{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:XVQWV3BZBEIDEW45FJ7BAVGIK2","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":"1452fd4dfd65cf566750d75afc0e0f3fb2ffa2a22b7a55c431bf575f628e1ed1","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-11-08T21:33:52Z","title_canon_sha256":"849076ffd70074451c5d38db5b7a5ee2a46e6ea2c9ea0c8b42eea7b25144da55"},"schema_version":"1.0","source":{"id":"2111.04842","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.04842","created_at":"2026-07-05T07:44:50Z"},{"alias_kind":"arxiv_version","alias_value":"2111.04842v3","created_at":"2026-07-05T07:44:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.04842","created_at":"2026-07-05T07:44:50Z"},{"alias_kind":"pith_short_12","alias_value":"XVQWV3BZBEID","created_at":"2026-07-05T07:44:50Z"},{"alias_kind":"pith_short_16","alias_value":"XVQWV3BZBEIDEW45","created_at":"2026-07-05T07:44:50Z"},{"alias_kind":"pith_short_8","alias_value":"XVQWV3BZ","created_at":"2026-07-05T07:44:50Z"}],"graph_snapshots":[{"event_id":"sha256:de3f5aecae8c9a5ddae4ce11b2f925a99feaa9c8eb1fb8595acc3914a4ef5041","target":"graph","created_at":"2026-07-05T07:44:50Z","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/2111.04842/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that for $\\beta<6\\pi$ the local extremal process of the massive sine-Gordon field on the unit torus in $d=2$ converges to a Poisson point process with random intensity measure ${\\rm Z}^{\\mathrm{SG}}(dx) \\otimes e^{-\\alpha h}dh$ for some $\\alpha>0$. The proof combines existing methods for the extremal process associated to the Gaussian free field, which was introduced and studied by Biskup and Louidor, and a strong coupling between the sine-Gordon field and the Gaussian free field.","authors_text":"Michael Hofstetter","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-11-08T21:33:52Z","title":"Extreme local extrema of the sine-Gordon field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.04842","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":"sha256:9b66bad053e335881087483205e76a789989a9749c3897faa1808c509dd7f0d0","target":"record","created_at":"2026-07-05T07:44:50Z","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":"1452fd4dfd65cf566750d75afc0e0f3fb2ffa2a22b7a55c431bf575f628e1ed1","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-11-08T21:33:52Z","title_canon_sha256":"849076ffd70074451c5d38db5b7a5ee2a46e6ea2c9ea0c8b42eea7b25144da55"},"schema_version":"1.0","source":{"id":"2111.04842","kind":"arxiv","version":3}},"canonical_sha256":"bd616aec390910325b9d2a7e1054c85698c5c45b8a9a618cab9f69321c7c4af6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd616aec390910325b9d2a7e1054c85698c5c45b8a9a618cab9f69321c7c4af6","first_computed_at":"2026-07-05T07:44:50.776809Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:44:50.776809Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T3P88wDhChDz4tjGjmMyMzsUqGfZDEMDfT8r9xRyMb88nEtRceA962+xFkvYKq28i0DFg44Dnht28VRDFuglAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:44:50.777264Z","signed_message":"canonical_sha256_bytes"},"source_id":"2111.04842","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b66bad053e335881087483205e76a789989a9749c3897faa1808c509dd7f0d0","sha256:de3f5aecae8c9a5ddae4ce11b2f925a99feaa9c8eb1fb8595acc3914a4ef5041"],"state_sha256":"14e965d518625c9240f28ece93656ffcb68489cef999a1e6e56094d78cc68200"}