{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:EXJBTVYL6UP3Y6OSRT2DSFDFNI","short_pith_number":"pith:EXJBTVYL","canonical_record":{"source":{"id":"1211.7366","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-30T20:28:40Z","cross_cats_sorted":[],"title_canon_sha256":"6606b83317003bab7ce3b3841a235ad483d1bbbab2f3f7afbf63458030d17a07","abstract_canon_sha256":"3ead90e3ade45b2038bb689649a92e3a82f7bf7b265c296653f3c77d99f51e30"},"schema_version":"1.0"},"canonical_sha256":"25d219d70bf51fbc79d28cf43914656a0b54039a2181f2fe9d77c65eead6d5d2","source":{"kind":"arxiv","id":"1211.7366","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.7366","created_at":"2026-05-18T03:38:34Z"},{"alias_kind":"arxiv_version","alias_value":"1211.7366v2","created_at":"2026-05-18T03:38:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.7366","created_at":"2026-05-18T03:38:34Z"},{"alias_kind":"pith_short_12","alias_value":"EXJBTVYL6UP3","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"EXJBTVYL6UP3Y6OS","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"EXJBTVYL","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:EXJBTVYL6UP3Y6OSRT2DSFDFNI","target":"record","payload":{"canonical_record":{"source":{"id":"1211.7366","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-30T20:28:40Z","cross_cats_sorted":[],"title_canon_sha256":"6606b83317003bab7ce3b3841a235ad483d1bbbab2f3f7afbf63458030d17a07","abstract_canon_sha256":"3ead90e3ade45b2038bb689649a92e3a82f7bf7b265c296653f3c77d99f51e30"},"schema_version":"1.0"},"canonical_sha256":"25d219d70bf51fbc79d28cf43914656a0b54039a2181f2fe9d77c65eead6d5d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:34.043133Z","signature_b64":"AXuIUpGIbGYGPs+9BAB06XHzuc8KzlrHqSOjEYzX9liHgFffogw59HI3Rtplqc6KncbAcYvvVSzbjCti27T8BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25d219d70bf51fbc79d28cf43914656a0b54039a2181f2fe9d77c65eead6d5d2","last_reissued_at":"2026-05-18T03:38:34.042514Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:34.042514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.7366","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":"2026-05-18T03:38:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"orWpnFbu4U5ANOLNPOXEYliC99v4DvZ2F7aXA3nHq5F/zmfzsFJpyyq1q6y6c8HKriP7VQY50SZOQ2719yrHCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:44:24.615115Z"},"content_sha256":"c3c732c295660cc9cba66c775446bae704aca46aefb2983462a7857d6bf23f16","schema_version":"1.0","event_id":"sha256:c3c732c295660cc9cba66c775446bae704aca46aefb2983462a7857d6bf23f16"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:EXJBTVYL6UP3Y6OSRT2DSFDFNI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Operators ideals and approximation properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Pablo Turco, Silvia Lassalle","submitted_at":"2012-11-30T20:28:40Z","abstract_excerpt":"We use the notion of $\\A$-compact sets, which are determined by a Banach operator ideal $\\A$, to show that most classic results of certain approximation properties and several Banach operator ideals can be systematically studied under this framework. We say that a Banach space enjoys the $\\A$-approximation property if the identity map is uniformly approximable on $\\A$-compact sets by finite rank operators. The Grothendieck's classic approximation property is the $\\K$-approximation property for $\\K$ the ideal of compact operators and the $p$-approximation property is obtained as the $\\mathcal N"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.7366","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":"2026-05-18T03:38:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DW/af3MDV3/CXcQSPAUlQxsPIs6Y5DRZHXiUnLwb4Sdl3pb54gKVWsD/BlXavDdrprEYuiaPdY8dYg4ocBLfCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:44:24.615481Z"},"content_sha256":"70a8aeea516d59654f26b5c88b76a6b7dd4b31409cf217e8bc31e10550651511","schema_version":"1.0","event_id":"sha256:70a8aeea516d59654f26b5c88b76a6b7dd4b31409cf217e8bc31e10550651511"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EXJBTVYL6UP3Y6OSRT2DSFDFNI/bundle.json","state_url":"https://pith.science/