{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:3N6NG2BKCFTU2FTER5WFYQ3EH3","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":"f59e776c7a9d2a7ad15aa3e2433423e6262478bbfce83637839a821aa6e269ec","cross_cats_sorted":["math.FA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-29T17:57:42Z","title_canon_sha256":"5010d15f85585336e3ae88be4604a9d466283ec06809dfd51f40f51fce99987a"},"schema_version":"1.0","source":{"id":"1810.12289","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.12289","created_at":"2026-05-18T00:02:03Z"},{"alias_kind":"arxiv_version","alias_value":"1810.12289v1","created_at":"2026-05-18T00:02:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.12289","created_at":"2026-05-18T00:02:03Z"},{"alias_kind":"pith_short_12","alias_value":"3N6NG2BKCFTU","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"3N6NG2BKCFTU2FTE","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"3N6NG2BK","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:70b82b2c3da913bf9dfb18f15440d296d1457ffb670cc8fc91ca8e1c9cb28342","target":"graph","created_at":"2026-05-18T00:02:03Z","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":"Given a subset $D$ of the Euclidean space, we study nonlocal quadratic forms that take into account tuples $(x,y) \\in D \\times D$ if and only if the line segment between $x$ and $y$ is contained in $D$. We discuss regularity of the corresponding Dirichlet form leading to the existence of a jump process with visibility constraint. Our main aim is to investigate corresponding Poincar\\'{e} inequalities and their scaling properties. For dumbbell shaped domains we show that the forms satisfy a Poincar\\'{e} inequality with diffusive scaling. This relates to the rate of convergence of eigenvalues in ","authors_text":"Moritz Kassmann, Vanja Wagner","cross_cats":["math.FA","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-29T17:57:42Z","title":"Nonlocal quadratic forms with visibility constraint"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12289","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:d367d2126fddc0fce2d886a4d4e18f25db521b5ed01084be755a68dd3ce0735d","target":"record","created_at":"2026-05-18T00:02:03Z","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":"f59e776c7a9d2a7ad15aa3e2433423e6262478bbfce83637839a821aa6e269ec","cross_cats_sorted":["math.FA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-29T17:57:42Z","title_canon_sha256":"5010d15f85585336e3ae88be4604a9d466283ec06809dfd51f40f51fce99987a"},"schema_version":"1.0","source":{"id":"1810.12289","kind":"arxiv","version":1}},"canonical_sha256":"db7cd3682a11674d16648f6c5c43643eda38f8b16d2307428cb7ea21e3add8f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db7cd3682a11674d16648f6c5c43643eda38f8b16d2307428cb7ea21e3add8f5","first_computed_at":"2026-05-18T00:02:03.702788Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:03.702788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0Y3k403VzLK6bmBb2+dnOvHwL7UNsg3ar4LGvfjRLIOrUH9fpl65fbN24I8xyjN1zDXHOrNYLWtgZVGrk67zDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:03.703472Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.12289","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d367d2126fddc0fce2d886a4d4e18f25db521b5ed01084be755a68dd3ce0735d","sha256:70b82b2c3da913bf9dfb18f15440d296d1457ffb670cc8fc91ca8e1c9cb28342"],"state_sha256":"049fcf4821b1f07dda11ae1d1643a280ebb25ba0cf7970ffe601c72fa42db25c"}