{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:LUBCCWUHJ3XDGGFG27M2UOQK42","short_pith_number":"pith:LUBCCWUH","canonical_record":{"source":{"id":"1506.00159","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-05-30T19:16:49Z","cross_cats_sorted":[],"title_canon_sha256":"06b2e7a3625a960b1df2d2b5ef8efe544986b5e4e089dc5a3ce814d0f31b2402","abstract_canon_sha256":"2a33d49f5a732ed690d6cbf46c6d0efc217ca1a4d2f0459e94a6293cd13e85ba"},"schema_version":"1.0"},"canonical_sha256":"5d02215a874eee3318a6d7d9aa3a0ae6ba11d4d95b2f41e25c868ecb0d98711a","source":{"kind":"arxiv","id":"1506.00159","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.00159","created_at":"2026-05-18T01:55:59Z"},{"alias_kind":"arxiv_version","alias_value":"1506.00159v2","created_at":"2026-05-18T01:55:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.00159","created_at":"2026-05-18T01:55:59Z"},{"alias_kind":"pith_short_12","alias_value":"LUBCCWUHJ3XD","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LUBCCWUHJ3XDGGFG","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LUBCCWUH","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:LUBCCWUHJ3XDGGFG27M2UOQK42","target":"record","payload":{"canonical_record":{"source":{"id":"1506.00159","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-05-30T19:16:49Z","cross_cats_sorted":[],"title_canon_sha256":"06b2e7a3625a960b1df2d2b5ef8efe544986b5e4e089dc5a3ce814d0f31b2402","abstract_canon_sha256":"2a33d49f5a732ed690d6cbf46c6d0efc217ca1a4d2f0459e94a6293cd13e85ba"},"schema_version":"1.0"},"canonical_sha256":"5d02215a874eee3318a6d7d9aa3a0ae6ba11d4d95b2f41e25c868ecb0d98711a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:55:59.451045Z","signature_b64":"JXUpQ4r8MHR/tqi5K9XYS1yvwRcX7TEq5VIGPEFOxwnkF4E2Hk0cbG9pl3uLhNMVSupJ2m6FIXvUjYaBHpr6Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d02215a874eee3318a6d7d9aa3a0ae6ba11d4d95b2f41e25c868ecb0d98711a","last_reissued_at":"2026-05-18T01:55:59.450655Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:55:59.450655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.00159","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":"2026-05-18T01:55:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j5nij2SBqQxcnNFaeSJeplU2TIXvJn21IsePGuDfS8cXlv/JiWwUNaJXa4M0RVFVqY+RcdCD0AsM9FIJ5ar8BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T03:45:15.543581Z"},"content_sha256":"09540b04e1a7a15c626c066a485f2376f0bd6a3eb86fbfeee8a7705595aa88d7","schema_version":"1.0","event_id":"sha256:09540b04e1a7a15c626c066a485f2376f0bd6a3eb86fbfeee8a7705595aa88d7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:LUBCCWUHJ3XDGGFG27M2UOQK42","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New lower bounds for the constants in the real polynomial Hardy--Littlewood inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"D. Nunez-Alarcon, D. Pellegrino, W. Cavalcante","submitted_at":"2015-05-30T19:16:49Z","abstract_excerpt":"In this short note we obtain new lower bounds for the constants of the real Hardy--Littlewood inequality for $m$-linear forms on $\\ell_{p}^{2}$ spaces when $p=2m$ and for certain values of $m$. The real and complex cases for the general case $\\ell_{p}^{n}$ were recently investigated by G. Araujo et al. When $n=2$ our results improve the best known estimates for these constants."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00159","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":"2026-05-18T01:55:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kG0faakVuHTNFH5ekV+HPSxOzGVhdJ6Q6vFniflusYlRBZpanccKLrCJjanJ9AJDJZvejyovxCVhPbaY2gAbAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T03:45:15.543934Z"},"content_sha256":"21d46f339b9a32fe85393a5f6cfe40de2d9e91ed277760d1516296483fbc87f2","schema_version":"1.0","event_id":"sha256:21d46f339b9a32fe85393a5f6cfe40de2d9e91ed277760d1516296483fbc87f2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LUBCCWUHJ3XDGGFG27M2UOQK42/bundle.json","state_url":"https://pith.science