{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:XRJZXYQEEKD3BNUCXBZBVQYUDW","short_pith_number":"pith:XRJZXYQE","canonical_record":{"source":{"id":"1005.0596","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-05-04T18:01:15Z","cross_cats_sorted":[],"title_canon_sha256":"1721f593fccfd773a7dddc378128998e799909114f6e422449667b7cf8d7429b","abstract_canon_sha256":"2dbcfbd520dfdeeb1278625fd758f51e9478d9dedb704cae3be898afa6bc5b01"},"schema_version":"1.0"},"canonical_sha256":"bc539be2042287b0b682b8721ac3141da76c88355e45709f94c2f1fbec052a4e","source":{"kind":"arxiv","id":"1005.0596","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.0596","created_at":"2026-05-18T03:46:49Z"},{"alias_kind":"arxiv_version","alias_value":"1005.0596v1","created_at":"2026-05-18T03:46:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.0596","created_at":"2026-05-18T03:46:49Z"},{"alias_kind":"pith_short_12","alias_value":"XRJZXYQEEKD3","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XRJZXYQEEKD3BNUC","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XRJZXYQE","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:XRJZXYQEEKD3BNUCXBZBVQYUDW","target":"record","payload":{"canonical_record":{"source":{"id":"1005.0596","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-05-04T18:01:15Z","cross_cats_sorted":[],"title_canon_sha256":"1721f593fccfd773a7dddc378128998e799909114f6e422449667b7cf8d7429b","abstract_canon_sha256":"2dbcfbd520dfdeeb1278625fd758f51e9478d9dedb704cae3be898afa6bc5b01"},"schema_version":"1.0"},"canonical_sha256":"bc539be2042287b0b682b8721ac3141da76c88355e45709f94c2f1fbec052a4e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:49.534404Z","signature_b64":"sPIrTnT7HSVXFYmSeruLnp2glcy5IOyCDyh0pW2mhGnZ5j6dtsMSKXPtyE3Zd7ALyof9qSh1vO+4nr5mgqWRAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc539be2042287b0b682b8721ac3141da76c88355e45709f94c2f1fbec052a4e","last_reissued_at":"2026-05-18T03:46:49.533814Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:49.533814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1005.0596","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":"2026-05-18T03:46:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jsJRkuMNZMDAXh8eO4Zx1kWqm3CxZ2k4Em8yR8B2G1nWRjZ2P9bZ9f2aKazmNJqqlHiJSX3b3UAySq2qSvnlBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T23:53:40.273421Z"},"content_sha256":"7e9b244c3997ba83ccdea11bbc7379175dc3e308bc208588fa30faddc698d93b","schema_version":"1.0","event_id":"sha256:7e9b244c3997ba83ccdea11bbc7379175dc3e308bc208588fa30faddc698d93b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:XRJZXYQEEKD3BNUCXBZBVQYUDW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spaceability in Banach and quasi-Banach sequence spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"D. Diniz, D. Pellegrino, G. Botelho, V.V. Favaro","submitted_at":"2010-05-04T18:01:15Z","abstract_excerpt":"Let $X$ be a Banach space. We prove that, for a large class of Banach or quasi-Banach spaces $E$ of $X$-valued sequences, the sets $E-\\bigcup _{q\\in\\Gamma}\\ell_{q}(X)$, where $\\Gamma$ is any subset of $(0,\\infty]$, and $E-c_{0}(X)$ contain closed infinite-dimensional subspaces of $E$ (if non-empty, of course). This result is applied in several particular cases and it is also shown that the same technique can be used to improve a result on the existence of spaces formed by norm-attaining linear operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.0596","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":"2026-05-18T03:46:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EHHnxrOTVW37s0Yo/O4aAYsdv8z46yJCGQAohfRI7UQpcuUzBT7h3eKh/hD8oSBo5zbyfeG+U42BYexh78yDCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T23:53:40.273765Z"},"content_sha256":"4e9181f9f887528c4f6bb10c8b35233f6c7a153e4d3c133acc1b7c5266a90437","schema_version":"1.0","event_id":"sha256:4e9181f9f887528c4f6bb10c8b35233f6c7a153e4d3c133acc1b7c5266a90437"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XRJZXYQEEKD3BNUCXBZBVQYUDW/bundle.json","state_url":"https://pith.science/