{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:FIQEJ7DUCPX7YXVAE3GNKJRUWM","short_pith_number":"pith:FIQEJ7DU","canonical_record":{"source":{"id":"2311.16574","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-11-28T07:32:02Z","cross_cats_sorted":["math-ph","math.FA","math.MP"],"title_canon_sha256":"a130b65cd99753c91509fd2b6b30f16d7895ea1104e1e35794c6bfda71ef90f1","abstract_canon_sha256":"a68ec1eeadf423e1d6f049eb4a859b16f4f4b5611b62b26bf43b7bf73b5bc06a"},"schema_version":"1.0"},"canonical_sha256":"2a2044fc7413effc5ea026ccd52634b328f14d63574275023132f375450bc109","source":{"kind":"arxiv","id":"2311.16574","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.16574","created_at":"2026-07-05T07:17:43Z"},{"alias_kind":"arxiv_version","alias_value":"2311.16574v1","created_at":"2026-07-05T07:17:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.16574","created_at":"2026-07-05T07:17:43Z"},{"alias_kind":"pith_short_12","alias_value":"FIQEJ7DUCPX7","created_at":"2026-07-05T07:17:43Z"},{"alias_kind":"pith_short_16","alias_value":"FIQEJ7DUCPX7YXVA","created_at":"2026-07-05T07:17:43Z"},{"alias_kind":"pith_short_8","alias_value":"FIQEJ7DU","created_at":"2026-07-05T07:17:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:FIQEJ7DUCPX7YXVAE3GNKJRUWM","target":"record","payload":{"canonical_record":{"source":{"id":"2311.16574","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-11-28T07:32:02Z","cross_cats_sorted":["math-ph","math.FA","math.MP"],"title_canon_sha256":"a130b65cd99753c91509fd2b6b30f16d7895ea1104e1e35794c6bfda71ef90f1","abstract_canon_sha256":"a68ec1eeadf423e1d6f049eb4a859b16f4f4b5611b62b26bf43b7bf73b5bc06a"},"schema_version":"1.0"},"canonical_sha256":"2a2044fc7413effc5ea026ccd52634b328f14d63574275023132f375450bc109","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:17:43.460067Z","signature_b64":"f8nTso6qpARiSXUcerS89ZPax4QbXaf5//0KLzXk72qnHHIsNgttFczgUvbJCOsiqpOIdt98C+rFJm6ZGvjZDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a2044fc7413effc5ea026ccd52634b328f14d63574275023132f375450bc109","last_reissued_at":"2026-07-05T07:17:43.459577Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:17:43.459577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2311.16574","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":"2026-07-05T07:17:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VQ5m0Ssa/G0IRdTfrfh+Lz0J+7ImYsKzcfNRUr8gjdql/3Awrb5p5D/7i4POrJqkU+XckaIDM2854LhRwZ1iCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T17:16:20.003100Z"},"content_sha256":"f6fc051a5660ff273dab30692d081822f8b540f3a7dcd0c92efe08e8e1a8c617","schema_version":"1.0","event_id":"sha256:f6fc051a5660ff273dab30692d081822f8b540f3a7dcd0c92efe08e8e1a8c617"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:FIQEJ7DUCPX7YXVAE3GNKJRUWM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Homogenization of nonlocal convolution type operators: Approximation for the resolvent with corrector","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"math.AP","authors_text":"Andrei Piatnitski, Elena Zhizhina, Tatiana Suslina, Vladimir Sloushch","submitted_at":"2023-11-28T07:32:02Z","abstract_excerpt":"In $L_2(\\mathbb{R}^d)$, we consider a selfadjoint bounded operator ${\\mathbb A}_\\varepsilon$, $\\varepsilon >0$, of the form $$ ({\\mathbb A}_\\varepsilon u) (\\mathbf{x}) = \\varepsilon^{-d-2} \\int_{\\mathbb{R}^d} a((\\mathbf{x} - \\mathbf{y} )/ \\varepsilon ) \\mu(\\mathbf{x} /\\varepsilon, \\mathbf{y} /\\varepsilon) \\left( u(\\mathbf{x}) - u(\\mathbf{y}) \\right)\\, d\\mathbf{y}. $$ It is assumed that $a(\\mathbf{x})$ is a nonnegative function of class $L_1(\\mathbb{R}^d)$ such that \\hbox{$a(-\\mathbf{x}) = a(\\mathbf{x})$} and $\\mu(\\mathbf{x},\\mathbf{y})$ is $\\mathbb{Z}^d$-periodic in each variable and such that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.16574","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/2311.16574/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":"2026-07-05T07:17:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iK+oP4Dw10+uvHaEyE4yWQxNe9GiIbIvw///u+GSZ5QlhMmxWxqxMpz9LIPqiyzo7vmO15yK/Zi1Nu79WNqWDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T17:16:20.003759Z"},"content_sha256":"678e70c58e6d417f22e24c11856800350e8d67bc53857079aa8af343365791c4","schema_version":"1.0","event_id":"sha256:678e70c58e6d417f22e24c11856800350e8d67bc53857079aa8af343365791c4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FIQEJ7DUCPX7YXVAE3GNKJRUWM/bundle.json","state_url":"https://pith.