{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:FGJOETBX6Q5PEWQ4XURGIH47FA","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":"c3fe0f24331eb57d81efab9303df624a7b33cfb2445d50975126528219bdd000","cross_cats_sorted":["math.FA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-01-11T09:51:20Z","title_canon_sha256":"a27c22ad71c74cf1ba09e4389a9ac75cefbe7378d0969b4c2e6293230b83d86d"},"schema_version":"1.0","source":{"id":"2601.06832","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.06832","created_at":"2026-06-01T01:02:29Z"},{"alias_kind":"arxiv_version","alias_value":"2601.06832v3","created_at":"2026-06-01T01:02:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.06832","created_at":"2026-06-01T01:02:29Z"},{"alias_kind":"pith_short_12","alias_value":"FGJOETBX6Q5P","created_at":"2026-06-01T01:02:29Z"},{"alias_kind":"pith_short_16","alias_value":"FGJOETBX6Q5PEWQ4","created_at":"2026-06-01T01:02:29Z"},{"alias_kind":"pith_short_8","alias_value":"FGJOETBX","created_at":"2026-06-01T01:02:29Z"}],"graph_snapshots":[{"event_id":"sha256:e7f18fb257b7938ab013bfc61d3263636f234aa71ffa097b9bbe4a9efd8c0143","target":"graph","created_at":"2026-06-01T01:02:29Z","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/2601.06832/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The goal of the paper is to study in $L_2(\\R^d)$ a self-adjoint operator ${\\mathbb A}_\\eps$, $\\eps >0$, of the form $$ ({\\mathbb A}_\\eps u) (\\x) = \\int_{\\R^d} \\mu(\\x/\\eps, \\y/\\eps) \\frac{\\left( u(\\x) - u(\\y) \\right)}{|\\x - \\y|^{d+\\alpha}}\\,d\\y $$ with $1< \\alpha < 2$;\n  here the function\n  $\\mu(\\x,\\y)$ is $\\Z^d$-periodic in the both variables, satisfies the symmetry relation $\\mu(\\x,\\y) = \\mu(\\y,\\x)$ and\n  the estimates $0< \\mu_- \\leqslant \\mu(\\x,\\y) \\leqslant \\mu_+< \\infty$. The rigorous definition of the operator ${\\mathbb A}_\\eps$ is given in terms of the corresponding quadratic form. In th","authors_text":"Andrey Piatnitski, Elena Zhizhina, Tatiana Suslina, Vladimir Sloushch","cross_cats":["math.FA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-01-11T09:51:20Z","title":"Homogenization of L\\'evy-type operators: operator estimates with correctors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.06832","kind":"arxiv","version":3},"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":"sha256:222a4495c0bd6d0ba512b1ba68ddab20575d96df625e4ba2eacbf4c966a61ac6","target":"record","created_at":"2026-06-01T01:02:29Z","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":"c3fe0f24331eb57d81efab9303df624a7b33cfb2445d50975126528219bdd000","cross_cats_sorted":["math.FA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-01-11T09:51:20Z","title_canon_sha256":"a27c22ad71c74cf1ba09e4389a9ac75cefbe7378d0969b4c2e6293230b83d86d"},"schema_version":"1.0","source":{"id":"2601.06832","kind":"arxiv","version":3}},"canonical_sha256":"2992e24c37f43af25a1cbd22641f9f28043329a0c32ed9caec8f64ce15fad9b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2992e24c37f43af25a1cbd22641f9f28043329a0c32ed9caec8f64ce15fad9b0","first_computed_at":"2026-06-01T01:02:29.009149Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-01T01:02:29.009149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mIyCApOG+p0gbvtHesAHdQnZ7q2AUVoYuPtS1MK8qi35sO1jucKG5cd6GPOTgrkUrZPvfd2KpYHK8NQecorWBQ==","signature_status":"signed_v1","signed_at":"2026-06-01T01:02:29.010177Z","signed_message":"canonical_sha256_bytes"},"source_id":"2601.06832","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:222a4495c0bd6d0ba512b1ba68ddab20575d96df625e4ba2eacbf4c966a61ac6","sha256:e7f18fb257b7938ab013bfc61d3263636f234aa71ffa097b9bbe4a9efd8c0143"],"state_sha256":"1f90405792c0d3eaa38332b42df3c72c7e0a7928be5d2b845dc4fe5d41a746b9"}