{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:EA6C7BVPSUP3KK5ZO4G4XZWNKI","short_pith_number":"pith:EA6C7BVP","canonical_record":{"source":{"id":"1406.5168","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-19T19:51:33Z","cross_cats_sorted":[],"title_canon_sha256":"687ba55ac9c9a5b07aed0b1aea3a8a0dae912e746b32e1936c97050dd42e0803","abstract_canon_sha256":"f479ded92055771ba04ef00b1fb219702388469fcb089938cf2bf37bfc16bfd9"},"schema_version":"1.0"},"canonical_sha256":"203c2f86af951fb52bb9770dcbe6cd522dd043e10b49c2dc1ac52c6a17fe3264","source":{"kind":"arxiv","id":"1406.5168","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.5168","created_at":"2026-05-18T02:30:15Z"},{"alias_kind":"arxiv_version","alias_value":"1406.5168v2","created_at":"2026-05-18T02:30:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5168","created_at":"2026-05-18T02:30:15Z"},{"alias_kind":"pith_short_12","alias_value":"EA6C7BVPSUP3","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"EA6C7BVPSUP3KK5Z","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"EA6C7BVP","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:EA6C7BVPSUP3KK5ZO4G4XZWNKI","target":"record","payload":{"canonical_record":{"source":{"id":"1406.5168","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-19T19:51:33Z","cross_cats_sorted":[],"title_canon_sha256":"687ba55ac9c9a5b07aed0b1aea3a8a0dae912e746b32e1936c97050dd42e0803","abstract_canon_sha256":"f479ded92055771ba04ef00b1fb219702388469fcb089938cf2bf37bfc16bfd9"},"schema_version":"1.0"},"canonical_sha256":"203c2f86af951fb52bb9770dcbe6cd522dd043e10b49c2dc1ac52c6a17fe3264","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:15.520990Z","signature_b64":"C5opHRWJRoxto3S7NpLeM188qhKaAU4Y4Y28a9P6fgnVeRZw68araLquaBKuJHu2sYFJUHOfoZwn2obGDjXuBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"203c2f86af951fb52bb9770dcbe6cd522dd043e10b49c2dc1ac52c6a17fe3264","last_reissued_at":"2026-05-18T02:30:15.520530Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:15.520530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.5168","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":"2026-05-18T02:30:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1YKRyqGHikyTSYDcut/X3kdiwijcKxriQ3CqqKQemCoxqTEG4Q9bZGgIMHclrVkF43+REDLd8aWLe5CObQQsCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T04:50:04.662670Z"},"content_sha256":"fd95b4aac731d4d98bdc5e5db386fb6e176e0b3f380c20b6de8668b4d3e18d5a","schema_version":"1.0","event_id":"sha256:fd95b4aac731d4d98bdc5e5db386fb6e176e0b3f380c20b6de8668b4d3e18d5a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:EA6C7BVPSUP3KK5ZO4G4XZWNKI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Qualitative properties of solutions for an integral system related to the Hardy-Sobolev inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"John Villavert","submitted_at":"2014-06-19T19:51:33Z","abstract_excerpt":"This article carries out a qualitative analysis on a system of integral equations of the Hardy--Sobolev type. Namely, results concerning Liouville type properties and the fast and slow decay rates of positive solutions for the system are established. For a bounded and decaying positive solution, it is shown that it either decays with the slow rates or the fast rates depending on its integrability. Particularly, a criterion for distinguishing integrable solutions from other bounded and decaying solutions in terms of their asymptotic behavior is provided. Moreover, related results on the