{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XVM5RWWEHYXDFQCHPWL4D5JV6T","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":"f6de7ee726b963426155ffb760ac0e1eb7e8484f21e9f2abba7246269ba157fd","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-16T07:33:18Z","title_canon_sha256":"fe208450cc3111585d7f264e14ce65f6d220a39a12e23cc079cc374639f69eb9"},"schema_version":"1.0","source":{"id":"1310.4285","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.4285","created_at":"2026-05-18T03:00:25Z"},{"alias_kind":"arxiv_version","alias_value":"1310.4285v3","created_at":"2026-05-18T03:00:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4285","created_at":"2026-05-18T03:00:25Z"},{"alias_kind":"pith_short_12","alias_value":"XVM5RWWEHYXD","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XVM5RWWEHYXDFQCH","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XVM5RWWE","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:0d36da9185167ef1b6c17abf3737c3774d0eaa5afcaa487ac46d292a0d50f503","target":"graph","created_at":"2026-05-18T03:00:25Z","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":"Assume that $(u_n)$ is a sequence of solutions to heterogeneous equations with rough coefficients and fractional derivatives, weakly converging to zero in ${\\rm L}^p(\\R^{d+m})$, with $p>1$.\n  We prove that the sequence of averaged quantities $(\\int \\rho(\\my) u_n(\\mx,\\my) d\\my)$ is strongly precompact in $\\Ljl\\Rd$ for any $\\rho\\in \\Cc{\\R^m}$, provided that restrictive non-degeneracy conditions are satisfied. These are fulfilled for elliptic, parabolic, fractional convection-diffusion equations, as well as for parabolic equations with a fractional time derivative. The main tool that we are using","authors_text":"Darko Mitrovic, Martin Lazar","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-16T07:33:18Z","title":"On the velocity averaging for equations with optimal heterogeneous rough coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4285","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":"sha256:577808c22dcf2e1a903ba032bdb659a4b73106decf48b365f144c90c26f92495","target":"record","created_at":"2026-05-18T03:00:25Z","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":"f6de7ee726b963426155ffb760ac0e1eb7e8484f21e9f2abba7246269ba157fd","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-16T07:33:18Z","title_canon_sha256":"fe208450cc3111585d7f264e14ce65f6d220a39a12e23cc079cc374639f69eb9"},"schema_version":"1.0","source":{"id":"1310.4285","kind":"arxiv","version":3}},"canonical_sha256":"bd59d8dac43e2e32c0477d97c1f535f4e88f01a76333855267508f5fd55b84f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd59d8dac43e2e32c0477d97c1f535f4e88f01a76333855267508f5fd55b84f7","first_computed_at":"2026-05-18T03:00:25.665857Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:25.665857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"deFddKfgxe0F6IS1/o/UoouEgkORSalzeTgvK5MS/Nkjgk6H4mvYNYb+w+hEhb2DDYn9hZM/LuK4Xt4tPhYxBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:25.666598Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.4285","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:577808c22dcf2e1a903ba032bdb659a4b73106decf48b365f144c90c26f92495","sha256:0d36da9185167ef1b6c17abf3737c3774d0eaa5afcaa487ac46d292a0d50f503"],"state_sha256":"9d4cf2f3f8f7e6944ba2a65295a28c12636c60fc74e69a26ca7fbf4247cfeb58"}