{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:LF4LIMKRG47X3VRHS42J4WTQWT","short_pith_number":"pith:LF4LIMKR","canonical_record":{"source":{"id":"2506.01434","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-06-02T08:50:23Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"eec53bc496839a9b3d54033879cb6aca491a655324c4837b6e84c30693792986","abstract_canon_sha256":"1bc43f19863f41cb89dbf3c7aa3a40b39a5422ec40c297dcae9946499d57dfe7"},"schema_version":"1.0"},"canonical_sha256":"5978b43151373f7dd62797349e5a70b4ef5f0271e8f18f1a033e7092c44cd497","source":{"kind":"arxiv","id":"2506.01434","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.01434","created_at":"2026-07-05T11:41:42Z"},{"alias_kind":"arxiv_version","alias_value":"2506.01434v2","created_at":"2026-07-05T11:41:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.01434","created_at":"2026-07-05T11:41:42Z"},{"alias_kind":"pith_short_12","alias_value":"LF4LIMKRG47X","created_at":"2026-07-05T11:41:42Z"},{"alias_kind":"pith_short_16","alias_value":"LF4LIMKRG47X3VRH","created_at":"2026-07-05T11:41:42Z"},{"alias_kind":"pith_short_8","alias_value":"LF4LIMKR","created_at":"2026-07-05T11:41:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:LF4LIMKRG47X3VRHS42J4WTQWT","target":"record","payload":{"canonical_record":{"source":{"id":"2506.01434","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-06-02T08:50:23Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"eec53bc496839a9b3d54033879cb6aca491a655324c4837b6e84c30693792986","abstract_canon_sha256":"1bc43f19863f41cb89dbf3c7aa3a40b39a5422ec40c297dcae9946499d57dfe7"},"schema_version":"1.0"},"canonical_sha256":"5978b43151373f7dd62797349e5a70b4ef5f0271e8f18f1a033e7092c44cd497","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:41:42.533846Z","signature_b64":"lxwcX7fO3cxFsD8sEOZIZu5VXo1CLIuBU+gtH+X7bmHm5bLGGhJM7c/gbr+xZvlMERl/6jh6pAjZanLM2DVqDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5978b43151373f7dd62797349e5a70b4ef5f0271e8f18f1a033e7092c44cd497","last_reissued_at":"2026-07-05T11:41:42.533212Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:41:42.533212Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.01434","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:41:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gJrNNMEjBlq5Q/pYQYr1WuC3ejTNb81t9ZYYbLFtBatshYNXJajhvFFzOZYef/lpkKWfxHR4immk4Sh3lvi0Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T10:41:50.311368Z"},"content_sha256":"9b30ec41debd9fdcfd8f0aca58da153ed0eda38e9ede312fe77ef5c0a8911e0d","schema_version":"1.0","event_id":"sha256:9b30ec41debd9fdcfd8f0aca58da153ed0eda38e9ede312fe77ef5c0a8911e0d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:LF4LIMKRG47X3VRHS42J4WTQWT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"General monotone formula for homogeneous $k$-Hessian equation in the exterior domain and its applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Jiabin Yin, Xingjian Zhou","submitted_at":"2025-06-02T08:50:23Z","abstract_excerpt":"In this paper, we deal with an overdetermined problem for the $k$-Hessian equation ($1\\leq k<\\frac n2$) in the exterior domain and prove the corresponding ball characterizations. Since that Weinberger type approach seems to fail to solve the problem, we give a new perspective to solve exterior overdetermined problem by combining two integral identities and geometric inequalities inspired by Brandolini-Nitsch-Salani's results \\cite{BNS}. Meanwhile, we establish general monotone formulas to derive geometric inequalities related to $k$-admissible solution $u$ in $\\mathbb R^n\\setminus\\Omega$, wher"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.01434","kind":"arxiv","version":2},"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/2506.01434/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":"2026-07-05T11:41:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mriy0XF4adMY2tGRGW8LIZnHFBrZpLxps4s/j0kVbvFRiebYhmvBw/C3WOCIt0l0PEqVX+aiSs9F4OGC2JFbCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T10:41:50.312336Z"},"content_sha256":"ddade2a8bd2a6f2b4fef0b3850cdbd8ba717f1a962aa84b6ee28b674e2f69b7c","schema_version":"1.0","event_id":"sha256:ddade2a8bd2a6f2b4fef0b3850cdbd8ba717f1a962aa84b6ee28b674e2f69b7c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LF4LIMKRG47X3VRHS42J4WTQWT/bundle.json","state_url":