"2306.15901","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.15901","created_at":"2026-07-05T06:25:46Z"},{"alias_kind":"arxiv_version","alias_value":"2306.15901v1","created_at":"2026-07-05T06:25:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.15901","created_at":"2026-07-05T06:25:46Z"},{"alias_kind":"pith_short_12","alias_value":"AF3JI4JWJVBV","created_at":"2026-07-05T06:25:46Z"},{"alias_kind":"pith_short_16","alias_value":"AF3JI4JWJVBV5RX3","created_at":"2026-07-05T06:25:46Z"},{"alias_kind":"pith_short_8","alias_value":"AF3JI4JW","created_at":"2026-07-05T06:25:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:AF3JI4JWJVBV5RX3AMKIUDXETR","target":"record","payload":{"canonical_record":{"source":{"id":"2306.15901","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-06-28T03:48:20Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"da4307a5f5f9c4feec83c5aa3be0f815ebab993de14b010979825ca6e6c53536","abstract_canon_sha256":"c5528c098d36a5eb0a8c3f6633ffecab994990cc3b50327497c2f87c4dc1833f"},"schema_version":"1.0"},"canonical_sha256":"01769471364d435ec6fb03148a0ee49c45eb9a5708499fb88b760b841f921fbd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:25:46.089736Z","signature_b64":"C/eKKs16PoSxyxvfrn6QjKWK6Cyrhx16c4bSxZSvd+k9onJrn90fzZKXtjkDsRUIXeImUtI4kje3GcfKMkS9Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01769471364d435ec6fb03148a0ee49c45eb9a5708499fb88b760b841f921fbd","last_reissued_at":"2026-07-05T06:25:46.089265Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:25:46.089265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2306.15901","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":"2026-07-05T06:25:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RNuLonGe4xoXHQUA/0LBdXmbawT/9N3IUnzv2Zg2O9Scu8RjB9FS+p6iy17CfdYURu2b5QYqyhlQZyz37iDvBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-16T00:38:46.613584Z"},"content_sha256":"3dc4d6d96a9b01c0f3e56307a01cbf619e00c6b010915a0c3fd75f4bc9b56fda","schema_version":"1.0","event_id":"sha256:3dc4d6d96a9b01c0f3e56307a01cbf619e00c6b010915a0c3fd75f4bc9b56fda"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:AF3JI4JWJVBV5RX3AMKIUDXETR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Error analysis of a first-order IMEX scheme for the logarithmic Schr\\\"odinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Jingye Yan, Lilian Wang, XiaoLong Zhang","submitted_at":"2023-06-28T03:48:20Z","abstract_excerpt":"The logarithmic Schr\\\"odinger equation (LogSE) has a logarithmic nonlinearity $f(u)=u\\ln |u|^2$ that is not differentiable at $u=0.$ Compared with its counterpart with a regular nonlinear term, it possesses richer and unusual dynamics, though the low regularity of the nonlinearity brings about significant challenges in both analysis and computation. Among very limited numerical studies, the semi-implicit regularized method via regularising $f(u)$ as $ u^{\\varepsilon}\\ln ({\\varepsilon}+ |u^{\\varepsilon}|)^2$ to overcome the blowup of $\\ln |u|^2$ at $u=0$ has been investigated recently in litera"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.15901","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/2306.15901/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":"2026-07-05T06:25:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/aBCwxagmMKWWLwZOTwuvLb6ev0g4jz49ISK6ZtJIWEuxULUFrkJ1H0S6i6c4DfsdOhPIfBlJVBmsSLDx8/YAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-16T00:38:46.613965Z"},"content_sha256":"ee25328a31e29fca7d5ecc41e2097726358ab033046b95513be6c2d7dfcd5b6e","schema_version":"1.0","event_id":"sha256:ee25328a31e29fca7d5ecc41e2097726358ab033046b95513be6c2d7dfcd5b6e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AF3JI4JWJVBV5RX3AMKIUDXETR/bundle.json","state_url":"https://pith.science/pith/AF3JI4JWJVBV5RX3AMKIUDXETR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AF3JI4JWJVBV5RX3AMKIUDXETR/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":"2026-07-16T00:38:46Z","links":{"resolver":"https://pith.science/pith/AF3JI4JWJVBV5RX3AMKIUDXETR","bundle":"https://pith.science