{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:2YCWM6Z3PQ3MNIF5NOYR6QBFTM","short_pith_number":"pith:2YCWM6Z3","canonical_record":{"source":{"id":"1703.10567","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-30T17:04:43Z","cross_cats_sorted":[],"title_canon_sha256":"5081a6fc0eed431a4ee3f09dc2917787db677c866ba1f1d84fb02f26ba59394d","abstract_canon_sha256":"f38c393317c63a8a067cb45a28b15495dcd46fe773ace79b4ccee4cb8acef7eb"},"schema_version":"1.0"},"canonical_sha256":"d605667b3b7c36c6a0bd6bb11f40259b005461dd1dc22a19033bf08d9fbcc68f","source":{"kind":"arxiv","id":"1703.10567","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.10567","created_at":"2026-05-18T00:39:12Z"},{"alias_kind":"arxiv_version","alias_value":"1703.10567v2","created_at":"2026-05-18T00:39:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.10567","created_at":"2026-05-18T00:39:12Z"},{"alias_kind":"pith_short_12","alias_value":"2YCWM6Z3PQ3M","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2YCWM6Z3PQ3MNIF5","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2YCWM6Z3","created_at":"2026-05-18T12:30:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:2YCWM6Z3PQ3MNIF5NOYR6QBFTM","target":"record","payload":{"canonical_record":{"source":{"id":"1703.10567","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-30T17:04:43Z","cross_cats_sorted":[],"title_canon_sha256":"5081a6fc0eed431a4ee3f09dc2917787db677c866ba1f1d84fb02f26ba59394d","abstract_canon_sha256":"f38c393317c63a8a067cb45a28b15495dcd46fe773ace79b4ccee4cb8acef7eb"},"schema_version":"1.0"},"canonical_sha256":"d605667b3b7c36c6a0bd6bb11f40259b005461dd1dc22a19033bf08d9fbcc68f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:12.468198Z","signature_b64":"usyf8ukY+7b7HKHZ3GVDISMiiDnWXhMacGI6hUtWCIqh+G/Ky5YzH4zjKLqM8gYJKYH+FS4dQgyVSkxgyRpBCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d605667b3b7c36c6a0bd6bb11f40259b005461dd1dc22a19033bf08d9fbcc68f","last_reissued_at":"2026-05-18T00:39:12.467667Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:12.467667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.10567","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":"2026-05-18T00:39:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uWmG854S10R5rTpjBgU82QoVV3i5BXyL4dBzBisDXJZ9PwMB45PQjO5y0Yx3OcSt2gcNU6JdKvWRMzMhVxxsCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:39:39.564664Z"},"content_sha256":"3912734a545a4ed8c3d8a0b37fd2c992127d32648cbc86055ead71c0048bdce2","schema_version":"1.0","event_id":"sha256:3912734a545a4ed8c3d8a0b37fd2c992127d32648cbc86055ead71c0048bdce2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:2YCWM6Z3PQ3MNIF5NOYR6QBFTM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weighted Hardy's inequalities and Kolmogorov-type operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Abdelaziz Rhandi, Anna Canale, Cristian Tacelli, Federica Gregorio","submitted_at":"2017-03-30T17:04:43Z","abstract_excerpt":"We give general conditions to state the weighted Hardy inequality \\[ c\\int_{\\mathbb{R}^N}\\frac{\\varphi^2} {|x|^2}d\\mu\\leq\\int_{\\mathbb{R}^N}|\\nabla \\varphi |^2 d\\mu+C\\int_{\\mathbb{R}^N} \\varphi^2d\\mu,\\quad \\varphi\\in C_c^{\\infty}(\\mathbb{R}^N),\\,c\\leq c_{0,\\mu}, \\] with respect to a probability measure $d\\mu$. Moreover, the optimality of the constant $c_{0,\\mu}$ is given. The inequality is related to the following Kolmogorov equation perturbed by a singular potential \\[ Lu+Vu=\\left(\\Delta u+\\frac{\\nabla \\mu}{\\mu}\\cdot \\nabla u\\right)+\\frac{c}{|x|^2}u \\] for which the existence of positive solu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10567","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":"2026-05-18T00:39:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3J9hy8naki1OF4M7zptc33tB2iXSR+Y7yBSVAGc018KNhT31p1gkmH8os1GJ5NKkFu89LQoDHj9bPhi31l69Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:39:39.565234Z"},"content_sha256":"499a58675d2f2bd45f4c4ef139810e55b43daa0b7f17a390bb69fea1b669a7d7","schema_version":"1.0","event_id":"sha256:499a58675d2f2bd45f4c4ef139810e55b43daa0b7f17a390bb69fea1b669a7d7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2YCWM6Z3PQ3MNIF5NOYR6QBFTM/bundle.json","state_url":"https