{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:XRL724GRDDHASD2NKGTFM6VPRK","short_pith_number":"pith:XRL724GR","canonical_record":{"source":{"id":"1803.01397","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-03-04T18:23:07Z","cross_cats_sorted":[],"title_canon_sha256":"56905bd94a8f1528aa31b5f5bfb89596342f976a33a68c06e84520ff8bbd4f7e","abstract_canon_sha256":"4779c3543f09d37080d94dea09ea5de8264116354b257094c349e29ab22b6091"},"schema_version":"1.0"},"canonical_sha256":"bc57fd70d118ce090f4d51a6567aaf8a8475e512d5090315eb9d761ec37fb3f2","source":{"kind":"arxiv","id":"1803.01397","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.01397","created_at":"2026-05-18T00:22:00Z"},{"alias_kind":"arxiv_version","alias_value":"1803.01397v1","created_at":"2026-05-18T00:22:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.01397","created_at":"2026-05-18T00:22:00Z"},{"alias_kind":"pith_short_12","alias_value":"XRL724GRDDHA","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XRL724GRDDHASD2N","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XRL724GR","created_at":"2026-05-18T12:33:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:XRL724GRDDHASD2NKGTFM6VPRK","target":"record","payload":{"canonical_record":{"source":{"id":"1803.01397","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-03-04T18:23:07Z","cross_cats_sorted":[],"title_canon_sha256":"56905bd94a8f1528aa31b5f5bfb89596342f976a33a68c06e84520ff8bbd4f7e","abstract_canon_sha256":"4779c3543f09d37080d94dea09ea5de8264116354b257094c349e29ab22b6091"},"schema_version":"1.0"},"canonical_sha256":"bc57fd70d118ce090f4d51a6567aaf8a8475e512d5090315eb9d761ec37fb3f2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:00.757416Z","signature_b64":"N8tSqcW70uOXKM0GsdnApj5AiuM6dO+iuREk+azP3bKVhtjWLYMLHeVqT1WTZ4XEY0X7gCATPueOvWDJOwjoCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc57fd70d118ce090f4d51a6567aaf8a8475e512d5090315eb9d761ec37fb3f2","last_reissued_at":"2026-05-18T00:22:00.757011Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:00.757011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.01397","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:22:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KJmAE7jY2t43bZtz0NB6e7+6Kp56NrRIA2BLOSrcosOtUOnP72Jsw4QeznZuwRUPsipwCimRJB4iJigEtc/kCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T00:56:30.817151Z"},"content_sha256":"5a9337433b7f21badbebe88688a624cc20d9a903480af602383aaace6c23a73b","schema_version":"1.0","event_id":"sha256:5a9337433b7f21badbebe88688a624cc20d9a903480af602383aaace6c23a73b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:XRL724GRDDHASD2NKGTFM6VPRK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Universal bounds for the Hardy--Littlewood inequalities on multilinear forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Gustavo Ara\\'ujo, Kleber C\\^amara","submitted_at":"2018-03-04T18:23:07Z","abstract_excerpt":"The Hardy--Littlewood inequalities for multilinear forms on sequence spaces state that for all positive integers $m,n\\geq2$ and all $m$-linear forms $T:\\ell_{p_{1}}^{n}\\times\\cdots\\times\\ell_{p_{m}}^{n}\\rightarrow\\mathbb{K}$ ($\\mathbb{K}=\\mathbb{R}$ or $\\mathbb{C}$) there are constants $C_{m}\\geq1$ (not depending on $n$) such that \\[ \\left( \\sum_{j_{1},\\ldots,j_{m}=1}^{n}\\left\\vert T(e_{j_{1}},\\ldots,e_{j_{m}})\\right\\vert ^{\\rho}\\right) ^{\\frac{1}{\\rho}}\\leq C_{m}\\sup_{\\left\\Vert x_{1}\\right\\Vert ,\\dots,\\left\\Vert x_{m}\\right\\Vert \\leq 1}\\left\\vert T(x_{1},\\dots,x_{m})\\right\\vert, \\] where $\\r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.01397","kind":"arxiv","version":1},"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":"2026-05-18T00:22:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6f5GHn9QkywH6c+YIMou2/sSZ0MxpUXT+zCGcucmwnZXxFgD9PF8LWqToRHgKkOxSl+tqbEflkTRK6a/+dQUDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T00:56:30.817507Z"},"content_sha256":"d1b0fa5c6d4dbd35f2d590ceea7a049acbb0b3c721caf73d3e057990c3bb0401","schema_version":"1.0","event_id":"sha256:d1b0fa5c6d4dbd35f2d590ceea7a049acbb0b3c721caf73d3e057990c3bb0401"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XRL724GRDDHASD2NKGTFM6VPRK/bundle.json","state_url":"