{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:K7OZYG4OX6QQ2OZIQRPKXREG7S","short_pith_number":"pith:K7OZYG4O","canonical_record":{"source":{"id":"0903.0583","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-03-03T17:37:41Z","cross_cats_sorted":[],"title_canon_sha256":"feb9e407d3d310fe8a624b6a1e0ab525209d615a8c835bb722c58f0f0fc50486","abstract_canon_sha256":"0e636af40a39ed584373c2792e3d54ec0e5209d69726efb9837b1b563f437595"},"schema_version":"1.0"},"canonical_sha256":"57dd9c1b8ebfa10d3b28845eabc486fc940c962ee2f761009f3dcf47b1acfb8c","source":{"kind":"arxiv","id":"0903.0583","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.0583","created_at":"2026-05-18T01:31:20Z"},{"alias_kind":"arxiv_version","alias_value":"0903.0583v2","created_at":"2026-05-18T01:31:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.0583","created_at":"2026-05-18T01:31:20Z"},{"alias_kind":"pith_short_12","alias_value":"K7OZYG4OX6QQ","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"K7OZYG4OX6QQ2OZI","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"K7OZYG4O","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:K7OZYG4OX6QQ2OZIQRPKXREG7S","target":"record","payload":{"canonical_record":{"source":{"id":"0903.0583","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-03-03T17:37:41Z","cross_cats_sorted":[],"title_canon_sha256":"feb9e407d3d310fe8a624b6a1e0ab525209d615a8c835bb722c58f0f0fc50486","abstract_canon_sha256":"0e636af40a39ed584373c2792e3d54ec0e5209d69726efb9837b1b563f437595"},"schema_version":"1.0"},"canonical_sha256":"57dd9c1b8ebfa10d3b28845eabc486fc940c962ee2f761009f3dcf47b1acfb8c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:20.211568Z","signature_b64":"azoMw1rDu0+pOQtXP1ji5CXUa/9/lba7aSzU2S8BlOLMxJ7CqTTAHuAi1T45MkXRISKMARJGTw/yf9YrYLt5Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"57dd9c1b8ebfa10d3b28845eabc486fc940c962ee2f761009f3dcf47b1acfb8c","last_reissued_at":"2026-05-18T01:31:20.210851Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:20.210851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0903.0583","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":"2026-05-18T01:31:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0YSi/IvRG6yGMT6L5o+49+PcV08cG0So3L6CNG4QMJypYDoSkqlN/26iUV6szr1PjZmNe7iijmdFC1r2OPhDAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T19:10:54.384814Z"},"content_sha256":"339679690a4c7dddf844ab96c316631b3310c60b6be1a3f90c58fa6aa1352224","schema_version":"1.0","event_id":"sha256:339679690a4c7dddf844ab96c316631b3310c60b6be1a3f90c58fa6aa1352224"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:K7OZYG4OX6QQ2OZIQRPKXREG7S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cotype and absolutely summing linear operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Pellegrino, Geraldo Botelho, Pilar Rueda","submitted_at":"2009-03-03T17:37:41Z","abstract_excerpt":"Cotype is used in this paper to prove new results concerning the existence of non-absolutely summing linear operators between Banach spaces. We derive consequences that extend/generalize/ complement some classic results. We also point out that some of our results are sharp."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.0583","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":"2026-05-18T01:31:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b3vIVjiDVycg/UlICeEhiwk68bd+g+Mp5Yfg17bfDCsdR1mOX4OzipsG9h9/QrPygU4Tnx86Q3mesobEDe2/CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T19:10:54.385542Z"},"content_sha256":"1cc0bfad90f2a9b47d3731d0188c63104cc6b4bbee2cf132b6baefbe96f02c69","schema_version":"1.0","event_id":"sha256:1cc0bfad90f2a9b47d3731d0188c63104cc6b4bbee2cf132b6baefbe96f02c69"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K7OZYG4OX6QQ2OZIQRPKXREG7S/bundle.json","state_url":"https://pith.science/pith/K7