{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:HIAAZ3WDILUPNRWBKKA47D7EYI","short_pith_number":"pith:HIAAZ3WD","canonical_record":{"source":{"id":"1705.07259","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-05-20T04:11:12Z","cross_cats_sorted":[],"title_canon_sha256":"0c573314cb60c6706b437af11c74f6f695f281ebb18eb14d35bb197d75a4266a","abstract_canon_sha256":"ab5263d67c207c9035e0ad52f345daae28d381306ea3da7547087d2ee1cb9043"},"schema_version":"1.0"},"canonical_sha256":"3a000ceec342e8f6c6c15281cf8fe4c221c7db15bc3b2f859383d5ac8342c60e","source":{"kind":"arxiv","id":"1705.07259","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.07259","created_at":"2026-05-18T00:11:11Z"},{"alias_kind":"arxiv_version","alias_value":"1705.07259v2","created_at":"2026-05-18T00:11:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.07259","created_at":"2026-05-18T00:11:11Z"},{"alias_kind":"pith_short_12","alias_value":"HIAAZ3WDILUP","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HIAAZ3WDILUPNRWB","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HIAAZ3WD","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:HIAAZ3WDILUPNRWBKKA47D7EYI","target":"record","payload":{"canonical_record":{"source":{"id":"1705.07259","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-05-20T04:11:12Z","cross_cats_sorted":[],"title_canon_sha256":"0c573314cb60c6706b437af11c74f6f695f281ebb18eb14d35bb197d75a4266a","abstract_canon_sha256":"ab5263d67c207c9035e0ad52f345daae28d381306ea3da7547087d2ee1cb9043"},"schema_version":"1.0"},"canonical_sha256":"3a000ceec342e8f6c6c15281cf8fe4c221c7db15bc3b2f859383d5ac8342c60e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:11.713201Z","signature_b64":"Pr7DIRyUlv3PO9gcRcrQnwM2zhRTGt9UJQrYGwt479PzHggnOy24HLsr/GNjpFgauyMhlKdkx+0v0qdfyQmBDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a000ceec342e8f6c6c15281cf8fe4c221c7db15bc3b2f859383d5ac8342c60e","last_reissued_at":"2026-05-18T00:11:11.712485Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:11.712485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.07259","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":"2026-05-18T00:11:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rVYnYY6Jz63iMwVJ4nGmm6El8fMw24VdJ36n8xmnPl0NlgbYwWpoh5lg0ox/kgSfRjGu591MwazacnCiR1OhCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T13:31:15.332460Z"},"content_sha256":"b5459f5d6c488dac68c5c1219f8af0b000b7c5b7253ceddb6ddb0393d3eff2ed","schema_version":"1.0","event_id":"sha256:b5459f5d6c488dac68c5c1219f8af0b000b7c5b7253ceddb6ddb0393d3eff2ed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:HIAAZ3WDILUPNRWBKKA47D7EYI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized multiple summing multilinear operators on Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Fabr\\'icio Santos, Joilson Ribeiro","submitted_at":"2017-05-20T04:11:12Z","abstract_excerpt":"In this paper we provide an abstract aproach to the study of classes of multiple summing multilinear operators between Banach spaces. The main purpose is unify the study of several known classes and results, for example multiple $(p, q_1,\\dots, q_n)$-summing operators, multiple mixing $(s, q, p)$-summing operators and multiple strong $(s, q, p)$-mixing summing operators. We also define new class of multiple summing multilinear operator that are particular cases of our construction and, therefore, satisfy the results proved in the paper."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07259","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":"2026-05-18T00:11:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mtY0LkvJl3VJDO1QzTsZ5ow9q54UjM86RgXWxSzeANe1IF0VEG4bQvjBjqJskx5of0OupexpAynUZjp1Xp34Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T13:31:15.332804Z"},"content_sha256":"cbbc30d5ff61ad06997ce9c3948c78d82cb6785c396f5371973e7dd795cbda46","schema_version":"1.0","event_id":"sha256:cbbc30d5ff61ad06997ce9c3948c78d82cb6785c396f5371973e7dd795cbda46"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HIAAZ3WDILUPNRWBKKA47D7EYI/bundle.json","state_url":"https://pith.science