{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:PUENM42MFQ5MOHDRS773TVKZVI","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":"971bec2919236da33b2a7b5b971b8c3478d3325f71959a588f521a770800da25","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-06-16T06:04:39Z","title_canon_sha256":"8ab15b1b85599e9be32e6eed695ef26f6c010f635c986e951820654e28515afd"},"schema_version":"1.0","source":{"id":"2606.17558","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.17558","created_at":"2026-06-19T16:10:15Z"},{"alias_kind":"arxiv_version","alias_value":"2606.17558v1","created_at":"2026-06-19T16:10:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.17558","created_at":"2026-06-19T16:10:15Z"},{"alias_kind":"pith_short_12","alias_value":"PUENM42MFQ5M","created_at":"2026-06-19T16:10:15Z"},{"alias_kind":"pith_short_16","alias_value":"PUENM42MFQ5MOHDR","created_at":"2026-06-19T16:10:15Z"},{"alias_kind":"pith_short_8","alias_value":"PUENM42M","created_at":"2026-06-19T16:10:15Z"}],"graph_snapshots":[{"event_id":"sha256:3a641d53910f30307f0db0a665ccd28f65aacc5844f77d5bda1108f4824124fc","target":"graph","created_at":"2026-06-19T16:10:15Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.17558/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we provide a complete characterization of the weighted Hardy inequalities involving the supremum operator, restricted to the cone of non-increasing sequences, for all positive parameters. We reduce such inequalities to equivalent ones on the cone of non-negative sequences. The latter setting provides a broader framework for analysis and significantly expands the range of proofs that can be established.","authors_text":"Amiran Gogatishvili, Nurgul Kuzeubayeva, Nurzhan Bokayev, Tu\\u{g}\\c{c}e \\\"Unver","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-06-16T06:04:39Z","title":"Weighted Hardy inequalities involving supremum for decreasing sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17558","kind":"arxiv","version":1},"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:e11b39016eb00028c8f65f3f724dcadf9cbe5f1bd78d6f200b1461dab509bfaf","target":"record","created_at":"2026-06-19T16:10:15Z","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":"971bec2919236da33b2a7b5b971b8c3478d3325f71959a588f521a770800da25","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-06-16T06:04:39Z","title_canon_sha256":"8ab15b1b85599e9be32e6eed695ef26f6c010f635c986e951820654e28515afd"},"schema_version":"1.0","source":{"id":"2606.17558","kind":"arxiv","version":1}},"canonical_sha256":"7d08d6734c2c3ac71c7197ffb9d559aa1fd79cbca01acd032590569e788f2581","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d08d6734c2c3ac71c7197ffb9d559aa1fd79cbca01acd032590569e788f2581","first_computed_at":"2026-06-19T16:10:15.931959Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:10:15.931959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BzlMcVEuS+jzkCPSedIIfhXQu7Hk93bvaJR8wM0mBhRi/kaEJzvFtMCM5lebjszBCNF+w4SIKohsPdiOwFJUAQ==","signature_status":"signed_v1","signed_at":"2026-06-19T16:10:15.932281Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.17558","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e11b39016eb00028c8f65f3f724dcadf9cbe5f1bd78d6f200b1461dab509bfaf","sha256:3a641d53910f30307f0db0a665ccd28f65aacc5844f77d5bda1108f4824124fc"],"state_sha256":"0d8f9f7fd94c53c147e8a1f6f99dd5a236ff8af906bced394902fd626c27b3df"}