{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:HEMSVI3FFXL6ZFRRJZEPEYDMNH","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":"9897eeaddf6273bb1663c53cc2040b90b4268071715ba442c16ea78d9c72c889","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-18T07:44:21Z","title_canon_sha256":"33e70317bce27b1977c0e8754929d7e83fe91ebe02863bd0222e4593b23610a2"},"schema_version":"1.0","source":{"id":"2606.19885","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.19885","created_at":"2026-06-19T16:12:37Z"},{"alias_kind":"arxiv_version","alias_value":"2606.19885v1","created_at":"2026-06-19T16:12:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.19885","created_at":"2026-06-19T16:12:37Z"},{"alias_kind":"pith_short_12","alias_value":"HEMSVI3FFXL6","created_at":"2026-06-19T16:12:37Z"},{"alias_kind":"pith_short_16","alias_value":"HEMSVI3FFXL6ZFRR","created_at":"2026-06-19T16:12:37Z"},{"alias_kind":"pith_short_8","alias_value":"HEMSVI3F","created_at":"2026-06-19T16:12:37Z"}],"graph_snapshots":[{"event_id":"sha256:c2fd54f904c8d397b919e350a2d22277c9363cc05e4139cff24c8d0246aae978","target":"graph","created_at":"2026-06-19T16:12:37Z","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/2606.19885/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we consider the classical overdetermined capillary problem:\n  \\begin{equation*}\n  \\begin{cases}\n  \\mathrm{div} \\left(\\frac{\\nabla u}{\\sqrt{1+|\\nabla u|^2}}\\right) - bu =0 &~~\\mbox{in}~~ \\Omega,\n  \\partial_{\\nu} u=\\kappa &~~\\mbox{on}~~\\partial\\Omega,\n  u=c &~~\\mbox{on}~~\\partial\\Omega,\n  \\end{cases} \\end{equation*}\n  where $b$, $c$ and $\\kappa$ are positive constants, and $\\Omega\\subset \\mathbb{R}^2$. When $\\Omega$ is an infinite strip, i.e., a domain bounded by two parallel straight lines, there exists a unique one-dimensional solution (called the trivial solution) to this probl","authors_text":"Pieralberto Sicbaldi, Yuanyuan Lian","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-18T07:44:21Z","title":"Bifurcation of overdetermined capillary problems in a strip domain"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19885","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:f2f139ef27d020d247276f4cd71a6538772716fbfe2ecad35d5cc94a92ce304b","target":"record","created_at":"2026-06-19T16:12:37Z","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":"9897eeaddf6273bb1663c53cc2040b90b4268071715ba442c16ea78d9c72c889","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-18T07:44:21Z","title_canon_sha256":"33e70317bce27b1977c0e8754929d7e83fe91ebe02863bd0222e4593b23610a2"},"schema_version":"1.0","source":{"id":"2606.19885","kind":"arxiv","version":1}},"canonical_sha256":"39192aa3652dd7ec96314e48f2606c69e75196cc13aa31bcdb4adba58aeb6da7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"39192aa3652dd7ec96314e48f2606c69e75196cc13aa31bcdb4adba58aeb6da7","first_computed_at":"2026-06-19T16:12:37.772155Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:12:37.772155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hOn/Gr+Y9t2z/pdQlusp/TjmFzI+bBjE2DCfBgY+609NWi6itZ4q5Ke8e5pNjhB8+oiUdtNDDN5C73r4U57xAw==","signature_status":"signed_v1","signed_at":"2026-06-19T16:12:37.772515Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.19885","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2f139ef27d020d247276f4cd71a6538772716fbfe2ecad35d5cc94a92ce304b","sha256:c2fd54f904c8d397b919e350a2d22277c9363cc05e4139cff24c8d0246aae978"],"state_sha256":"4757b569805771eebbf644a55d9df4a3bfbf520fde8bfb6c6b64db4c3ea17018"}