pith/EXJBTVYL6UP3Y6OSRT2DSFDFNI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EXJBTVYL6UP3Y6OSRT2DSFDFNI/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":"2026-06-04T06:44:24Z","links":{"resolver":"https://pith.science/pith/EXJBTVYL6UP3Y6OSRT2DSFDFNI","bundle":"https://pith.science/pith/EXJBTVYL6UP3Y6OSRT2DSFDFNI/bundle.json","state":"https://pith.science/pith/EXJBTVYL6UP3Y6OSRT2DSFDFNI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EXJBTVYL6UP3Y6OSRT2DSFDFNI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:EXJBTVYL6UP3Y6OSRT2DSFDFNI","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":"3ead90e3ade45b2038bb689649a92e3a82f7bf7b265c296653f3c77d99f51e30","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-30T20:28:40Z","title_canon_sha256":"6606b83317003bab7ce3b3841a235ad483d1bbbab2f3f7afbf63458030d17a07"},"schema_version":"1.0","source":{"id":"1211.7366","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.7366","created_at":"2026-05-18T03:38:34Z"},{"alias_kind":"arxiv_version","alias_value":"1211.7366v2","created_at":"2026-05-18T03:38:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.7366","created_at":"2026-05-18T03:38:34Z"},{"alias_kind":"pith_short_12","alias_value":"EXJBTVYL6UP3","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"EXJBTVYL6UP3Y6OS","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"EXJBTVYL","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:70a8aeea516d59654f26b5c88b76a6b7dd4b31409cf217e8bc31e10550651511","target":"graph","created_at":"2026-05-18T03:38:34Z","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":"We use the notion of $\\A$-compact sets, which are determined by a Banach operator ideal $\\A$, to show that most classic results of certain approximation properties and several Banach operator ideals can be systematically studied under this framework. We say that a Banach space enjoys the $\\A$-approximation property if the identity map is uniformly approximable on $\\A$-compact sets by finite rank operators. The Grothendieck's classic approximation property is the $\\K$-approximation property for $\\K$ the ideal of compact operators and the $p$-approximation property is obtained as the $\\mathcal N","authors_text":"Pablo Turco, Silvia Lassalle","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-30T20:28:40Z","title":"Operators ideals and approximation properties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.7366","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:c3c732c295660cc9cba66c775446bae704aca46aefb2983462a7857d6bf23f16","target":"record","created_at":"2026-05-18T03:38:34Z","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":"3ead90e3ade45b2038bb689649a92e3a82f7bf7b265c296653f3c77d99f51e30","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-30T20:28:40Z","title_canon_sha256":"6606b83317003bab7ce3b3841a235ad483d1bbbab2f3f7afbf63458030d17a07"},"schema_version":"1.0","source":{"id":"1211.7366","kind":"arxiv","version":2}},"canonical_sha256":"25d219d70bf51fbc79d28cf43914656a0b54039a2181f2fe9d77c65eead6d5d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25d219d70bf51fbc79d28cf43914656a0b54039a2181f2fe9d77c65eead6d5d2","first_computed_at":"2026-05-18T03:38:34.042514Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:34.042514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AXuIUpGIbGYGPs+9BAB06XHzuc8KzlrHqSOjEYzX9liHgFffogw59HI3Rtplqc6KncbAcYvvVSzbjCti27T8BA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:34.043133Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.7366","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3c732c295660cc9cba66c775446bae704aca46aefb2983462a7857d6bf23f16","sha256:70a8aeea516d59654f26b5c88b76a6b7dd4b31409cf217e8bc31e10550651511"],"state_sha256":"ec342860113e96aaae281a522c822827a91e817a17a570eec78f971aa946b561"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sFzN27Ot4KRJui4XvZBeEZ7KC4koN5fx5eFJqzuwS1GgP4XYgeRgAKCGrbnvm5pIPuhLXfRjhxKRd/sriN2XCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T06:44:24.617350Z","bundle_sha256":"cd90a33270d38c0a657e8abd5eaa7c70b3580283f4a5988409f9503697756a5f"}}