https://pith.science/pith/XRL724GRDDHASD2NKGTFM6VPRK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XRL724GRDDHASD2NKGTFM6VPRK/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":"2026-07-03T00:56:30Z","links":{"resolver":"https://pith.science/pith/XRL724GRDDHASD2NKGTFM6VPRK","bundle":"https://pith.science/pith/XRL724GRDDHASD2NKGTFM6VPRK/bundle.json","state":"https://pith.science/pith/XRL724GRDDHASD2NKGTFM6VPRK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XRL724GRDDHASD2NKGTFM6VPRK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XRL724GRDDHASD2NKGTFM6VPRK","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":"4779c3543f09d37080d94dea09ea5de8264116354b257094c349e29ab22b6091","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-03-04T18:23:07Z","title_canon_sha256":"56905bd94a8f1528aa31b5f5bfb89596342f976a33a68c06e84520ff8bbd4f7e"},"schema_version":"1.0","source":{"id":"1803.01397","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.01397","created_at":"2026-05-18T00:22:00Z"},{"alias_kind":"arxiv_version","alias_value":"1803.01397v1","created_at":"2026-05-18T00:22:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.01397","created_at":"2026-05-18T00:22:00Z"},{"alias_kind":"pith_short_12","alias_value":"XRL724GRDDHA","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XRL724GRDDHASD2N","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XRL724GR","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:d1b0fa5c6d4dbd35f2d590ceea7a049acbb0b3c721caf73d3e057990c3bb0401","target":"graph","created_at":"2026-05-18T00:22:00Z","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":"The Hardy--Littlewood inequalities for multilinear forms on sequence spaces state that for all positive integers $m,n\\geq2$ and all $m$-linear forms $T:\\ell_{p_{1}}^{n}\\times\\cdots\\times\\ell_{p_{m}}^{n}\\rightarrow\\mathbb{K}$ ($\\mathbb{K}=\\mathbb{R}$ or $\\mathbb{C}$) there are constants $C_{m}\\geq1$ (not depending on $n$) such that \\[ \\left( \\sum_{j_{1},\\ldots,j_{m}=1}^{n}\\left\\vert T(e_{j_{1}},\\ldots,e_{j_{m}})\\right\\vert ^{\\rho}\\right) ^{\\frac{1}{\\rho}}\\leq C_{m}\\sup_{\\left\\Vert x_{1}\\right\\Vert ,\\dots,\\left\\Vert x_{m}\\right\\Vert \\leq 1}\\left\\vert T(x_{1},\\dots,x_{m})\\right\\vert, \\] where $\\r","authors_text":"Gustavo Ara\\'ujo, Kleber C\\^amara","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-03-04T18:23:07Z","title":"Universal bounds for the Hardy--Littlewood inequalities on multilinear forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.01397","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":"sha256:5a9337433b7f21badbebe88688a624cc20d9a903480af602383aaace6c23a73b","target":"record","created_at":"2026-05-18T00:22:00Z","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":"4779c3543f09d37080d94dea09ea5de8264116354b257094c349e29ab22b6091","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-03-04T18:23:07Z","title_canon_sha256":"56905bd94a8f1528aa31b5f5bfb89596342f976a33a68c06e84520ff8bbd4f7e"},"schema_version":"1.0","source":{"id":"1803.01397","kind":"arxiv","version":1}},"canonical_sha256":"bc57fd70d118ce090f4d51a6567aaf8a8475e512d5090315eb9d761ec37fb3f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc57fd70d118ce090f4d51a6567aaf8a8475e512d5090315eb9d761ec37fb3f2","first_computed_at":"2026-05-18T00:22:00.757011Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:00.757011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N8tSqcW70uOXKM0GsdnApj5AiuM6dO+iuREk+azP3bKVhtjWLYMLHeVqT1WTZ4XEY0X7gCATPueOvWDJOwjoCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:00.757416Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.01397","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a9337433b7f21badbebe88688a624cc20d9a903480af602383aaace6c23a73b","sha256:d1b0fa5c6d4dbd35f2d590ceea7a049acbb0b3c721caf73d3e057990c3bb0401"],"state_sha256":"49e5bfdfb3aadb0d3a98ae343270313f503c04a7aebca04f9873e106424ad0af"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kt7bNirYZbUiEK8firF19KESX+Zm+clgYN4Pbnhofb0qykxne+0JkwfKX/za+1OFqHrJdt3igaCWmR3lqw7PDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T00:56:30.819384Z","bundle_sha256":"6d3f3d5884fb4d83c1e9824a074ac7f46643c8ed5ca2ee69f62bbf9a87cc7c40"}}