{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:3WEMEGHMW56TFA6D7QX4K7GHG6","short_pith_number":"pith:3WEMEGHM","canonical_record":{"source":{"id":"2006.08079","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-06-15T01:29:12Z","cross_cats_sorted":[],"title_canon_sha256":"0e49794654b791639c3d9e9b0c44788fbfa1a9004cdea56daab407bd78161cc1","abstract_canon_sha256":"6febc8f0265ae9053a8581f1594c27c968da5a844bac6560863ff3fef65ab2de"},"schema_version":"1.0"},"canonical_sha256":"dd88c218ecb77d3283c3fc2fc57cc7378dd95395f0c154f565f2cc9c7929c02b","source":{"kind":"arxiv","id":"2006.08079","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.08079","created_at":"2026-07-05T01:10:18Z"},{"alias_kind":"arxiv_version","alias_value":"2006.08079v1","created_at":"2026-07-05T01:10:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.08079","created_at":"2026-07-05T01:10:18Z"},{"alias_kind":"pith_short_12","alias_value":"3WEMEGHMW56T","created_at":"2026-07-05T01:10:18Z"},{"alias_kind":"pith_short_16","alias_value":"3WEMEGHMW56TFA6D","created_at":"2026-07-05T01:10:18Z"},{"alias_kind":"pith_short_8","alias_value":"3WEMEGHM","created_at":"2026-07-05T01:10:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:3WEMEGHMW56TFA6D7QX4K7GHG6","target":"record","payload":{"canonical_record":{"source":{"id":"2006.08079","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-06-15T01:29:12Z","cross_cats_sorted":[],"title_canon_sha256":"0e49794654b791639c3d9e9b0c44788fbfa1a9004cdea56daab407bd78161cc1","abstract_canon_sha256":"6febc8f0265ae9053a8581f1594c27c968da5a844bac6560863ff3fef65ab2de"},"schema_version":"1.0"},"canonical_sha256":"dd88c218ecb77d3283c3fc2fc57cc7378dd95395f0c154f565f2cc9c7929c02b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:10:18.024501Z","signature_b64":"V/3BkJjLQH+ZP9x63PQW+fifhSZFkcJlWpZ0qfixxERuLa9KOfhIFvvYMtlDKeg+BvHFTJu/bcHZmxdFJkcbAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd88c218ecb77d3283c3fc2fc57cc7378dd95395f0c154f565f2cc9c7929c02b","last_reissued_at":"2026-07-05T01:10:18.024063Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:10:18.024063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2006.08079","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":"2026-07-05T01:10:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"icAUP2F0qmdEDQl4pdIQu0u9ddhd7aCFIG+79CARtldywLs/S2IT6549y0S9Nc0WNx26zPrdGwV48akYqqvwDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T05:08:35.845197Z"},"content_sha256":"dd3e7dda4647ba8227c85cdf26cdbd5fb37223e4f893830aeca8c9945787daf9","schema_version":"1.0","event_id":"sha256:dd3e7dda4647ba8227c85cdf26cdbd5fb37223e4f893830aeca8c9945787daf9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:3WEMEGHMW56TFA6D7QX4K7GHG6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regularized finite difference methods for the logarithmic Klein-Gordon equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hong Zhang, Jingye Yan, Songhe Song, Xu Qian","submitted_at":"2020-06-15T01:29:12Z","abstract_excerpt":"We propose and analyze two regularized finite difference methods for the logarithmic Klein-Gordon equation (LogKGE). Due to the blowup phenomena caused by the logarithmic nonlinearity of the LogKGE, it is difficult to construct numerical schemes and establish their error bounds. In order to avoid singularity, we present a regularized logarithmic Klein-Gordon equation (RLogKGE) with a small regularized parameter $0<\\varepsilon\\ll1$. Besides, two finite difference methods are adopted to solve the regularized logarithmic Klein-Gordon equation (RLogKGE) and rigorous error bounds are estimated in t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.08079","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/2006.08079/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":"2026-07-05T01:10:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VE8STN4A9Sw/k+Nsh1fQXe8HXNjqS8DOR4tSHVM8iTcL+oG7kHb0HbfEzZZ9uOfu8o2zajPcKK09t0tsEulADQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T05:08:35.845719Z"},"content_sha256":"af5e1338b74e64071b24c43127c8bd1a72c4860ee9d7233c9797a7ed81f2cf9c","schema_version":"1.0","event_id":"sha256:af5e1338b74e64071b24c43127c8bd1a72c4860ee9d7233c9797a7ed81f2cf9c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3WEMEGHMW56TFA6D7QX4K7GHG6/bundle.json","state_url":"https://