{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:L3LMRUZ7PKEG5JXMZOZXG6YYQ7","short_pith_number":"pith:L3LMRUZ7","canonical_record":{"source":{"id":"2406.16735","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AP","submitted_at":"2024-06-24T15:43:27Z","cross_cats_sorted":[],"title_canon_sha256":"7b9986a65178f2c6b1df2d6eef14077cc0f569aee01ac2d0ec492b53a017fed4","abstract_canon_sha256":"ed859c8598a8f737bc20e738b869f9f3cd475f2336edf7e8c973c7a2f782ad12"},"schema_version":"1.0"},"canonical_sha256":"5ed6c8d33f7a886ea6eccbb3737b1887c928f25398822d7da2289432107aa2c4","source":{"kind":"arxiv","id":"2406.16735","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.16735","created_at":"2026-07-05T08:36:02Z"},{"alias_kind":"arxiv_version","alias_value":"2406.16735v1","created_at":"2026-07-05T08:36:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.16735","created_at":"2026-07-05T08:36:02Z"},{"alias_kind":"pith_short_12","alias_value":"L3LMRUZ7PKEG","created_at":"2026-07-05T08:36:02Z"},{"alias_kind":"pith_short_16","alias_value":"L3LMRUZ7PKEG5JXM","created_at":"2026-07-05T08:36:02Z"},{"alias_kind":"pith_short_8","alias_value":"L3LMRUZ7","created_at":"2026-07-05T08:36:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:L3LMRUZ7PKEG5JXMZOZXG6YYQ7","target":"record","payload":{"canonical_record":{"source":{"id":"2406.16735","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AP","submitted_at":"2024-06-24T15:43:27Z","cross_cats_sorted":[],"title_canon_sha256":"7b9986a65178f2c6b1df2d6eef14077cc0f569aee01ac2d0ec492b53a017fed4","abstract_canon_sha256":"ed859c8598a8f737bc20e738b869f9f3cd475f2336edf7e8c973c7a2f782ad12"},"schema_version":"1.0"},"canonical_sha256":"5ed6c8d33f7a886ea6eccbb3737b1887c928f25398822d7da2289432107aa2c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:36:02.990375Z","signature_b64":"SUhsEUzHE4aXQiJ2Ej49Q3g4qfR63uiyJtsaQKmoAbRcHyM0JSp2+y/oxcLDUe+xtcykLDiLmIXUgqCg1IRRBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ed6c8d33f7a886ea6eccbb3737b1887c928f25398822d7da2289432107aa2c4","last_reissued_at":"2026-07-05T08:36:02.989957Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:36:02.989957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2406.16735","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":"2026-07-05T08:36:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dsCLwDZs/LtO6vp4BpqKfraqMIzdj9i0oyL0gxyEcQmahPUlBDFdwNW8B2TpNymSiZFFJjjgCcTtsMWbTwLRCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T23:59:03.278445Z"},"content_sha256":"f0239d8465176fe30441cedc4fab69e8506eb5ce8d6465779959daadfe361072","schema_version":"1.0","event_id":"sha256:f0239d8465176fe30441cedc4fab69e8506eb5ce8d6465779959daadfe361072"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:L3LMRUZ7PKEG5JXMZOZXG6YYQ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The $L^p$ Poisson-Neumann problem and its relation to the Neumann problem","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Joseph Feneuil, Linhan Li","submitted_at":"2024-06-24T15:43:27Z","abstract_excerpt":"We introduce the $L^p$ Poisson-Neumann problem for an uniformly elliptic operator $L=-\\rm{div }A\\nabla$ in divergence form in a bounded 1-sided Chord Arc Domain $\\Omega$, which considers solutions to $Lu=h-\\rm{div}\\vec{F}$ in $\\Omega$ with zero Neumann data on the boundary for $h$ and $\\vec F$ in some tent spaces. We give different characterizations of solvability of the $L^p$ Poisson-Neumann problem and its weaker variants, and in particular, we show that solvability of the weak $L^p$ Poisson-Neumann probelm is equivalent to a weak reverse H\\\"older inequality. We show that the Poisson-Neumman"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.16735","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/2406.16735/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":"2026-07-05T08:36:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RsU2cjpJWQvoEbnDs9KSjNB8DmiyP1gxf9y8+MOe1VlfzF6g8fB5N0Y9SSJ4j7YzX8YnnPxZ//jfoI2XGe1eBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T23:59:03.279113Z"},"content_sha256":"5892e42d33c836eb4d1ab1b19a6205e50c77c52d24b6c1df76705dcae6a3857b","schema_version":"1.0","event_id":"sha256:5892e42d33c836eb4d1ab1b19a6205e50c77c52d24b6c1df76705dcae6a3857b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L3LMRUZ7PKEG5JXMZOZXG6YYQ7/bundle.json","state_url":"https://pith.