{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:JOLCAGKPZD3JCTNSLLJ33RG7O3","short_pith_number":"pith:JOLCAGKP","canonical_record":{"source":{"id":"1609.01080","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-05T10:04:56Z","cross_cats_sorted":[],"title_canon_sha256":"97f022d095399bba3828a61df8423b38ec924f69a63e58dac54ee14c3fb2b599","abstract_canon_sha256":"17a9614740500ae865f990ade9fee7c590c7b2ebbd3719f9ab272dccda3cd902"},"schema_version":"1.0"},"canonical_sha256":"4b9620194fc8f6914db25ad3bdc4df76c9707aabd388a4b5a05a3420693b714a","source":{"kind":"arxiv","id":"1609.01080","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.01080","created_at":"2026-05-18T00:36:39Z"},{"alias_kind":"arxiv_version","alias_value":"1609.01080v3","created_at":"2026-05-18T00:36:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01080","created_at":"2026-05-18T00:36:39Z"},{"alias_kind":"pith_short_12","alias_value":"JOLCAGKPZD3J","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JOLCAGKPZD3JCTNS","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JOLCAGKP","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:JOLCAGKPZD3JCTNSLLJ33RG7O3","target":"record","payload":{"canonical_record":{"source":{"id":"1609.01080","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-05T10:04:56Z","cross_cats_sorted":[],"title_canon_sha256":"97f022d095399bba3828a61df8423b38ec924f69a63e58dac54ee14c3fb2b599","abstract_canon_sha256":"17a9614740500ae865f990ade9fee7c590c7b2ebbd3719f9ab272dccda3cd902"},"schema_version":"1.0"},"canonical_sha256":"4b9620194fc8f6914db25ad3bdc4df76c9707aabd388a4b5a05a3420693b714a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:39.281727Z","signature_b64":"dQhWrUN7k7LhmQw4UG6zN54bleFloDfx4AKdjTClqoqK1+JP3zXu66nDCMErSdLabPuqfOtNAtOt0aAdYlzdAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b9620194fc8f6914db25ad3bdc4df76c9707aabd388a4b5a05a3420693b714a","last_reissued_at":"2026-05-18T00:36:39.281089Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:39.281089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.01080","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:36:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c/Sb7Y6zIifxv967jOc3GoTM/zBB9uHIUIpWMi1Pr1i4oHfYiH09bL5dzRGyoR3kTcagm+MVweQeVpbDqQ8PDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T04:58:39.976485Z"},"content_sha256":"455796a68eb6a2bfa3b49f6580c7fda58e7f30731adbe23d19f28fb5f76bcd7e","schema_version":"1.0","event_id":"sha256:455796a68eb6a2bfa3b49f6580c7fda58e7f30731adbe23d19f28fb5f76bcd7e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:JOLCAGKPZD3JCTNSLLJ33RG7O3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multipolar Hardy inequalities on Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexandru Krist\\'aly, Csaba Farkas, Francesca Faraci","submitted_at":"2016-09-05T10:04:56Z","abstract_excerpt":"We prove multipolar Hardy inequalities on complete Riemannian manifolds, providing various curved counterparts of some Euclidean multipolar inequalities due to Cazacu and Zuazua [Improved multipolar Hardy inequalities, 2013]. We notice that our inequalities deeply depend on the curvature, providing (quantitative) information about the deflection from the flat case. By using these inequalities together with variational methods and group-theoretical arguments, we also establish non-existence, existence and multiplicity results for certain Schr\\\"odinger-type problems involving the Laplace-Beltram"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01080","kind":"arxiv","version":3},"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":"2026-05-18T00:36:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C+9DIOEXdaF6IV7WIM4F4HlCgMrvppUs2ZOXBfvXEib1tWUjh0iX1+M00fl9t4UNXB9i6ljVbOUxalO4GwJnDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T04:58:39.976818Z"},"content_sha256":"da238a60f686ae7140104dc609e13f7b71a6703d6a176f298e4f13a7484c170c","schema_version":"1.0","event_id":"sha256:da238a60f686ae7140104dc609e13f7b71a6703d6a176f298e4f13a7484c170c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JOLCAGKPZD3JCTNSLLJ33RG7O3/bundle.json","state_url":"https://pith.science/pith/JOLCAGKPZD3