OZYG4OX6QQ2OZIQRPKXREG7S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K7OZYG4OX6QQ2OZIQRPKXREG7S/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":"2026-06-07T19:10:54Z","links":{"resolver":"https://pith.science/pith/K7OZYG4OX6QQ2OZIQRPKXREG7S","bundle":"https://pith.science/pith/K7OZYG4OX6QQ2OZIQRPKXREG7S/bundle.json","state":"https://pith.science/pith/K7OZYG4OX6QQ2OZIQRPKXREG7S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K7OZYG4OX6QQ2OZIQRPKXREG7S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:K7OZYG4OX6QQ2OZIQRPKXREG7S","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":"0e636af40a39ed584373c2792e3d54ec0e5209d69726efb9837b1b563f437595","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-03-03T17:37:41Z","title_canon_sha256":"feb9e407d3d310fe8a624b6a1e0ab525209d615a8c835bb722c58f0f0fc50486"},"schema_version":"1.0","source":{"id":"0903.0583","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.0583","created_at":"2026-05-18T01:31:20Z"},{"alias_kind":"arxiv_version","alias_value":"0903.0583v2","created_at":"2026-05-18T01:31:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.0583","created_at":"2026-05-18T01:31:20Z"},{"alias_kind":"pith_short_12","alias_value":"K7OZYG4OX6QQ","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"K7OZYG4OX6QQ2OZI","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"K7OZYG4O","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:1cc0bfad90f2a9b47d3731d0188c63104cc6b4bbee2cf132b6baefbe96f02c69","target":"graph","created_at":"2026-05-18T01:31:20Z","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":"Cotype is used in this paper to prove new results concerning the existence of non-absolutely summing linear operators between Banach spaces. We derive consequences that extend/generalize/ complement some classic results. We also point out that some of our results are sharp.","authors_text":"Daniel Pellegrino, Geraldo Botelho, Pilar Rueda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-03-03T17:37:41Z","title":"Cotype and absolutely summing linear operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.0583","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":"sha256:339679690a4c7dddf844ab96c316631b3310c60b6be1a3f90c58fa6aa1352224","target":"record","created_at":"2026-05-18T01:31:20Z","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":"0e636af40a39ed584373c2792e3d54ec0e5209d69726efb9837b1b563f437595","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-03-03T17:37:41Z","title_canon_sha256":"feb9e407d3d310fe8a624b6a1e0ab525209d615a8c835bb722c58f0f0fc50486"},"schema_version":"1.0","source":{"id":"0903.0583","kind":"arxiv","version":2}},"canonical_sha256":"57dd9c1b8ebfa10d3b28845eabc486fc940c962ee2f761009f3dcf47b1acfb8c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"57dd9c1b8ebfa10d3b28845eabc486fc940c962ee2f761009f3dcf47b1acfb8c","first_computed_at":"2026-05-18T01:31:20.210851Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:20.210851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"azoMw1rDu0+pOQtXP1ji5CXUa/9/lba7aSzU2S8BlOLMxJ7CqTTAHuAi1T45MkXRISKMARJGTw/yf9YrYLt5Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:20.211568Z","signed_message":"canonical_sha256_bytes"},"source_id":"0903.0583","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:339679690a4c7dddf844ab96c316631b3310c60b6be1a3f90c58fa6aa1352224","sha256:1cc0bfad90f2a9b47d3731d0188c63104cc6b4bbee2cf132b6baefbe96f02c69"],"state_sha256":"c81c754da7de45704e22f2d26fddebc953728e1aa9b3aa56135653559e570153"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oKfNw8WSPmPCsgqv0vDLelTiZODOXuJKMu4If5OzeIBB+V855lwBKTp/ynHOMO1v3nHDAWNY1bWmRskNooDGBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T19:10:54.389214Z","bundle_sha256":"1fd892c42c49ed8be2aed63a5c8909bf02fdc3adc68632cd32e7caa08546e307"}}