://pith.science/pith/2YCWM6Z3PQ3MNIF5NOYR6QBFTM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2YCWM6Z3PQ3MNIF5NOYR6QBFTM/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":"2026-06-11T22:39:39Z","links":{"resolver":"https://pith.science/pith/2YCWM6Z3PQ3MNIF5NOYR6QBFTM","bundle":"https://pith.science/pith/2YCWM6Z3PQ3MNIF5NOYR6QBFTM/bundle.json","state":"https://pith.science/pith/2YCWM6Z3PQ3MNIF5NOYR6QBFTM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2YCWM6Z3PQ3MNIF5NOYR6QBFTM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2YCWM6Z3PQ3MNIF5NOYR6QBFTM","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":"f38c393317c63a8a067cb45a28b15495dcd46fe773ace79b4ccee4cb8acef7eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-30T17:04:43Z","title_canon_sha256":"5081a6fc0eed431a4ee3f09dc2917787db677c866ba1f1d84fb02f26ba59394d"},"schema_version":"1.0","source":{"id":"1703.10567","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.10567","created_at":"2026-05-18T00:39:12Z"},{"alias_kind":"arxiv_version","alias_value":"1703.10567v2","created_at":"2026-05-18T00:39:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.10567","created_at":"2026-05-18T00:39:12Z"},{"alias_kind":"pith_short_12","alias_value":"2YCWM6Z3PQ3M","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2YCWM6Z3PQ3MNIF5","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2YCWM6Z3","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:499a58675d2f2bd45f4c4ef139810e55b43daa0b7f17a390bb69fea1b669a7d7","target":"graph","created_at":"2026-05-18T00:39:12Z","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 give general conditions to state the weighted Hardy inequality \\[ c\\int_{\\mathbb{R}^N}\\frac{\\varphi^2} {|x|^2}d\\mu\\leq\\int_{\\mathbb{R}^N}|\\nabla \\varphi |^2 d\\mu+C\\int_{\\mathbb{R}^N} \\varphi^2d\\mu,\\quad \\varphi\\in C_c^{\\infty}(\\mathbb{R}^N),\\,c\\leq c_{0,\\mu}, \\] with respect to a probability measure $d\\mu$. Moreover, the optimality of the constant $c_{0,\\mu}$ is given. The inequality is related to the following Kolmogorov equation perturbed by a singular potential \\[ Lu+Vu=\\left(\\Delta u+\\frac{\\nabla \\mu}{\\mu}\\cdot \\nabla u\\right)+\\frac{c}{|x|^2}u \\] for which the existence of positive solu","authors_text":"Abdelaziz Rhandi, Anna Canale, Cristian Tacelli, Federica Gregorio","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-30T17:04:43Z","title":"Weighted Hardy's inequalities and Kolmogorov-type operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10567","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":"sha256:3912734a545a4ed8c3d8a0b37fd2c992127d32648cbc86055ead71c0048bdce2","target":"record","created_at":"2026-05-18T00:39:12Z","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":"f38c393317c63a8a067cb45a28b15495dcd46fe773ace79b4ccee4cb8acef7eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-30T17:04:43Z","title_canon_sha256":"5081a6fc0eed431a4ee3f09dc2917787db677c866ba1f1d84fb02f26ba59394d"},"schema_version":"1.0","source":{"id":"1703.10567","kind":"arxiv","version":2}},"canonical_sha256":"d605667b3b7c36c6a0bd6bb11f40259b005461dd1dc22a19033bf08d9fbcc68f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d605667b3b7c36c6a0bd6bb11f40259b005461dd1dc22a19033bf08d9fbcc68f","first_computed_at":"2026-05-18T00:39:12.467667Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:12.467667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"usyf8ukY+7b7HKHZ3GVDISMiiDnWXhMacGI6hUtWCIqh+G/Ky5YzH4zjKLqM8gYJKYH+FS4dQgyVSkxgyRpBCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:12.468198Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.10567","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3912734a545a4ed8c3d8a0b37fd2c992127d32648cbc86055ead71c0048bdce2","sha256:499a58675d2f2bd45f4c4ef139810e55b43daa0b7f17a390bb69fea1b669a7d7"],"state_sha256":"5819f24df6146999d301b0bc381d08fc98a4dfdd3f941bd557f54fdf2bd0f3fd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GfBUI9v/pnlmF+uMwkwjkeZU+nqt/2GCjP34BG72PiX8EGkAveyQTT7EVypToJVXBGXwf7p+p/qcsCdyfBDSCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T22:39:39.568604Z","bundle_sha256":"0ae505cb331291d11e49e7471fea5399407ec00d50b1fe2ede7d065cdb659a34"}}