science/pith/FIQEJ7DUCPX7YXVAE3GNKJRUWM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FIQEJ7DUCPX7YXVAE3GNKJRUWM/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":"2026-08-10T17:16:20Z","links":{"resolver":"https://pith.science/pith/FIQEJ7DUCPX7YXVAE3GNKJRUWM","bundle":"https://pith.science/pith/FIQEJ7DUCPX7YXVAE3GNKJRUWM/bundle.json","state":"https://pith.science/pith/FIQEJ7DUCPX7YXVAE3GNKJRUWM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FIQEJ7DUCPX7YXVAE3GNKJRUWM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:FIQEJ7DUCPX7YXVAE3GNKJRUWM","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":"a68ec1eeadf423e1d6f049eb4a859b16f4f4b5611b62b26bf43b7bf73b5bc06a","cross_cats_sorted":["math-ph","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-11-28T07:32:02Z","title_canon_sha256":"a130b65cd99753c91509fd2b6b30f16d7895ea1104e1e35794c6bfda71ef90f1"},"schema_version":"1.0","source":{"id":"2311.16574","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.16574","created_at":"2026-07-05T07:17:43Z"},{"alias_kind":"arxiv_version","alias_value":"2311.16574v1","created_at":"2026-07-05T07:17:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.16574","created_at":"2026-07-05T07:17:43Z"},{"alias_kind":"pith_short_12","alias_value":"FIQEJ7DUCPX7","created_at":"2026-07-05T07:17:43Z"},{"alias_kind":"pith_short_16","alias_value":"FIQEJ7DUCPX7YXVA","created_at":"2026-07-05T07:17:43Z"},{"alias_kind":"pith_short_8","alias_value":"FIQEJ7DU","created_at":"2026-07-05T07:17:43Z"}],"graph_snapshots":[{"event_id":"sha256:678e70c58e6d417f22e24c11856800350e8d67bc53857079aa8af343365791c4","target":"graph","created_at":"2026-07-05T07:17:43Z","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/2311.16574/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In $L_2(\\mathbb{R}^d)$, we consider a selfadjoint bounded operator ${\\mathbb A}_\\varepsilon$, $\\varepsilon >0$, of the form $$ ({\\mathbb A}_\\varepsilon u) (\\mathbf{x}) = \\varepsilon^{-d-2} \\int_{\\mathbb{R}^d} a((\\mathbf{x} - \\mathbf{y} )/ \\varepsilon ) \\mu(\\mathbf{x} /\\varepsilon, \\mathbf{y} /\\varepsilon) \\left( u(\\mathbf{x}) - u(\\mathbf{y}) \\right)\\, d\\mathbf{y}. $$ It is assumed that $a(\\mathbf{x})$ is a nonnegative function of class $L_1(\\mathbb{R}^d)$ such that \\hbox{$a(-\\mathbf{x}) = a(\\mathbf{x})$} and $\\mu(\\mathbf{x},\\mathbf{y})$ is $\\mathbb{Z}^d$-periodic in each variable and such that","authors_text":"Andrei Piatnitski, Elena Zhizhina, Tatiana Suslina, Vladimir Sloushch","cross_cats":["math-ph","math.FA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-11-28T07:32:02Z","title":"Homogenization of nonlocal convolution type operators: Approximation for the resolvent with corrector"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.16574","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:f6fc051a5660ff273dab30692d081822f8b540f3a7dcd0c92efe08e8e1a8c617","target":"record","created_at":"2026-07-05T07:17:43Z","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":"a68ec1eeadf423e1d6f049eb4a859b16f4f4b5611b62b26bf43b7bf73b5bc06a","cross_cats_sorted":["math-ph","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-11-28T07:32:02Z","title_canon_sha256":"a130b65cd99753c91509fd2b6b30f16d7895ea1104e1e35794c6bfda71ef90f1"},"schema_version":"1.0","source":{"id":"2311.16574","kind":"arxiv","version":1}},"canonical_sha256":"2a2044fc7413effc5ea026ccd52634b328f14d63574275023132f375450bc109","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a2044fc7413effc5ea026ccd52634b328f14d63574275023132f375450bc109","first_computed_at":"2026-07-05T07:17:43.459577Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:17:43.459577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f8nTso6qpARiSXUcerS89ZPax4QbXaf5//0KLzXk72qnHHIsNgttFczgUvbJCOsiqpOIdt98C+rFJm6ZGvjZDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:17:43.460067Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.16574","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6fc051a5660ff273dab30692d081822f8b540f3a7dcd0c92efe08e8e1a8c617","sha256:678e70c58e6d417f22e24c11856800350e8d67bc53857079aa8af343365791c4"],"state_sha256":"e2c6bbd0ec6a7d35b435765e9d1f6e6266c94974497425cefea9c61d71f39e77"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n/sz+9dxPk8A379MCVpjmhvJEtebw9auqP3VficrXkGr/QmJup8ktXfGeVTXFexOdJLb96ez1NOKj+2eKWrlBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T17:16:20.010887Z","bundle_sha256":"0ed005237b584c28313915e7983379fd4dab6976043981ae262f91ef16a19439"}}