"https://pith.science/pith/LF4LIMKRG47X3VRHS42J4WTQWT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LF4LIMKRG47X3VRHS42J4WTQWT/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":"2026-08-08T10:41:50Z","links":{"resolver":"https://pith.science/pith/LF4LIMKRG47X3VRHS42J4WTQWT","bundle":"https://pith.science/pith/LF4LIMKRG47X3VRHS42J4WTQWT/bundle.json","state":"https://pith.science/pith/LF4LIMKRG47X3VRHS42J4WTQWT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LF4LIMKRG47X3VRHS42J4WTQWT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:LF4LIMKRG47X3VRHS42J4WTQWT","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":"1bc43f19863f41cb89dbf3c7aa3a40b39a5422ec40c297dcae9946499d57dfe7","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-06-02T08:50:23Z","title_canon_sha256":"eec53bc496839a9b3d54033879cb6aca491a655324c4837b6e84c30693792986"},"schema_version":"1.0","source":{"id":"2506.01434","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.01434","created_at":"2026-07-05T11:41:42Z"},{"alias_kind":"arxiv_version","alias_value":"2506.01434v2","created_at":"2026-07-05T11:41:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.01434","created_at":"2026-07-05T11:41:42Z"},{"alias_kind":"pith_short_12","alias_value":"LF4LIMKRG47X","created_at":"2026-07-05T11:41:42Z"},{"alias_kind":"pith_short_16","alias_value":"LF4LIMKRG47X3VRH","created_at":"2026-07-05T11:41:42Z"},{"alias_kind":"pith_short_8","alias_value":"LF4LIMKR","created_at":"2026-07-05T11:41:42Z"}],"graph_snapshots":[{"event_id":"sha256:ddade2a8bd2a6f2b4fef0b3850cdbd8ba717f1a962aa84b6ee28b674e2f69b7c","target":"graph","created_at":"2026-07-05T11:41:42Z","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/2506.01434/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we deal with an overdetermined problem for the $k$-Hessian equation ($1\\leq k<\\frac n2$) in the exterior domain and prove the corresponding ball characterizations. Since that Weinberger type approach seems to fail to solve the problem, we give a new perspective to solve exterior overdetermined problem by combining two integral identities and geometric inequalities inspired by Brandolini-Nitsch-Salani's results \\cite{BNS}. Meanwhile, we establish general monotone formulas to derive geometric inequalities related to $k$-admissible solution $u$ in $\\mathbb R^n\\setminus\\Omega$, wher","authors_text":"Jiabin Yin, Xingjian Zhou","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-06-02T08:50:23Z","title":"General monotone formula for homogeneous $k$-Hessian equation in the exterior domain and its applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.01434","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":"sha256:9b30ec41debd9fdcfd8f0aca58da153ed0eda38e9ede312fe77ef5c0a8911e0d","target":"record","created_at":"2026-07-05T11:41:42Z","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":"1bc43f19863f41cb89dbf3c7aa3a40b39a5422ec40c297dcae9946499d57dfe7","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-06-02T08:50:23Z","title_canon_sha256":"eec53bc496839a9b3d54033879cb6aca491a655324c4837b6e84c30693792986"},"schema_version":"1.0","source":{"id":"2506.01434","kind":"arxiv","version":2}},"canonical_sha256":"5978b43151373f7dd62797349e5a70b4ef5f0271e8f18f1a033e7092c44cd497","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5978b43151373f7dd62797349e5a70b4ef5f0271e8f18f1a033e7092c44cd497","first_computed_at":"2026-07-05T11:41:42.533212Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:41:42.533212Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lxwcX7fO3cxFsD8sEOZIZu5VXo1CLIuBU+gtH+X7bmHm5bLGGhJM7c/gbr+xZvlMERl/6jh6pAjZanLM2DVqDw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:41:42.533846Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.01434","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b30ec41debd9fdcfd8f0aca58da153ed0eda38e9ede312fe77ef5c0a8911e0d","sha256:ddade2a8bd2a6f2b4fef0b3850cdbd8ba717f1a962aa84b6ee28b674e2f69b7c"],"state_sha256":"f39049e62776676822f2a118c3821ec2e9bb764d2675c1ede9e65199fe56ec05"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bncsKHnsB9GBFZndzI/nPaHMFJJ/HSJF0hjiREZhgFViBxWtrd1SyIGV8vNWk1RWLE3W+92AQm48IUPk5zxdAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T10:41:50.318374Z","bundle_sha256":"76a7f67d38151abe88d4caae62cfd439fceab6fe216cf2d69c859ed142ff9579"}}