optimal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5168","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":""},"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":"/bR+JHtcNfJJ62Z0JiSMAkZ73RC0sK+NokHKi200aP1Xg8hLW3FI76pGbrEWL9R/n80ilWHDhTJvCcpQbkTfBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T04:50:04.663024Z"},"content_sha256":"61bdd134e59ae68bde0158a4d31cef8862712ce7871d151602a64a06b532d6a3","schema_version":"1.0","event_id":"sha256:61bdd134e59ae68bde0158a4d31cef8862712ce7871d151602a64a06b532d6a3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EA6C7BVPSUP3KK5ZO4G4XZWNKI/bundle.json","state_url":"https://pith.science/pith/EA6C7BVPSUP3KK5ZO4G4XZWNKI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EA6C7BVPSUP3KK5ZO4G4XZWNKI/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":"2026-06-01T04:50:04Z","links":{"resolver":"https://pith.science/pith/EA6C7BVPSUP3KK5ZO4G4XZWNKI","bundle":"https://pith.science/pith/EA6C7BVPSUP3KK5ZO4G4XZWNKI/bundle.json","state":"https://pith.science/pith/EA6C7BVPSUP3KK5ZO4G4XZWNKI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EA6C7BVPSUP3KK5ZO4G4XZWNKI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:EA6C7BVPSUP3KK5ZO4G4XZWNKI","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":"f479ded92055771ba04ef00b1fb219702388469fcb089938cf2bf37bfc16bfd9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-19T19:51:33Z","title_canon_sha256":"687ba55ac9c9a5b07aed0b1aea3a8a0dae912e746b32e1936c97050dd42e0803"},"schema_version":"1.0","source":{"id":"1406.5168","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.5168","created_at":"2026-05-18T02:30:15Z"},{"alias_kind":"arxiv_version","alias_value":"1406.5168v2","created_at":"2026-05-18T02:30:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5168","created_at":"2026-05-18T02:30:15Z"},{"alias_kind":"pith_short_12","alias_value":"EA6C7BVPSUP3","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"EA6C7BVPSUP3KK5Z","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"EA6C7BVP","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:61bdd134e59ae68bde0158a4d31cef8862712ce7871d151602a64a06b532d6a3","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 article carries out a qualitative analysis on a system of integral equations of the Hardy--Sobolev type. Namely, results concerning Liouville type properties and the fast and slow decay rates of positive solutions for the system are established. For a bounded and decaying positive solution, it is shown that it either decays with the slow rates or the fast rates depending on its integrability. Particularly, a criterion for distinguishing integrable solutions from other bounded and decaying solutions in terms of their asymptotic behavior is provided. Moreover, related results on the optimal","authors_text":"John Villavert","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-19T19:51:33Z","title":"Qualitative properties of solutions for an integral system related to the Hardy-Sobolev inequality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5168","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:fd95b4aac731d4d98bdc5e5db386fb6e176e0b3f380c20b6de8668b4d3e18d5a","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":"f479ded92055771ba04ef00b1fb219702388469fcb089938cf2bf37bfc16bfd9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-19T19:51:33Z","title_canon_sha256":"687ba55ac9c9a5b07aed0b1aea3a8a0dae912e746b32e1936c97050dd42e0803"},"schema_version":"1.0","source":{"id":"1406.5168","kind":"arxiv","version":2}},"canonical_sha256":"203c2f86af951fb52bb9770dcbe6cd522dd043e10b49c2dc1ac52c6a17fe3264","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"203c2f86af951fb52bb9770dcbe6cd522dd043e10b49c2dc1ac52c6a17fe3264","first_computed_at":"2026-05-18T02:30:15.520530Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:15.520530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C5opHRWJRoxto3S7NpLeM188qhKaAU4Y4Y28a9P6fgnVeRZw68araLquaBKuJHu2sYFJUHOfoZwn2obGDjXuBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:15.520990Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.5168","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd95b4aac731d4d98bdc5e5db386fb6e176e0b3f380c20b6de8668b4d3e18d5a","sha256:61bdd134e59ae68bde0158a4d31cef8862712ce7871d151602a64a06b532d6a3"],"state_sha256":"4302cc08276434c79d4ebbbdccb947870f6c8accfc09f34eb74f4e0ec8b0d366"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fX1DsBoOg3807CQU0vidsFzM4QzUUFoPeo8sGPrGQzXYnmPDUdu8TbIx24I2vgLlLUUl3SCKmxIxJMFH8ACeDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T04:50:04.665304Z","bundle_sha256":"96bd428253b34310f82c0e177b483ea4692038b570087a3803a7eabde6d68fbd"}}