{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ROKFSCFA7X3LDDIQWYD3K4O3AX","short_pith_number":"pith:ROKFSCFA","canonical_record":{"source":{"id":"1512.05126","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-16T10:50:45Z","cross_cats_sorted":[],"title_canon_sha256":"81ca9371be458b278d374ee9b6e0cb8365b8b21a91323e71a3683b4d1eb52a68","abstract_canon_sha256":"725ebbfd7ee8c2f91a4bfaf8b6a770b3ff6a5eaefe7c37b0c311e2fbb84129de"},"schema_version":"1.0"},"canonical_sha256":"8b945908a0fdf6b18d10b607b571db05d78efdeb41b8387f01e9ae33818bb9d7","source":{"kind":"arxiv","id":"1512.05126","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.05126","created_at":"2026-05-18T01:24:13Z"},{"alias_kind":"arxiv_version","alias_value":"1512.05126v1","created_at":"2026-05-18T01:24:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.05126","created_at":"2026-05-18T01:24:13Z"},{"alias_kind":"pith_short_12","alias_value":"ROKFSCFA7X3L","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"ROKFSCFA7X3LDDIQ","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"ROKFSCFA","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ROKFSCFA7X3LDDIQWYD3K4O3AX","target":"record","payload":{"canonical_record":{"source":{"id":"1512.05126","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-16T10:50:45Z","cross_cats_sorted":[],"title_canon_sha256":"81ca9371be458b278d374ee9b6e0cb8365b8b21a91323e71a3683b4d1eb52a68","abstract_canon_sha256":"725ebbfd7ee8c2f91a4bfaf8b6a770b3ff6a5eaefe7c37b0c311e2fbb84129de"},"schema_version":"1.0"},"canonical_sha256":"8b945908a0fdf6b18d10b607b571db05d78efdeb41b8387f01e9ae33818bb9d7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:13.426291Z","signature_b64":"90yp4yPWS2AyMui7apfU6Ep3UMew2eH8VI+xGBdwTWdMAEo1pTMZvdqaAv5aOHDN8NJX/4grPIK5LJPGUOhOAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8b945908a0fdf6b18d10b607b571db05d78efdeb41b8387f01e9ae33818bb9d7","last_reissued_at":"2026-05-18T01:24:13.425758Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:13.425758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.05126","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:24:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xPRgmZ1kPT05/fMNiuDTmxRLYc84fD6E6x6eWefFi+Yyoh70jwtjOpuVHqnwSSfCCvWD93WFJ1FKqCF8kyQCBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T02:33:41.268080Z"},"content_sha256":"fe4803862e84daad3575c515a9b7052abddc77c662120c1294500de4085c38b0","schema_version":"1.0","event_id":"sha256:fe4803862e84daad3575c515a9b7052abddc77c662120c1294500de4085c38b0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ROKFSCFA7X3LDDIQWYD3K4O3AX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symmetry for a general class of overdetermined elliptic problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Friedemann Brock","submitted_at":"2015-12-16T10:50:45Z","abstract_excerpt":"Let $\\Omega $ be a bounded domain in $\\mathbb{R} ^N $, and let $u\\in C^1 (\\overline{\\Omega }) $ be a weak solution of the following overdetermined BVP: $-\\nabla (g(|\\nabla u|)|\\nabla u|^{-1} \\nabla u )=f(|x|,u)$, $ u>0 $ in $\\Omega $ and $u(x)=0, \\ |\\nabla u (x)| =\\lambda (|x|)$ on $\\partial \\Omega $, where $g\\in C([0,+\\infty ))\\cap C^1 ((0,+\\infty ) ) $ with $g(0)=0$, $g'(t)>0$ for $t>0$, $f\\in C([0,+\\infty )) \\times [0, +\\infty ) )$, $f$ is nonincreasing in $|x|$, $\\lambda \\in C([0, +\\infty )) $ and $\\lambda $ is positive and nondecreasing. We show that $\\Omega $ is a ball and $u$ satisfies "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05126","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:24:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fH90KRI/4i1QcmJdJHyEZn0VrnjYouOXWTIHRo807ZZO96MM2taAsCpgLcwaNNsRoK7jXoVqyF+dnl61jvMcAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T02:33:41.268433Z"},"content_sha256":"6f5baf456c2ea356e36b3ed7c1dbdfc8c769050364a91921626e7cf69cfa96e9","schema_version":"1.0","event_id":"sha256:6f5baf456c2ea356e36b3ed7c1dbdfc8c769050364a91921626e7cf69cfa96e9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ROKFSCFA7X3LDDIQWYD3K4O3AX/bundle.json","state_url":"https://pith.science/pith