{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:RLKUXQGEBTLROEFASK5BSXA6M6","short_pith_number":"pith:RLKUXQGE","canonical_record":{"source":{"id":"2608.00199","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-31T18:26:07Z","cross_cats_sorted":[],"title_canon_sha256":"cd6a2fd94222a1e527971acdbfa8410666af2a73555218b45d8116853eed989b","abstract_canon_sha256":"d3f494951f31d5d76952f6eee683fa2d801a60c7862a48ac390ab7b4277120f8"},"schema_version":"1.0"},"canonical_sha256":"8ad54bc0c40cd71710a092ba195c1e67aeef2248abb6e2fed36f2a2d4cb6de4e","source":{"kind":"arxiv","id":"2608.00199","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.00199","created_at":"2026-08-04T00:33:56Z"},{"alias_kind":"arxiv_version","alias_value":"2608.00199v1","created_at":"2026-08-04T00:33:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.00199","created_at":"2026-08-04T00:33:56Z"},{"alias_kind":"pith_short_12","alias_value":"RLKUXQGEBTLR","created_at":"2026-08-04T00:33:56Z"},{"alias_kind":"pith_short_16","alias_value":"RLKUXQGEBTLROEFA","created_at":"2026-08-04T00:33:56Z"},{"alias_kind":"pith_short_8","alias_value":"RLKUXQGE","created_at":"2026-08-04T00:33:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:RLKUXQGEBTLROEFASK5BSXA6M6","target":"record","payload":{"canonical_record":{"source":{"id":"2608.00199","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-31T18:26:07Z","cross_cats_sorted":[],"title_canon_sha256":"cd6a2fd94222a1e527971acdbfa8410666af2a73555218b45d8116853eed989b","abstract_canon_sha256":"d3f494951f31d5d76952f6eee683fa2d801a60c7862a48ac390ab7b4277120f8"},"schema_version":"1.0"},"canonical_sha256":"8ad54bc0c40cd71710a092ba195c1e67aeef2248abb6e2fed36f2a2d4cb6de4e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-04T00:33:56.350210Z","signature_b64":"SRPUBAZIUBHgUHGH06TS+xtcmB4BORBrebDK66V+OiJ+ZTPDLfN1ksxzz1P0UeRzw5xwFnrKoW5roOT0kkImAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ad54bc0c40cd71710a092ba195c1e67aeef2248abb6e2fed36f2a2d4cb6de4e","last_reissued_at":"2026-08-04T00:33:56.348424Z","signature_status":"signed_v1","first_computed_at":"2026-08-04T00:33:56.348424Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.00199","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":"2026-08-04T00:33:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QICiYUHpgXKoNQtEQ+4Jl+5yxpTB+16T/CSPmMuwQXDHZ+9HLK26k1pY2ZPq5zDLW4QMex9BMmgscX8WXqMUBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T15:08:21.529787Z"},"content_sha256":"1f0de75d167a36a477fbd5c5654ccedaf058159096b6f3aee8c13c70527ab111","schema_version":"1.0","event_id":"sha256:1f0de75d167a36a477fbd5c5654ccedaf058159096b6f3aee8c13c70527ab111"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:RLKUXQGEBTLROEFASK5BSXA6M6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regularity results for elliptic equations on cones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Camilla Chiara Polvara, Carlo Alberto Antonini, Filomena Pacella, Luigi Provenzano","submitted_at":"2026-07-31T18:26:07Z","abstract_excerpt":"We study global regularity of solutions to Dirichlet or Neumann elliptic problems in spherical sectors $S_{D,R}$ of radius $R>0$ in $\\mathbb{R}^N, N\\ge 2$, where $D$ is the bounded domain on the unit sphere $\\mathbb{S}^{N-1}$ which spans the spherical sector. One of the main results shows that boundedness of the gradient of the solutions of Poisson equations holds whenever $\\lambda_1(D)\\ge N-1$, where $\\lambda_1(D)$ is the first nontrivial eigenvalue of the Laplace Beltrami operator $-\\Delta_{\\mathbb{S}^{N-1}}$ on the domain $D$ with Dirichlet or Neumann boundary conditions on $\\partial D$.