pith.science/pith/3WEMEGHMW56TFA6D7QX4K7GHG6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3WEMEGHMW56TFA6D7QX4K7GHG6/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":"2026-08-15T05:08:35Z","links":{"resolver":"https://pith.science/pith/3WEMEGHMW56TFA6D7QX4K7GHG6","bundle":"https://pith.science/pith/3WEMEGHMW56TFA6D7QX4K7GHG6/bundle.json","state":"https://pith.science/pith/3WEMEGHMW56TFA6D7QX4K7GHG6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3WEMEGHMW56TFA6D7QX4K7GHG6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:3WEMEGHMW56TFA6D7QX4K7GHG6","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":"6febc8f0265ae9053a8581f1594c27c968da5a844bac6560863ff3fef65ab2de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-06-15T01:29:12Z","title_canon_sha256":"0e49794654b791639c3d9e9b0c44788fbfa1a9004cdea56daab407bd78161cc1"},"schema_version":"1.0","source":{"id":"2006.08079","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.08079","created_at":"2026-07-05T01:10:18Z"},{"alias_kind":"arxiv_version","alias_value":"2006.08079v1","created_at":"2026-07-05T01:10:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.08079","created_at":"2026-07-05T01:10:18Z"},{"alias_kind":"pith_short_12","alias_value":"3WEMEGHMW56T","created_at":"2026-07-05T01:10:18Z"},{"alias_kind":"pith_short_16","alias_value":"3WEMEGHMW56TFA6D","created_at":"2026-07-05T01:10:18Z"},{"alias_kind":"pith_short_8","alias_value":"3WEMEGHM","created_at":"2026-07-05T01:10:18Z"}],"graph_snapshots":[{"event_id":"sha256:af5e1338b74e64071b24c43127c8bd1a72c4860ee9d7233c9797a7ed81f2cf9c","target":"graph","created_at":"2026-07-05T01:10:18Z","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/2006.08079/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose and analyze two regularized finite difference methods for the logarithmic Klein-Gordon equation (LogKGE). Due to the blowup phenomena caused by the logarithmic nonlinearity of the LogKGE, it is difficult to construct numerical schemes and establish their error bounds. In order to avoid singularity, we present a regularized logarithmic Klein-Gordon equation (RLogKGE) with a small regularized parameter $0<\\varepsilon\\ll1$. Besides, two finite difference methods are adopted to solve the regularized logarithmic Klein-Gordon equation (RLogKGE) and rigorous error bounds are estimated in t","authors_text":"Hong Zhang, Jingye Yan, Songhe Song, Xu Qian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-06-15T01:29:12Z","title":"Regularized finite difference methods for the logarithmic Klein-Gordon equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.08079","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:dd3e7dda4647ba8227c85cdf26cdbd5fb37223e4f893830aeca8c9945787daf9","target":"record","created_at":"2026-07-05T01:10:18Z","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":"6febc8f0265ae9053a8581f1594c27c968da5a844bac6560863ff3fef65ab2de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-06-15T01:29:12Z","title_canon_sha256":"0e49794654b791639c3d9e9b0c44788fbfa1a9004cdea56daab407bd78161cc1"},"schema_version":"1.0","source":{"id":"2006.08079","kind":"arxiv","version":1}},"canonical_sha256":"dd88c218ecb77d3283c3fc2fc57cc7378dd95395f0c154f565f2cc9c7929c02b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd88c218ecb77d3283c3fc2fc57cc7378dd95395f0c154f565f2cc9c7929c02b","first_computed_at":"2026-07-05T01:10:18.024063Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:10:18.024063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V/3BkJjLQH+ZP9x63PQW+fifhSZFkcJlWpZ0qfixxERuLa9KOfhIFvvYMtlDKeg+BvHFTJu/bcHZmxdFJkcbAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:10:18.024501Z","signed_message":"canonical_sha256_bytes"},"source_id":"2006.08079","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd3e7dda4647ba8227c85cdf26cdbd5fb37223e4f893830aeca8c9945787daf9","sha256:af5e1338b74e64071b24c43127c8bd1a72c4860ee9d7233c9797a7ed81f2cf9c"],"state_sha256":"e9d42b952a1c7febb6f61a197548536dfad944460cfbe827cbcaabd4300b1ed5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S+f2U+rMd5cIwk6/l+hz6cjMCaPKFW1tmccsI3RDZF7YI2SoK8PEf+gs+m8HL2f3DsnFKlBh61KF7KrPG7zTAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T05:08:35.851394Z","bundle_sha256":"fe979411667c49507bea7eda9f68b0101b07da46b14bd4ef84b2ac16e4b62598"}}