/pith/LUBCCWUHJ3XDGGFG27M2UOQK42/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LUBCCWUHJ3XDGGFG27M2UOQK42/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":"2026-06-25T03:45:15Z","links":{"resolver":"https://pith.science/pith/LUBCCWUHJ3XDGGFG27M2UOQK42","bundle":"https://pith.science/pith/LUBCCWUHJ3XDGGFG27M2UOQK42/bundle.json","state":"https://pith.science/pith/LUBCCWUHJ3XDGGFG27M2UOQK42/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LUBCCWUHJ3XDGGFG27M2UOQK42/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:LUBCCWUHJ3XDGGFG27M2UOQK42","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":"2a33d49f5a732ed690d6cbf46c6d0efc217ca1a4d2f0459e94a6293cd13e85ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-05-30T19:16:49Z","title_canon_sha256":"06b2e7a3625a960b1df2d2b5ef8efe544986b5e4e089dc5a3ce814d0f31b2402"},"schema_version":"1.0","source":{"id":"1506.00159","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.00159","created_at":"2026-05-18T01:55:59Z"},{"alias_kind":"arxiv_version","alias_value":"1506.00159v2","created_at":"2026-05-18T01:55:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.00159","created_at":"2026-05-18T01:55:59Z"},{"alias_kind":"pith_short_12","alias_value":"LUBCCWUHJ3XD","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LUBCCWUHJ3XDGGFG","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LUBCCWUH","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:21d46f339b9a32fe85393a5f6cfe40de2d9e91ed277760d1516296483fbc87f2","target":"graph","created_at":"2026-05-18T01:55:59Z","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":"In this short note we obtain new lower bounds for the constants of the real Hardy--Littlewood inequality for $m$-linear forms on $\\ell_{p}^{2}$ spaces when $p=2m$ and for certain values of $m$. The real and complex cases for the general case $\\ell_{p}^{n}$ were recently investigated by G. Araujo et al. When $n=2$ our results improve the best known estimates for these constants.","authors_text":"D. Nunez-Alarcon, D. Pellegrino, W. Cavalcante","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-05-30T19:16:49Z","title":"New lower bounds for the constants in the real polynomial Hardy--Littlewood inequality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00159","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":"sha256:09540b04e1a7a15c626c066a485f2376f0bd6a3eb86fbfeee8a7705595aa88d7","target":"record","created_at":"2026-05-18T01:55:59Z","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":"2a33d49f5a732ed690d6cbf46c6d0efc217ca1a4d2f0459e94a6293cd13e85ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-05-30T19:16:49Z","title_canon_sha256":"06b2e7a3625a960b1df2d2b5ef8efe544986b5e4e089dc5a3ce814d0f31b2402"},"schema_version":"1.0","source":{"id":"1506.00159","kind":"arxiv","version":2}},"canonical_sha256":"5d02215a874eee3318a6d7d9aa3a0ae6ba11d4d95b2f41e25c868ecb0d98711a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d02215a874eee3318a6d7d9aa3a0ae6ba11d4d95b2f41e25c868ecb0d98711a","first_computed_at":"2026-05-18T01:55:59.450655Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:59.450655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JXUpQ4r8MHR/tqi5K9XYS1yvwRcX7TEq5VIGPEFOxwnkF4E2Hk0cbG9pl3uLhNMVSupJ2m6FIXvUjYaBHpr6Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:59.451045Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.00159","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09540b04e1a7a15c626c066a485f2376f0bd6a3eb86fbfeee8a7705595aa88d7","sha256:21d46f339b9a32fe85393a5f6cfe40de2d9e91ed277760d1516296483fbc87f2"],"state_sha256":"4116fde67b7c21602d344578ed94cadb842dc15ebe279731a8066440110cabc2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lXFVFU80zy552w8GliufkS7JL1pLdv947JD1naXvjyX+oeQtC9KxoqPcxv8JCZSceQboXOgDm3qomYn/ZcA2BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T03:45:15.546218Z","bundle_sha256":"c55faa8cbef3250b9ae2025f1f34ec368a2661cf78b07075f5a8c77d6b9e087e"}}