pith/XRJZXYQEEKD3BNUCXBZBVQYUDW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XRJZXYQEEKD3BNUCXBZBVQYUDW/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":"2026-06-24T23:53:40Z","links":{"resolver":"https://pith.science/pith/XRJZXYQEEKD3BNUCXBZBVQYUDW","bundle":"https://pith.science/pith/XRJZXYQEEKD3BNUCXBZBVQYUDW/bundle.json","state":"https://pith.science/pith/XRJZXYQEEKD3BNUCXBZBVQYUDW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XRJZXYQEEKD3BNUCXBZBVQYUDW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:XRJZXYQEEKD3BNUCXBZBVQYUDW","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":"2dbcfbd520dfdeeb1278625fd758f51e9478d9dedb704cae3be898afa6bc5b01","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-05-04T18:01:15Z","title_canon_sha256":"1721f593fccfd773a7dddc378128998e799909114f6e422449667b7cf8d7429b"},"schema_version":"1.0","source":{"id":"1005.0596","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.0596","created_at":"2026-05-18T03:46:49Z"},{"alias_kind":"arxiv_version","alias_value":"1005.0596v1","created_at":"2026-05-18T03:46:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.0596","created_at":"2026-05-18T03:46:49Z"},{"alias_kind":"pith_short_12","alias_value":"XRJZXYQEEKD3","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XRJZXYQEEKD3BNUC","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XRJZXYQE","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:4e9181f9f887528c4f6bb10c8b35233f6c7a153e4d3c133acc1b7c5266a90437","target":"graph","created_at":"2026-05-18T03:46:49Z","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":"Let $X$ be a Banach space. We prove that, for a large class of Banach or quasi-Banach spaces $E$ of $X$-valued sequences, the sets $E-\\bigcup _{q\\in\\Gamma}\\ell_{q}(X)$, where $\\Gamma$ is any subset of $(0,\\infty]$, and $E-c_{0}(X)$ contain closed infinite-dimensional subspaces of $E$ (if non-empty, of course). This result is applied in several particular cases and it is also shown that the same technique can be used to improve a result on the existence of spaces formed by norm-attaining linear operators.","authors_text":"D. Diniz, D. Pellegrino, G. Botelho, V.V. Favaro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-05-04T18:01:15Z","title":"Spaceability in Banach and quasi-Banach sequence spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.0596","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":"sha256:7e9b244c3997ba83ccdea11bbc7379175dc3e308bc208588fa30faddc698d93b","target":"record","created_at":"2026-05-18T03:46:49Z","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":"2dbcfbd520dfdeeb1278625fd758f51e9478d9dedb704cae3be898afa6bc5b01","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-05-04T18:01:15Z","title_canon_sha256":"1721f593fccfd773a7dddc378128998e799909114f6e422449667b7cf8d7429b"},"schema_version":"1.0","source":{"id":"1005.0596","kind":"arxiv","version":1}},"canonical_sha256":"bc539be2042287b0b682b8721ac3141da76c88355e45709f94c2f1fbec052a4e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc539be2042287b0b682b8721ac3141da76c88355e45709f94c2f1fbec052a4e","first_computed_at":"2026-05-18T03:46:49.533814Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:49.533814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sPIrTnT7HSVXFYmSeruLnp2glcy5IOyCDyh0pW2mhGnZ5j6dtsMSKXPtyE3Zd7ALyof9qSh1vO+4nr5mgqWRAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:49.534404Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.0596","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e9b244c3997ba83ccdea11bbc7379175dc3e308bc208588fa30faddc698d93b","sha256:4e9181f9f887528c4f6bb10c8b35233f6c7a153e4d3c133acc1b7c5266a90437"],"state_sha256":"006f1fe1dacf6d058b17906fcc625f82fe48fa6042c840f8270af715293854d5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VlTGu9y3z6S3jbVBU5F1uf7FN9tcdjH9+mW5mJw8SX9TKAPPHkiySEl5gTScASwN65Z+SZmrS1sM08EojyLpDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T23:53:40.275691Z","bundle_sha256":"857775860ae1d15c540dec99d4c812fe4849c381bb4036c2d437acb6468a84ad"}}