{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:AL7OOZ4XKAXBJN74AM7J7GF54Y","short_pith_number":"pith:AL7OOZ4X","canonical_record":{"source":{"id":"1401.5454","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-21T20:33:33Z","cross_cats_sorted":[],"title_canon_sha256":"1e9688324b39ded264260abcd2844f2f7303c99ade14ba3f25596c700e476cee","abstract_canon_sha256":"9939eb01023807dd949549112955203c83d9b8987cad6cf08ade1f69a9ba24bf"},"schema_version":"1.0"},"canonical_sha256":"02fee76797502e14b7fc033e9f98bde63149129a26ee7e452698dc12c74ff595","source":{"kind":"arxiv","id":"1401.5454","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.5454","created_at":"2026-05-18T02:30:15Z"},{"alias_kind":"arxiv_version","alias_value":"1401.5454v3","created_at":"2026-05-18T02:30:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.5454","created_at":"2026-05-18T02:30:15Z"},{"alias_kind":"pith_short_12","alias_value":"AL7OOZ4XKAXB","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AL7OOZ4XKAXBJN74","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AL7OOZ4X","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:AL7OOZ4XKAXBJN74AM7J7GF54Y","target":"record","payload":{"canonical_record":{"source":{"id":"1401.5454","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-21T20:33:33Z","cross_cats_sorted":[],"title_canon_sha256":"1e9688324b39ded264260abcd2844f2f7303c99ade14ba3f25596c700e476cee","abstract_canon_sha256":"9939eb01023807dd949549112955203c83d9b8987cad6cf08ade1f69a9ba24bf"},"schema_version":"1.0"},"canonical_sha256":"02fee76797502e14b7fc033e9f98bde63149129a26ee7e452698dc12c74ff595","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:15.739147Z","signature_b64":"hUf6p5TKe2/rPczQmGYseGMSqvRoEp0bIr0IBI58zU8hSU0AEGQcrrINs7Itz5H0ah+/+hQgT2biTVmRZ54ACw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02fee76797502e14b7fc033e9f98bde63149129a26ee7e452698dc12c74ff595","last_reissued_at":"2026-05-18T02:30:15.738763Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:15.738763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.5454","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":"2026-05-18T02:30:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4mbKYdPSs/kNkrb5qdL5lwPL4bjcF8JEHOtYLuxGgw5Up8uuFS2zyGsR9ifmjR4UVUQezNeKEBIy4dtmVgnlAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:18:50.830366Z"},"content_sha256":"f0e40afb708878ba49825ad1d17594cd51f60e794c92cee6433189979375954b","schema_version":"1.0","event_id":"sha256:f0e40afb708878ba49825ad1d17594cd51f60e794c92cee6433189979375954b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:AL7OOZ4XKAXBJN74AM7J7GF54Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sharp existence criteria for positive solutions of Hardy-Sobolev type systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"John Villavert","submitted_at":"2014-01-21T20:33:33Z","abstract_excerpt":"This paper examines systems of poly-harmonic equations of the Hardy--Sobolev type and the closely related weighted systems of integral equations involving Riesz potentials. Namely, it is shown that the two systems are equivalent under some appropriate conditions. Then a sharp criterion for the existence and non-existence of positive solutions is determined for both differential and integral versions of a Hardy--Sobolev type system with variable coefficients. In the constant coefficient case, Liouville type theorems for positive radial solutions are also established using radial decay estimates"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5454","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":"2026-05-18T02:30:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IqSnAsR0jQvBDm2ojthb/4UV9iRHQnRcI9sFvcoFZXwEjHEegL+3jbpVIpuNZo14oRM1WiAr5M9G6THW93l/Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:18:50.830710Z"},"content_sha256":"9b4afc848e39020f32856cb40152fc05dea0bc015327974f049fefb31bd7620f","schema_version":"1.0","event_id":"sha256:9b4afc848e39020f32856cb40152fc05dea0bc015327974f049fefb31bd7620f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AL7OOZ4XKAXBJN74AM7J7GF54Y/bundle.json","state_url":"https://pith.science