{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BDAJFZB7BHNSKTHQHU3GE4PC73","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":"18dfe12df4af6a8ca314c6ea6ead7302985439c91c30e28951aa78ff108ae27a","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-08-25T09:35:08Z","title_canon_sha256":"d7f8ae1c1bc5733b079e70fb4ce0bf7f938dd27bf4b74348914611ff7eafc015"},"schema_version":"1.0","source":{"id":"1308.5391","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.5391","created_at":"2026-05-18T03:15:04Z"},{"alias_kind":"arxiv_version","alias_value":"1308.5391v1","created_at":"2026-05-18T03:15:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.5391","created_at":"2026-05-18T03:15:04Z"},{"alias_kind":"pith_short_12","alias_value":"BDAJFZB7BHNS","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BDAJFZB7BHNSKTHQ","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BDAJFZB7","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:4fee310f9b12790e5d7ac68753689d0d9f60d15c0fbe69a15f0d93fcb42022d4","target":"graph","created_at":"2026-05-18T03:15:04Z","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":"We consider a small random perturbation of the energy functional $$ [u]^2_{H^s(\\Lambda, R^d)} + \\int_\\Lambda W(u(x)) dx $$ for $s \\in (0,1),$ where the non-local part $ [u]^2_{H^s(\\Lambda,R^d)}$ denotes the total contribution from $\\Lambda \\subset R^d$ in the $H^s (R^d)$ Gagliardo semi-norm of $u$ and $W$ is a double well potential. We show that there exists, as $\\Lambda $ invades $ R^d$, for almost all realizations of the random term a minimizer under compact perturbations, which is unique when $d=2$, $s \\in (\\frac 12,1)$ and when $d=1$, $s \\in [\\frac 14, 1).$ This uniqueness is a consequence","authors_text":"Enza Orlandi, Nicolas Dir","cross_cats":["math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-08-25T09:35:08Z","title":"Uniqueness of the minimizer for a random nonlocal functional with double-well potential in $d\\le2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5391","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:f7fe8e474f6740092f07b0524361ccaf19f391edfaa4087565990a5e82f0289c","target":"record","created_at":"2026-05-18T03:15:04Z","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":"18dfe12df4af6a8ca314c6ea6ead7302985439c91c30e28951aa78ff108ae27a","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-08-25T09:35:08Z","title_canon_sha256":"d7f8ae1c1bc5733b079e70fb4ce0bf7f938dd27bf4b74348914611ff7eafc015"},"schema_version":"1.0","source":{"id":"1308.5391","kind":"arxiv","version":1}},"canonical_sha256":"08c092e43f09db254cf03d366271e2fee2e442351c108777a9e281ee22bb816e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08c092e43f09db254cf03d366271e2fee2e442351c108777a9e281ee22bb816e","first_computed_at":"2026-05-18T03:15:04.826866Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:04.826866Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XzOSamnaj/ejvvni6+18WJffAeP9IFUBQJilxW1WnBkfH5nBPJbl1zRH6m0dor6quTIGfH9C+0ddiCeDIm1nBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:04.827810Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.5391","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7fe8e474f6740092f07b0524361ccaf19f391edfaa4087565990a5e82f0289c","sha256:4fee310f9b12790e5d7ac68753689d0d9f60d15c0fbe69a15f0d93fcb42022d4"],"state_sha256":"3c3d3c478a830073de8d5e6c1324a2d144d3d8048b059c6bb39c7f11bcc2f990"}