{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QMB5SX2Z6FSDL6A7GGO652YHY4","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":"2047a94c0d0bc73ba3f860d0ab8f96b233bdc5b717ec172f59009b20509f58e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-03T13:20:14Z","title_canon_sha256":"545aa35adea5d768075092c8eb7770c3df51022c3964496403a0435c2bbe517a"},"schema_version":"1.0","source":{"id":"1710.01137","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.01137","created_at":"2026-05-18T00:31:58Z"},{"alias_kind":"arxiv_version","alias_value":"1710.01137v2","created_at":"2026-05-18T00:31:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.01137","created_at":"2026-05-18T00:31:58Z"},{"alias_kind":"pith_short_12","alias_value":"QMB5SX2Z6FSD","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QMB5SX2Z6FSDL6A7","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QMB5SX2Z","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:f79399714ef34729dbbf7704789e6ee1c8c04c4e93d277d5fc47545716b0ffe8","target":"graph","created_at":"2026-05-18T00:31:58Z","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 prove a one-dimensional symmetry result for a weighted Dirichlet-to-Neumann problem arising in a model for water waves in dimension 3. More precisely we prove that minimizers and bounded monotone solutions depend on only one Euclidean variable. The analogue of this result for the 2-dimensional case (and without weights) was established in an article by De La Llave and the third author. In this paper, a crucial ingredient in the proof is given by an energy estimate for minimizers obtained via a comparison argument.","authors_text":"Eleonora Cinti, Enrico Valdinoci, Pietro Miraglio","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-03T13:20:14Z","title":"One-dimensional symmetry for the solutions of a three-dimensional water wave problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.01137","kind":"arxiv","version":2},"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:a782158cafe4a7048f6ddac2bf092c002ca5e1865f00bd685dcc907e92c9500d","target":"record","created_at":"2026-05-18T00:31:58Z","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":"2047a94c0d0bc73ba3f860d0ab8f96b233bdc5b717ec172f59009b20509f58e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-03T13:20:14Z","title_canon_sha256":"545aa35adea5d768075092c8eb7770c3df51022c3964496403a0435c2bbe517a"},"schema_version":"1.0","source":{"id":"1710.01137","kind":"arxiv","version":2}},"canonical_sha256":"8303d95f59f16435f81f319deeeb07c73f17107edb455e68771847c2fc70eba8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8303d95f59f16435f81f319deeeb07c73f17107edb455e68771847c2fc70eba8","first_computed_at":"2026-05-18T00:31:58.631455Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:58.631455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9lEvNv9fnvcUnmfqkURLxeTKf5DUk2n9UHaocrmR0aeUOmf+hyOEU7maffXVQ17AhqwIYCB13XrXuyFdWQmIBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:58.631949Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.01137","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a782158cafe4a7048f6ddac2bf092c002ca5e1865f00bd685dcc907e92c9500d","sha256:f79399714ef34729dbbf7704789e6ee1c8c04c4e93d277d5fc47545716b0ffe8"],"state_sha256":"c5d06ef083f34db18504beec00653e7d2a46177c52710a26f7d85b43d93442a2"}