/pith/AL7OOZ4XKAXBJN74AM7J7GF54Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AL7OOZ4XKAXBJN74AM7J7GF54Y/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":"2026-06-01T07:18:50Z","links":{"resolver":"https://pith.science/pith/AL7OOZ4XKAXBJN74AM7J7GF54Y","bundle":"https://pith.science/pith/AL7OOZ4XKAXBJN74AM7J7GF54Y/bundle.json","state":"https://pith.science/pith/AL7OOZ4XKAXBJN74AM7J7GF54Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AL7OOZ4XKAXBJN74AM7J7GF54Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:AL7OOZ4XKAXBJN74AM7J7GF54Y","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":"9939eb01023807dd949549112955203c83d9b8987cad6cf08ade1f69a9ba24bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-21T20:33:33Z","title_canon_sha256":"1e9688324b39ded264260abcd2844f2f7303c99ade14ba3f25596c700e476cee"},"schema_version":"1.0","source":{"id":"1401.5454","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.5454","created_at":"2026-05-18T02:30:15Z"},{"alias_kind":"arxiv_version","alias_value":"1401.5454v3","created_at":"2026-05-18T02:30:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.5454","created_at":"2026-05-18T02:30:15Z"},{"alias_kind":"pith_short_12","alias_value":"AL7OOZ4XKAXB","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AL7OOZ4XKAXBJN74","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AL7OOZ4X","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:9b4afc848e39020f32856cb40152fc05dea0bc015327974f049fefb31bd7620f","target":"graph","created_at":"2026-05-18T02:30:15Z","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":"This paper examines systems of poly-harmonic equations of the Hardy--Sobolev type and the closely related weighted systems of integral equations involving Riesz potentials. Namely, it is shown that the two systems are equivalent under some appropriate conditions. Then a sharp criterion for the existence and non-existence of positive solutions is determined for both differential and integral versions of a Hardy--Sobolev type system with variable coefficients. In the constant coefficient case, Liouville type theorems for positive radial solutions are also established using radial decay estimates","authors_text":"John Villavert","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-21T20:33:33Z","title":"Sharp existence criteria for positive solutions of Hardy-Sobolev type systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5454","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:f0e40afb708878ba49825ad1d17594cd51f60e794c92cee6433189979375954b","target":"record","created_at":"2026-05-18T02:30:15Z","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":"9939eb01023807dd949549112955203c83d9b8987cad6cf08ade1f69a9ba24bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-21T20:33:33Z","title_canon_sha256":"1e9688324b39ded264260abcd2844f2f7303c99ade14ba3f25596c700e476cee"},"schema_version":"1.0","source":{"id":"1401.5454","kind":"arxiv","version":3}},"canonical_sha256":"02fee76797502e14b7fc033e9f98bde63149129a26ee7e452698dc12c74ff595","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02fee76797502e14b7fc033e9f98bde63149129a26ee7e452698dc12c74ff595","first_computed_at":"2026-05-18T02:30:15.738763Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:15.738763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hUf6p5TKe2/rPczQmGYseGMSqvRoEp0bIr0IBI58zU8hSU0AEGQcrrINs7Itz5H0ah+/+hQgT2biTVmRZ54ACw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:15.739147Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.5454","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0e40afb708878ba49825ad1d17594cd51f60e794c92cee6433189979375954b","sha256:9b4afc848e39020f32856cb40152fc05dea0bc015327974f049fefb31bd7620f"],"state_sha256":"d15c948eed3f60a554fdc9ed7504f1abdaf8190c9cd35bbed81c53caf24a2877"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WeMN2q0sR+ZLODcXig/aqLtF1gUkqvTPpqMPPMbkOD1WdIsZmtXffgyGzgHmY8o5QsCGBkEVCktivF3qbJHOBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T07:18:50.832591Z","bundle_sha256":"1fa678f2bee4f13c5c8d9bc91b93fe3f882aa48fded9097e60b3529bb6ffc4e0"}}