/ROKFSCFA7X3LDDIQWYD3K4O3AX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ROKFSCFA7X3LDDIQWYD3K4O3AX/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-27T02:33:41Z","links":{"resolver":"https://pith.science/pith/ROKFSCFA7X3LDDIQWYD3K4O3AX","bundle":"https://pith.science/pith/ROKFSCFA7X3LDDIQWYD3K4O3AX/bundle.json","state":"https://pith.science/pith/ROKFSCFA7X3LDDIQWYD3K4O3AX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ROKFSCFA7X3LDDIQWYD3K4O3AX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ROKFSCFA7X3LDDIQWYD3K4O3AX","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":"725ebbfd7ee8c2f91a4bfaf8b6a770b3ff6a5eaefe7c37b0c311e2fbb84129de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-16T10:50:45Z","title_canon_sha256":"81ca9371be458b278d374ee9b6e0cb8365b8b21a91323e71a3683b4d1eb52a68"},"schema_version":"1.0","source":{"id":"1512.05126","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.05126","created_at":"2026-05-18T01:24:13Z"},{"alias_kind":"arxiv_version","alias_value":"1512.05126v1","created_at":"2026-05-18T01:24:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.05126","created_at":"2026-05-18T01:24:13Z"},{"alias_kind":"pith_short_12","alias_value":"ROKFSCFA7X3L","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"ROKFSCFA7X3LDDIQ","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"ROKFSCFA","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:6f5baf456c2ea356e36b3ed7c1dbdfc8c769050364a91921626e7cf69cfa96e9","target":"graph","created_at":"2026-05-18T01:24:13Z","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":"Let $\\Omega $ be a bounded domain in $\\mathbb{R} ^N $, and let $u\\in C^1 (\\overline{\\Omega }) $ be a weak solution of the following overdetermined BVP: $-\\nabla (g(|\\nabla u|)|\\nabla u|^{-1} \\nabla u )=f(|x|,u)$, $ u>0 $ in $\\Omega $ and $u(x)=0, \\ |\\nabla u (x)| =\\lambda (|x|)$ on $\\partial \\Omega $, where $g\\in C([0,+\\infty ))\\cap C^1 ((0,+\\infty ) ) $ with $g(0)=0$, $g'(t)>0$ for $t>0$, $f\\in C([0,+\\infty )) \\times [0, +\\infty ) )$, $f$ is nonincreasing in $|x|$, $\\lambda \\in C([0, +\\infty )) $ and $\\lambda $ is positive and nondecreasing. We show that $\\Omega $ is a ball and $u$ satisfies ","authors_text":"Friedemann Brock","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-16T10:50:45Z","title":"Symmetry for a general class of overdetermined elliptic problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05126","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:fe4803862e84daad3575c515a9b7052abddc77c662120c1294500de4085c38b0","target":"record","created_at":"2026-05-18T01:24:13Z","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":"725ebbfd7ee8c2f91a4bfaf8b6a770b3ff6a5eaefe7c37b0c311e2fbb84129de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-16T10:50:45Z","title_canon_sha256":"81ca9371be458b278d374ee9b6e0cb8365b8b21a91323e71a3683b4d1eb52a68"},"schema_version":"1.0","source":{"id":"1512.05126","kind":"arxiv","version":1}},"canonical_sha256":"8b945908a0fdf6b18d10b607b571db05d78efdeb41b8387f01e9ae33818bb9d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b945908a0fdf6b18d10b607b571db05d78efdeb41b8387f01e9ae33818bb9d7","first_computed_at":"2026-05-18T01:24:13.425758Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:13.425758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"90yp4yPWS2AyMui7apfU6Ep3UMew2eH8VI+xGBdwTWdMAEo1pTMZvdqaAv5aOHDN8NJX/4grPIK5LJPGUOhOAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:13.426291Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.05126","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe4803862e84daad3575c515a9b7052abddc77c662120c1294500de4085c38b0","sha256:6f5baf456c2ea356e36b3ed7c1dbdfc8c769050364a91921626e7cf69cfa96e9"],"state_sha256":"9510a3385934c923b034d2257bc3a6cfd5e8bd5e1fba3315bccccad397f0c218"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D/hCVfy2zBpiMabWNWYJn6OMfypgZCK64SH3IvFlh4caAU4toS9eNuJpx8qlPBtF093BDgPSbePBipN3nrDtBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T02:33:41.270223Z","bundle_sha256":"c84e5bdd7b84b91356434121e7ff47f72fcf956fe27b8253c64c8acda9b50b2c"}}