JCTNSLLJ33RG7O3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JOLCAGKPZD3JCTNSLLJ33RG7O3/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":"2026-06-20T04:58:39Z","links":{"resolver":"https://pith.science/pith/JOLCAGKPZD3JCTNSLLJ33RG7O3","bundle":"https://pith.science/pith/JOLCAGKPZD3JCTNSLLJ33RG7O3/bundle.json","state":"https://pith.science/pith/JOLCAGKPZD3JCTNSLLJ33RG7O3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JOLCAGKPZD3JCTNSLLJ33RG7O3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JOLCAGKPZD3JCTNSLLJ33RG7O3","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":"17a9614740500ae865f990ade9fee7c590c7b2ebbd3719f9ab272dccda3cd902","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-05T10:04:56Z","title_canon_sha256":"97f022d095399bba3828a61df8423b38ec924f69a63e58dac54ee14c3fb2b599"},"schema_version":"1.0","source":{"id":"1609.01080","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.01080","created_at":"2026-05-18T00:36:39Z"},{"alias_kind":"arxiv_version","alias_value":"1609.01080v3","created_at":"2026-05-18T00:36:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01080","created_at":"2026-05-18T00:36:39Z"},{"alias_kind":"pith_short_12","alias_value":"JOLCAGKPZD3J","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JOLCAGKPZD3JCTNS","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JOLCAGKP","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:da238a60f686ae7140104dc609e13f7b71a6703d6a176f298e4f13a7484c170c","target":"graph","created_at":"2026-05-18T00:36:39Z","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":"We prove multipolar Hardy inequalities on complete Riemannian manifolds, providing various curved counterparts of some Euclidean multipolar inequalities due to Cazacu and Zuazua [Improved multipolar Hardy inequalities, 2013]. We notice that our inequalities deeply depend on the curvature, providing (quantitative) information about the deflection from the flat case. By using these inequalities together with variational methods and group-theoretical arguments, we also establish non-existence, existence and multiplicity results for certain Schr\\\"odinger-type problems involving the Laplace-Beltram","authors_text":"Alexandru Krist\\'aly, Csaba Farkas, Francesca Faraci","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-05T10:04:56Z","title":"Multipolar Hardy inequalities on Riemannian manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01080","kind":"arxiv","version":3},"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":"sha256:455796a68eb6a2bfa3b49f6580c7fda58e7f30731adbe23d19f28fb5f76bcd7e","target":"record","created_at":"2026-05-18T00:36:39Z","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":"17a9614740500ae865f990ade9fee7c590c7b2ebbd3719f9ab272dccda3cd902","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-05T10:04:56Z","title_canon_sha256":"97f022d095399bba3828a61df8423b38ec924f69a63e58dac54ee14c3fb2b599"},"schema_version":"1.0","source":{"id":"1609.01080","kind":"arxiv","version":3}},"canonical_sha256":"4b9620194fc8f6914db25ad3bdc4df76c9707aabd388a4b5a05a3420693b714a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b9620194fc8f6914db25ad3bdc4df76c9707aabd388a4b5a05a3420693b714a","first_computed_at":"2026-05-18T00:36:39.281089Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:39.281089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dQhWrUN7k7LhmQw4UG6zN54bleFloDfx4AKdjTClqoqK1+JP3zXu66nDCMErSdLabPuqfOtNAtOt0aAdYlzdAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:39.281727Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.01080","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:455796a68eb6a2bfa3b49f6580c7fda58e7f30731adbe23d19f28fb5f76bcd7e","sha256:da238a60f686ae7140104dc609e13f7b71a6703d6a176f298e4f13a7484c170c"],"state_sha256":"6f482adae7a586cf962704dc5457c792fe2c54ba2a50333921b981e77b851e49"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8OqJLjH4dWtvIOK0vliHVMw6YT+S0+Xadh+GOcG2gU0p5kwbS2eAXvD3UG9YjlGqfijb5nxXjXs72wM5hT9FCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T04:58:39.978693Z","bundle_sha256":"1f0ea438f58638777fb0f1d622068ea83c1de72372bb326a5507764f7c982ad2"}}