/pith/AF3JI4JWJVBV5RX3AMKIUDXETR/bundle.json","state":"https://pith.science/pith/AF3JI4JWJVBV5RX3AMKIUDXETR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AF3JI4JWJVBV5RX3AMKIUDXETR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:AF3JI4JWJVBV5RX3AMKIUDXETR","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":"c5528c098d36a5eb0a8c3f6633ffecab994990cc3b50327497c2f87c4dc1833f","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-06-28T03:48:20Z","title_canon_sha256":"da4307a5f5f9c4feec83c5aa3be0f815ebab993de14b010979825ca6e6c53536"},"schema_version":"1.0","source":{"id":"2306.15901","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.15901","created_at":"2026-07-05T06:25:46Z"},{"alias_kind":"arxiv_version","alias_value":"2306.15901v1","created_at":"2026-07-05T06:25:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.15901","created_at":"2026-07-05T06:25:46Z"},{"alias_kind":"pith_short_12","alias_value":"AF3JI4JWJVBV","created_at":"2026-07-05T06:25:46Z"},{"alias_kind":"pith_short_16","alias_value":"AF3JI4JWJVBV5RX3","created_at":"2026-07-05T06:25:46Z"},{"alias_kind":"pith_short_8","alias_value":"AF3JI4JW","created_at":"2026-07-05T06:25:46Z"}],"graph_snapshots":[{"event_id":"sha256:ee25328a31e29fca7d5ecc41e2097726358ab033046b95513be6c2d7dfcd5b6e","target":"graph","created_at":"2026-07-05T06:25:46Z","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/2306.15901/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The logarithmic Schr\\\"odinger equation (LogSE) has a logarithmic nonlinearity $f(u)=u\\ln |u|^2$ that is not differentiable at $u=0.$ Compared with its counterpart with a regular nonlinear term, it possesses richer and unusual dynamics, though the low regularity of the nonlinearity brings about significant challenges in both analysis and computation. Among very limited numerical studies, the semi-implicit regularized method via regularising $f(u)$ as $ u^{\\varepsilon}\\ln ({\\varepsilon}+ |u^{\\varepsilon}|)^2$ to overcome the blowup of $\\ln |u|^2$ at $u=0$ has been investigated recently in litera","authors_text":"Jingye Yan, Lilian Wang, XiaoLong Zhang","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-06-28T03:48:20Z","title":"Error analysis of a first-order IMEX scheme for the logarithmic Schr\\\"odinger equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.15901","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":"sha256:3dc4d6d96a9b01c0f3e56307a01cbf619e00c6b010915a0c3fd75f4bc9b56fda","target":"record","created_at":"2026-07-05T06:25:46Z","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":"c5528c098d36a5eb0a8c3f6633ffecab994990cc3b50327497c2f87c4dc1833f","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-06-28T03:48:20Z","title_canon_sha256":"da4307a5f5f9c4feec83c5aa3be0f815ebab993de14b010979825ca6e6c53536"},"schema_version":"1.0","source":{"id":"2306.15901","kind":"arxiv","version":1}},"canonical_sha256":"01769471364d435ec6fb03148a0ee49c45eb9a5708499fb88b760b841f921fbd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01769471364d435ec6fb03148a0ee49c45eb9a5708499fb88b760b841f921fbd","first_computed_at":"2026-07-05T06:25:46.089265Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:25:46.089265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C/eKKs16PoSxyxvfrn6QjKWK6Cyrhx16c4bSxZSvd+k9onJrn90fzZKXtjkDsRUIXeImUtI4kje3GcfKMkS9Cg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:25:46.089736Z","signed_message":"canonical_sha256_bytes"},"source_id":"2306.15901","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3dc4d6d96a9b01c0f3e56307a01cbf619e00c6b010915a0c3fd75f4bc9b56fda","sha256:ee25328a31e29fca7d5ecc41e2097726358ab033046b95513be6c2d7dfcd5b6e"],"state_sha256":"3105ee8eba55beec7660c3a4edc308b708aabaf4cb5cf5d6eac2bd95936fcb0d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5BpmQBJ4K6DdvN84Vtsd+S8et9LSeztCJVK3PgJkJ3tC3Vh7V/lJ1h3mmN6U/bKVwBbSlGOhjq/IzEOCJfaXDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-16T00:38:46.616557Z","bundle_sha256":"e15253273ec9b2d07c3646d7fb9cbce674f2a13a299a558acd90f8ae83136678"}}