\n  "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.00199","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.00199/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-08-04T00:33:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c8/FvYXeLUG1AGRqSwmtZPFgAW4deIO1Kg7mIsgh8t6563/8urkuAunJGjSINFW70RkL+AIzXGzSVT4B8gApCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T15:08:21.530641Z"},"content_sha256":"11ba4ab1b687973e4db91a879e6d17a295347eae35b5e3cce654403f50612d05","schema_version":"1.0","event_id":"sha256:11ba4ab1b687973e4db91a879e6d17a295347eae35b5e3cce654403f50612d05"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:RLKUXQGEBTLROEFASK5BSXA6M6","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1007/s00526-024-02902-6) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"L. Montoro, L. Muglia, B. Sciunzi,Optimal second order boundary regularity for solutions top-Laplace equa- tions, Calc. Var. Partial Differential Equations, vol. 64, no. 2, Paper No. 50, 22, (2025), doi = 10.1007/s00526- 024-02902-6","arxiv_id":"2608.00199","detector":"doi_compliance","evidence":{"ref_index":47,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"10.1007/s00526-","reconstructed_doi":"10.1007/s00526-024-02902-6"},"severity":"advisory","ref_index":47,"audited_at":"2026-08-04T01:18:22.459020Z","event_type":"pith.integrity.v1","detected_doi":"10.1007/s00526-024-02902-6","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"4a59d2a560bbef0c17b6d63847b500e074421ca1fff41d80f55634083f6e44ce","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.1.0","detected_arxiv_id":null,"integrity_event_id":17774,"payload_sha256":"72ba4d9861e5deca5a5c3fea9920c3ca597491b6014c83a39035275c54ceb46e","signature_b64":"9JKEKtRq01tmKqQzhnP+NBa00s944XdxbAlh3WzZ9dCkC4+qoevkZAkUH1aFe26ig8d4Xb36wTd5GYLfKOShBg==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-04T01:18:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sLpUZTsbsHQDATZzrYGJ0fNdAQome9rCGG/hSwGHQMcd0I66tY+ThmLHmRCj/0UUxpuxB3yW9jb4qNGXzTsACA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T15:08:21.542919Z"},"content_sha256":"d2290868f65f5c201c0ef0131cf375f4daea37d45c28a07ef7a9345911e487e4","schema_version":"1.0","event_id":"sha256:d2290868f65f5c201c0ef0131cf375f4daea37d45c28a07ef7a9345911e487e4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RLKUXQGEBTLROEFASK5BSXA6M6/bundle.json","state_url":"https://pith.science/pith/RLKUXQGEBTLROEFASK5BSXA6M6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RLKUXQGEBTLROEFASK5BSXA6M6/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":"2026-08-13T15:08:21Z","links":{"resolver":"https://pith.science/pith/RLKUXQGEBTLROEFASK5BSXA6M6","bundle":"https://pith.science/pith/RLKUXQGEBTLROEFASK5BSXA6M6/bundle.json","state":"https://pith.science/pith/RLKUXQGEBTLROEFASK5BSXA6M6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RLKUXQGEBTLROEFASK5BSXA6M6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:RLKUXQGEBTLROEFASK5BSXA6M6","merge_version":"pith-open-graph-merge-v1","event_count":3,"valid_event_count":3,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d3f494951f31d5d76952f6eee683fa2d801a60c7862a48ac390ab7b4277120f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-31T18:26:07Z","title_canon_sha256":"cd6a2fd94222a1e527971acdbfa8410666af2a73555218b45d8116853eed989b"},"schema_version":"1.0","source":{"id":"2608.00199","