/pith/HIAAZ3WDILUPNRWBKKA47D7EYI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HIAAZ3WDILUPNRWBKKA47D7EYI/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":"2026-06-26T13:31:15Z","links":{"resolver":"https://pith.science/pith/HIAAZ3WDILUPNRWBKKA47D7EYI","bundle":"https://pith.science/pith/HIAAZ3WDILUPNRWBKKA47D7EYI/bundle.json","state":"https://pith.science/pith/HIAAZ3WDILUPNRWBKKA47D7EYI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HIAAZ3WDILUPNRWBKKA47D7EYI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:HIAAZ3WDILUPNRWBKKA47D7EYI","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":"ab5263d67c207c9035e0ad52f345daae28d381306ea3da7547087d2ee1cb9043","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-05-20T04:11:12Z","title_canon_sha256":"0c573314cb60c6706b437af11c74f6f695f281ebb18eb14d35bb197d75a4266a"},"schema_version":"1.0","source":{"id":"1705.07259","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.07259","created_at":"2026-05-18T00:11:11Z"},{"alias_kind":"arxiv_version","alias_value":"1705.07259v2","created_at":"2026-05-18T00:11:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.07259","created_at":"2026-05-18T00:11:11Z"},{"alias_kind":"pith_short_12","alias_value":"HIAAZ3WDILUP","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HIAAZ3WDILUPNRWB","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HIAAZ3WD","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:cbbc30d5ff61ad06997ce9c3948c78d82cb6785c396f5371973e7dd795cbda46","target":"graph","created_at":"2026-05-18T00:11:11Z","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 paper we provide an abstract aproach to the study of classes of multiple summing multilinear operators between Banach spaces. The main purpose is unify the study of several known classes and results, for example multiple $(p, q_1,\\dots, q_n)$-summing operators, multiple mixing $(s, q, p)$-summing operators and multiple strong $(s, q, p)$-mixing summing operators. We also define new class of multiple summing multilinear operator that are particular cases of our construction and, therefore, satisfy the results proved in the paper.","authors_text":"Fabr\\'icio Santos, Joilson Ribeiro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-05-20T04:11:12Z","title":"Generalized multiple summing multilinear operators on Banach spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07259","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:b5459f5d6c488dac68c5c1219f8af0b000b7c5b7253ceddb6ddb0393d3eff2ed","target":"record","created_at":"2026-05-18T00:11:11Z","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":"ab5263d67c207c9035e0ad52f345daae28d381306ea3da7547087d2ee1cb9043","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-05-20T04:11:12Z","title_canon_sha256":"0c573314cb60c6706b437af11c74f6f695f281ebb18eb14d35bb197d75a4266a"},"schema_version":"1.0","source":{"id":"1705.07259","kind":"arxiv","version":2}},"canonical_sha256":"3a000ceec342e8f6c6c15281cf8fe4c221c7db15bc3b2f859383d5ac8342c60e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a000ceec342e8f6c6c15281cf8fe4c221c7db15bc3b2f859383d5ac8342c60e","first_computed_at":"2026-05-18T00:11:11.712485Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:11.712485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pr7DIRyUlv3PO9gcRcrQnwM2zhRTGt9UJQrYGwt479PzHggnOy24HLsr/GNjpFgauyMhlKdkx+0v0qdfyQmBDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:11.713201Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.07259","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5459f5d6c488dac68c5c1219f8af0b000b7c5b7253ceddb6ddb0393d3eff2ed","sha256:cbbc30d5ff61ad06997ce9c3948c78d82cb6785c396f5371973e7dd795cbda46"],"state_sha256":"ab689433ad9024fe63a700ea473dd7137635ebad0bb56eb4ec68af656a23818c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cziNl2esdvRltRqVrvNj24MzQfEPAMJYbrr6a5XxrPYO6qTJn4JUXL6JQ/stSQC8d0eOgtuQOZDt41434et0BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T13:31:15.334964Z","bundle_sha256":"efffb3aec8179d34186abcfc2b8dd697437e98c0d939206a2efa50bc2272bd36"}}