{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:FRJ5BSEHNPJJUQ2HIL627KY2W2","short_pith_number":"pith:FRJ5BSEH","canonical_record":{"source":{"id":"1604.05038","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-04-18T08:46:57Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"78614e8943f50e9233c4dae2676f001d49a8629d723fb2301588ba516d025e75","abstract_canon_sha256":"5bdcb2c2883f3b5cbae0a55ebbeae26fab3e4479737ee3d54257e6fb8308945c"},"schema_version":"1.0"},"canonical_sha256":"2c53d0c8876bd29a434742fdafab1ab68cd6748b0858cb8595f5b5f46060b912","source":{"kind":"arxiv","id":"1604.05038","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.05038","created_at":"2026-05-18T01:16:55Z"},{"alias_kind":"arxiv_version","alias_value":"1604.05038v1","created_at":"2026-05-18T01:16:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.05038","created_at":"2026-05-18T01:16:55Z"},{"alias_kind":"pith_short_12","alias_value":"FRJ5BSEHNPJJ","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FRJ5BSEHNPJJUQ2H","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FRJ5BSEH","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:FRJ5BSEHNPJJUQ2HIL627KY2W2","target":"record","payload":{"canonical_record":{"source":{"id":"1604.05038","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-04-18T08:46:57Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"78614e8943f50e9233c4dae2676f001d49a8629d723fb2301588ba516d025e75","abstract_canon_sha256":"5bdcb2c2883f3b5cbae0a55ebbeae26fab3e4479737ee3d54257e6fb8308945c"},"schema_version":"1.0"},"canonical_sha256":"2c53d0c8876bd29a434742fdafab1ab68cd6748b0858cb8595f5b5f46060b912","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:55.988157Z","signature_b64":"bRX51S4g/yFYOfpBkQFHMcakaQnVbXUWZwfTaaQ/a16kmAIeQwCtHXL5LpwhssKypd4Wc+zcgSJlKX9aCz/rDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c53d0c8876bd29a434742fdafab1ab68cd6748b0858cb8595f5b5f46060b912","last_reissued_at":"2026-05-18T01:16:55.987430Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:55.987430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.05038","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":"2026-05-18T01:16:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zs/mw3yj9il0D+dt7cknhxoOZeNdf2KCbF0eZKSZVEHAQBIlxH51pqhJKuLMxKr2+sSRMm4feUfH42F4vMMqAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T17:40:07.718742Z"},"content_sha256":"9ce4700e8312a7198564c0f692e044060e1176247c3f3a12f689333663e5cf17","schema_version":"1.0","event_id":"sha256:9ce4700e8312a7198564c0f692e044060e1176247c3f3a12f689333663e5cf17"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:FRJ5BSEHNPJJUQ2HIL627KY2W2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Periodic homogenization of non-local operators with a convolution type kernel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.FA","authors_text":"Andrey Piatnitski, Elena Zhizhina","submitted_at":"2016-04-18T08:46:57Z","abstract_excerpt":"The paper deals with homogenization problem for a non-local linear operator with a kernel of convolution type in a medium with a periodic structure. We consider the natural diffusive scaling of this operator and study the limit behaviour of the rescaled operators as the scaling parameter tends to 0. More precisely we show that in the topology of resolvent convergence the family of rescaled operators converges to a second order elliptic operator with constant coefficients. We also prove the convergence of the corresponding semigroups both in $L^2$ space and the space of continuous functions, an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.05038","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":""},"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":"2026-05-18T01:16:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6hKfs6TaqXQ3PgOgS62g4Xw+d+nwAOTf7JOW11GlDmjBz7hFLb7Yvs8csNhDMigQ8as1z9uMSwfOtYF4XCSfAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T17:40:07.719098Z"},"content_sha256":"93cf616e4e5b4adcc26f38cffdfabaee88c4da240049d9e2b21b2d13c97cf6a8","schema_version":"1.0","event_id":"sha256:93cf616e4e5b4adcc26f38cffdfabaee88c4da240049d9e2b21b2d13c97cf6a8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FRJ5BSEHNPJJUQ2HIL627KY2W2/bundle.json","state_url":"https://pith.science/pith/FRJ5BSEHNPJJUQ2HIL627KY2W2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FRJ5BSEHNPJJUQ2HIL627KY2W2/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":"2026-06-02T17:40:07Z","links":{"resolver":"https://pith.science/pith/FRJ5BSEHNPJJUQ2HIL627KY2W2","bundle":"https://pith.science/pith/FRJ5BSEHNPJJUQ2HIL627KY2W2/bundle.json","state":"https://pith.science/pith/FRJ5BSEHNPJJUQ2HIL627KY2W2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FRJ5BSEHNPJJUQ2HIL627KY2W2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FRJ5BSEHNPJJUQ2HIL627KY2W2","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":"5bdcb2c2883f3b5cbae0a55ebbeae26fab3e4479737ee3d54257e6fb8308945c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-04-18T08:46:57Z","title_canon_sha256":"78614e8943f50e9233c4dae2676f001d49a8629d723fb2301588ba516d025e75"},"schema_version":"1.0","source":{"id":"1604.05038","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.05038","created_at":"2026-05-18T01:16:55Z"},{"alias_kind":"arxiv_version","alias_value":"1604.05038v1","created_at":"2026-05-18T01:16:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.05038","created_at":"2026-05-18T01:16:55Z"},{"alias_kind":"pith_short_12","alias_value":"FRJ5BSEHNPJJ","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FRJ5BSEHNPJJUQ2H","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FRJ5BSEH","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:93cf616e4e5b4adcc26f38cffdfabaee88c4da240049d9e2b21b2d13c97cf6a8","target":"graph","created_at":"2026-05-18T01:16:55Z","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 paper deals with homogenization problem for a non-local linear operator with a kernel of convolution type in a medium with a periodic structure. We consider the natural diffusive scaling of this operator and study the limit behaviour of the rescaled operators as the scaling parameter tends to 0. More precisely we show that in the topology of resolvent convergence the family of rescaled operators converges to a second order elliptic operator with constant coefficients. We also prove the convergence of the corresponding semigroups both in $L^2$ space and the space of continuous functions, an","authors_text":"Andrey Piatnitski, Elena Zhizhina","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-04-18T08:46:57Z","title":"Periodic homogenization of non-local operators with a convolution type kernel"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.05038","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":"sha256:9ce4700e8312a7198564c0f692e044060e1176247c3f3a12f689333663e5cf17","target":"record","created_at":"2026-05-18T01:16:55Z","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":"5bdcb2c2883f3b5cbae0a55ebbeae26fab3e4479737ee3d54257e6fb8308945c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-04-18T08:46:57Z","title_canon_sha256":"78614e8943f50e9233c4dae2676f001d49a8629d723fb2301588ba516d025e75"},"schema_version":"1.0","source":{"id":"1604.05038","kind":"arxiv","version":1}},"canonical_sha256":"2c53d0c8876bd29a434742fdafab1ab68cd6748b0858cb8595f5b5f46060b912","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c53d0c8876bd29a434742fdafab1ab68cd6748b0858cb8595f5b5f46060b912","first_computed_at":"2026-05-18T01:16:55.987430Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:55.987430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bRX51S4g/yFYOfpBkQFHMcakaQnVbXUWZwfTaaQ/a16kmAIeQwCtHXL5LpwhssKypd4Wc+zcgSJlKX9aCz/rDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:55.988157Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.05038","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ce4700e8312a7198564c0f692e044060e1176247c3f3a12f689333663e5cf17","sha256:93cf616e4e5b4adcc26f38cffdfabaee88c4da240049d9e2b21b2d13c97cf6a8"],"state_sha256":"569a6c8c7ef0583704cf210e488eb0e423a9c11f6d4f0a15a1dab1a1b70cb1c5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3Tgp64exXYtttPkaSIH8HMbgMAo8+EiF6lG3/ErqhBHOhbQNzS3LU7tr3J2LuTJht5m66j3IOEH8pKXL8QRVAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T17:40:07.721238Z","bundle_sha256":"f7ef758aaa8c195e6ffe05be0530f319ed9c5a0136cc95a0bf2c70abc6e9f294"}}