science/pith/L3LMRUZ7PKEG5JXMZOZXG6YYQ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L3LMRUZ7PKEG5JXMZOZXG6YYQ7/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":"2026-08-09T23:59:03Z","links":{"resolver":"https://pith.science/pith/L3LMRUZ7PKEG5JXMZOZXG6YYQ7","bundle":"https://pith.science/pith/L3LMRUZ7PKEG5JXMZOZXG6YYQ7/bundle.json","state":"https://pith.science/pith/L3LMRUZ7PKEG5JXMZOZXG6YYQ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L3LMRUZ7PKEG5JXMZOZXG6YYQ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:L3LMRUZ7PKEG5JXMZOZXG6YYQ7","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":"ed859c8598a8f737bc20e738b869f9f3cd475f2336edf7e8c973c7a2f782ad12","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AP","submitted_at":"2024-06-24T15:43:27Z","title_canon_sha256":"7b9986a65178f2c6b1df2d6eef14077cc0f569aee01ac2d0ec492b53a017fed4"},"schema_version":"1.0","source":{"id":"2406.16735","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.16735","created_at":"2026-07-05T08:36:02Z"},{"alias_kind":"arxiv_version","alias_value":"2406.16735v1","created_at":"2026-07-05T08:36:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.16735","created_at":"2026-07-05T08:36:02Z"},{"alias_kind":"pith_short_12","alias_value":"L3LMRUZ7PKEG","created_at":"2026-07-05T08:36:02Z"},{"alias_kind":"pith_short_16","alias_value":"L3LMRUZ7PKEG5JXM","created_at":"2026-07-05T08:36:02Z"},{"alias_kind":"pith_short_8","alias_value":"L3LMRUZ7","created_at":"2026-07-05T08:36:02Z"}],"graph_snapshots":[{"event_id":"sha256:5892e42d33c836eb4d1ab1b19a6205e50c77c52d24b6c1df76705dcae6a3857b","target":"graph","created_at":"2026-07-05T08:36:02Z","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/2406.16735/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce the $L^p$ Poisson-Neumann problem for an uniformly elliptic operator $L=-\\rm{div }A\\nabla$ in divergence form in a bounded 1-sided Chord Arc Domain $\\Omega$, which considers solutions to $Lu=h-\\rm{div}\\vec{F}$ in $\\Omega$ with zero Neumann data on the boundary for $h$ and $\\vec F$ in some tent spaces. We give different characterizations of solvability of the $L^p$ Poisson-Neumann problem and its weaker variants, and in particular, we show that solvability of the weak $L^p$ Poisson-Neumann probelm is equivalent to a weak reverse H\\\"older inequality. We show that the Poisson-Neumman","authors_text":"Joseph Feneuil, Linhan Li","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AP","submitted_at":"2024-06-24T15:43:27Z","title":"The $L^p$ Poisson-Neumann problem and its relation to the Neumann problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.16735","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:f0239d8465176fe30441cedc4fab69e8506eb5ce8d6465779959daadfe361072","target":"record","created_at":"2026-07-05T08:36:02Z","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":"ed859c8598a8f737bc20e738b869f9f3cd475f2336edf7e8c973c7a2f782ad12","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AP","submitted_at":"2024-06-24T15:43:27Z","title_canon_sha256":"7b9986a65178f2c6b1df2d6eef14077cc0f569aee01ac2d0ec492b53a017fed4"},"schema_version":"1.0","source":{"id":"2406.16735","kind":"arxiv","version":1}},"canonical_sha256":"5ed6c8d33f7a886ea6eccbb3737b1887c928f25398822d7da2289432107aa2c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ed6c8d33f7a886ea6eccbb3737b1887c928f25398822d7da2289432107aa2c4","first_computed_at":"2026-07-05T08:36:02.989957Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:36:02.989957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SUhsEUzHE4aXQiJ2Ej49Q3g4qfR63uiyJtsaQKmoAbRcHyM0JSp2+y/oxcLDUe+xtcykLDiLmIXUgqCg1IRRBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:36:02.990375Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.16735","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0239d8465176fe30441cedc4fab69e8506eb5ce8d6465779959daadfe361072","sha256:5892e42d33c836eb4d1ab1b19a6205e50c77c52d24b6c1df76705dcae6a3857b"],"state_sha256":"3a53b1d95213f5db9dfe6c56dfd9843c379ce75e102a6eea660d4ec6aac5b272"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MLJkL11+NTFdByAPPCgB4MZLRCZfdQq1SfF9sH/sEHjGKgNdSVfltRoc2VCIb3H+e0jw7nkElqtgVHqs2dafCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T23:59:03.285140Z","bundle_sha256":"1378f8210159c95a4cd8ee368efe8b9fda9d2f899b202bebcce9b2536a4411a7"}}