{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:5REOHHSX2YFKRWSC7IVMQQA3I5","short_pith_number":"pith:5REOHHSX","canonical_record":{"source":{"id":"2410.18407","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-10-24T03:47:25Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"25c77e4d82bd57af320739ea2f8f04eac997b09a768d89c296cb59ff8dce8cfc","abstract_canon_sha256":"8dc154537d8749c8a9da7d59f2b93d87803798bd6b6f97f97d74e75b3d18adc5"},"schema_version":"1.0"},"canonical_sha256":"ec48e39e57d60aa8da42fa2ac8401b474bda0482c0f6cb6f8bf6a144fb156ef5","source":{"kind":"arxiv","id":"2410.18407","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.18407","created_at":"2026-07-05T09:38:31Z"},{"alias_kind":"arxiv_version","alias_value":"2410.18407v2","created_at":"2026-07-05T09:38:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.18407","created_at":"2026-07-05T09:38:31Z"},{"alias_kind":"pith_short_12","alias_value":"5REOHHSX2YFK","created_at":"2026-07-05T09:38:31Z"},{"alias_kind":"pith_short_16","alias_value":"5REOHHSX2YFKRWSC","created_at":"2026-07-05T09:38:31Z"},{"alias_kind":"pith_short_8","alias_value":"5REOHHSX","created_at":"2026-07-05T09:38:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:5REOHHSX2YFKRWSC7IVMQQA3I5","target":"record","payload":{"canonical_record":{"source":{"id":"2410.18407","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-10-24T03:47:25Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"25c77e4d82bd57af320739ea2f8f04eac997b09a768d89c296cb59ff8dce8cfc","abstract_canon_sha256":"8dc154537d8749c8a9da7d59f2b93d87803798bd6b6f97f97d74e75b3d18adc5"},"schema_version":"1.0"},"canonical_sha256":"ec48e39e57d60aa8da42fa2ac8401b474bda0482c0f6cb6f8bf6a144fb156ef5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:38:31.388514Z","signature_b64":"QDDrtQkHINvhQ9LZkNWUHdcoS1pTnmQtJ0vsevDDn9+UPg1Oo71VfmU+MIu6NCcxNegFTpaLOx32A7w41U1ZCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec48e39e57d60aa8da42fa2ac8401b474bda0482c0f6cb6f8bf6a144fb156ef5","last_reissued_at":"2026-07-05T09:38:31.388030Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:38:31.388030Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.18407","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":"2026-07-05T09:38:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YL1TrluL40+HJLyXOPGtS9jaGlyyWRL3FpQJgvHX2KGWkQ3ze3NK1SFSNpNESl77TkYs5mRbxZfEQVilvWxaAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T09:18:58.820066Z"},"content_sha256":"cf3c84d0f1b03d31d2ea2d86d69577beead9943bf9395cc1a93cd4f0037aa5c5","schema_version":"1.0","event_id":"sha256:cf3c84d0f1b03d31d2ea2d86d69577beead9943bf9395cc1a93cd4f0037aa5c5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:5REOHHSX2YFKRWSC7IVMQQA3I5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On topological solutions to a generalized Chern-Simons equation on lattice graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Songbo Hou, Xiaoqing Kong","submitted_at":"2024-10-24T03:47:25Z","abstract_excerpt":"For $n \\geq 2$, consider $\\mathbb{Z}^n$ as a lattice graph. We explore a generalized Chern-Simons equation on $\\mathbb{Z}^n$. Employing the method of exhaustion, we prove that there exists a global solution that also qualifies as a topological solution. Our results extend those of Hua et al. [arXiv:2310.13905] and complement the findings of Chao and Hou [J. Math. Anal. Appl. $\\bf{519}$(1), 126787(2023)], as well as those of Hou and Qiao [J. Math. Phys. $\\bf{65}$(8), 081503(2024)]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.18407","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.18407/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":"2026-07-05T09:38:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N4760RIQd6DleIFDaoDfDpqNFr1GeQMeFKbBRd/B6jqpd99lMSYqK0h+9jS9glm9Nk6x+ZJWUSGaMP8j5RvNBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T09:18:58.820587Z"},"content_sha256":"c7eaffc6060388d809ec0a5f85ae4da54a894b855e14e83ba1a20a9581bdf7d0","schema_version":"1.0","event_id":"sha256:c7eaffc6060388d809ec0a5f85ae4da54a894b855e14e83ba1a20a9581bdf7d0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5REOHHSX2YFKRWSC7IVMQQA3I5/bundle.json","state_url":"https://pith.science/pith/5REOHHSX2YFKRWSC7IVMQQA3I5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5REOHHSX2YFKRWSC7IVMQQA3I5/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":"2026-08-09T09:18:58Z","links":{"resolver":"https://pith.science/pith/5REOHHSX2YFKRWSC7IVMQQA3I5","bundle":"https://pith.science/pith/5REOHHSX2YFKRWSC7IVMQQA3I5/bundle.json","state":"https://pith.science/pith/5REOHHSX2YFKRWSC7IVMQQA3I5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5REOHHSX2YFKRWSC7IVMQQA3I5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:5REOHHSX2YFKRWSC7IVMQQA3I5","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":"8dc154537d8749c8a9da7d59f2b93d87803798bd6b6f97f97d74e75b3d18adc5","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-10-24T03:47:25Z","title_canon_sha256":"25c77e4d82bd57af320739ea2f8f04eac997b09a768d89c296cb59ff8dce8cfc"},"schema_version":"1.0","source":{"id":"2410.18407","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.18407","created_at":"2026-07-05T09:38:31Z"},{"alias_kind":"arxiv_version","alias_value":"2410.18407v2","created_at":"2026-07-05T09:38:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.18407","created_at":"2026-07-05T09:38:31Z"},{"alias_kind":"pith_short_12","alias_value":"5REOHHSX2YFK","created_at":"2026-07-05T09:38:31Z"},{"alias_kind":"pith_short_16","alias_value":"5REOHHSX2YFKRWSC","created_at":"2026-07-05T09:38:31Z"},{"alias_kind":"pith_short_8","alias_value":"5REOHHSX","created_at":"2026-07-05T09:38:31Z"}],"graph_snapshots":[{"event_id":"sha256:c7eaffc6060388d809ec0a5f85ae4da54a894b855e14e83ba1a20a9581bdf7d0","target":"graph","created_at":"2026-07-05T09:38:31Z","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/2410.18407/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For $n \\geq 2$, consider $\\mathbb{Z}^n$ as a lattice graph. We explore a generalized Chern-Simons equation on $\\mathbb{Z}^n$. Employing the method of exhaustion, we prove that there exists a global solution that also qualifies as a topological solution. Our results extend those of Hua et al. [arXiv:2310.13905] and complement the findings of Chao and Hou [J. Math. Anal. Appl. $\\bf{519}$(1), 126787(2023)], as well as those of Hou and Qiao [J. Math. Phys. $\\bf{65}$(8), 081503(2024)].","authors_text":"Songbo Hou, Xiaoqing Kong","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-10-24T03:47:25Z","title":"On topological solutions to a generalized Chern-Simons equation on lattice graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.18407","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:cf3c84d0f1b03d31d2ea2d86d69577beead9943bf9395cc1a93cd4f0037aa5c5","target":"record","created_at":"2026-07-05T09:38:31Z","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":"8dc154537d8749c8a9da7d59f2b93d87803798bd6b6f97f97d74e75b3d18adc5","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-10-24T03:47:25Z","title_canon_sha256":"25c77e4d82bd57af320739ea2f8f04eac997b09a768d89c296cb59ff8dce8cfc"},"schema_version":"1.0","source":{"id":"2410.18407","kind":"arxiv","version":2}},"canonical_sha256":"ec48e39e57d60aa8da42fa2ac8401b474bda0482c0f6cb6f8bf6a144fb156ef5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec48e39e57d60aa8da42fa2ac8401b474bda0482c0f6cb6f8bf6a144fb156ef5","first_computed_at":"2026-07-05T09:38:31.388030Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:38:31.388030Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QDDrtQkHINvhQ9LZkNWUHdcoS1pTnmQtJ0vsevDDn9+UPg1Oo71VfmU+MIu6NCcxNegFTpaLOx32A7w41U1ZCA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:38:31.388514Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.18407","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf3c84d0f1b03d31d2ea2d86d69577beead9943bf9395cc1a93cd4f0037aa5c5","sha256:c7eaffc6060388d809ec0a5f85ae4da54a894b855e14e83ba1a20a9581bdf7d0"],"state_sha256":"f2c23d9b74a9e9f3326bddf2301a0786c3f6495c0df717c0ff1f267487f8391f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p6p+98KqMR3DE0X+j9GKneV3hLcZPfKFeQGLNeJejFdJhV3qRNe49P23ExrQEJfpSTgX70pyLT4y17nVmYtQBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T09:18:58.824546Z","bundle_sha256":"773cfa734619744ca256693f27cae3d997887bd57f2f9671db85647b0d09f321"}}