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.00199","created_at":"2026-08-04T00:33:56Z"},{"alias_kind":"arxiv_version","alias_value":"2608.00199v1","created_at":"2026-08-04T00:33:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.00199","created_at":"2026-08-04T00:33:56Z"},{"alias_kind":"pith_short_12","alias_value":"RLKUXQGEBTLR","created_at":"2026-08-04T00:33:56Z"},{"alias_kind":"pith_short_16","alias_value":"RLKUXQGEBTLROEFA","created_at":"2026-08-04T00:33:56Z"},{"alias_kind":"pith_short_8","alias_value":"RLKUXQGE","created_at":"2026-08-04T00:33:56Z"}],"graph_snapshots":[{"event_id":"sha256:11ba4ab1b687973e4db91a879e6d17a295347eae35b5e3cce654403f50612d05","target":"graph","created_at":"2026-08-04T00:33:56Z","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/2608.00199/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study global regularity of solutions to Dirichlet or Neumann elliptic problems in spherical sectors $S_{D,R}$ of radius $R>0$ in $\\mathbb{R}^N, N\\ge 2$, where $D$ is the bounded domain on the unit sphere $\\mathbb{S}^{N-1}$ which spans the spherical sector. One of the main results shows that boundedness of the gradient of the solutions of Poisson equations holds whenever $\\lambda_1(D)\\ge N-1$, where $\\lambda_1(D)$ is the first nontrivial eigenvalue of the Laplace Beltrami operator $-\\Delta_{\\mathbb{S}^{N-1}}$ on the domain $D$ with Dirichlet or Neumann boundary conditions on $\\partial D$.\n  ","authors_text":"Camilla Chiara Polvara, Carlo Alberto Antonini, Filomena Pacella, Luigi Provenzano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-31T18:26:07Z","title":"Regularity results for elliptic equations on cones"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.00199","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":"sha256:1f0de75d167a36a477fbd5c5654ccedaf058159096b6f3aee8c13c70527ab111","target":"record","created_at":"2026-08-04T00:33:56Z","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":"d3f494951f31d5d76952f6eee683fa2d801a60c7862a48ac390ab7b4277120f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-31T18:26:07Z","title_canon_sha256":"cd6a2fd94222a1e527971acdbfa8410666af2a73555218b45d8116853eed989b"},"schema_version":"1.0","source":{"id":"2608.00199","kind":"arxiv","version":1}},"canonical_sha256":"8ad54bc0c40cd71710a092ba195c1e67aeef2248abb6e2fed36f2a2d4cb6de4e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ad54bc0c40cd71710a092ba195c1e67aeef2248abb6e2fed36f2a2d4cb6de4e","first_computed_at":"2026-08-04T00:33:56.348424Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-04T00:33:56.348424Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SRPUBAZIUBHgUHGH06TS+xtcmB4BORBrebDK66V+OiJ+ZTPDLfN1ksxzz1P0UeRzw5xwFnrKoW5roOT0kkImAA==","signature_status":"signed_v1","signed_at":"2026-08-04T00:33:56.350210Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.00199","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f0de75d167a36a477fbd5c5654ccedaf058159096b6f3aee8c13c70527ab111","sha256:11ba4ab1b687973e4db91a879e6d17a295347eae35b5e3cce654403f50612d05","sha256:d2290868f65f5c201c0ef0131cf375f4daea37d45c28a07ef7a9345911e487e4"],"state_sha256":"ce1b9b403c9b768fe17522f57d45423225b704d1cae104ec62333f4f84804049"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+/Dvd409yXkTv8E5pUBLdd+X/RORNxCUIXW13JaQ4gxqoijQD3j6AvAPC/Ed2Iglp1K+ZGo2lJ1yMf+wshCUDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T15:08:21.546836Z","bundle_sha256":"ea34de85ea75e249af30d8a53d6a16e29bbad8d7b39f805a1cbc879093c76927"}}