{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:6Y6KE4AMWSQ7OYW2PPH6ZAM6QX","short_pith_number":"pith:6Y6KE4AM","canonical_record":{"source":{"id":"1708.03823","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-08-12T21:24:25Z","cross_cats_sorted":[],"title_canon_sha256":"36667521ff39dec37c91db88ffea1cf47c2dae8907b7fa076d55e2fecffd1343","abstract_canon_sha256":"db9480fc2f4ffb7a19420ab23a5f56ab4f6e2f9d29bc284dd45e31396a95012c"},"schema_version":"1.0"},"canonical_sha256":"f63ca2700cb4a1f762da7bcfec819e85e6247d67e6bd6295489348615bf63254","source":{"kind":"arxiv","id":"1708.03823","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.03823","created_at":"2026-05-18T00:38:07Z"},{"alias_kind":"arxiv_version","alias_value":"1708.03823v1","created_at":"2026-05-18T00:38:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.03823","created_at":"2026-05-18T00:38:07Z"},{"alias_kind":"pith_short_12","alias_value":"6Y6KE4AMWSQ7","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6Y6KE4AMWSQ7OYW2","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6Y6KE4AM","created_at":"2026-05-18T12:31:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:6Y6KE4AMWSQ7OYW2PPH6ZAM6QX","target":"record","payload":{"canonical_record":{"source":{"id":"1708.03823","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-08-12T21:24:25Z","cross_cats_sorted":[],"title_canon_sha256":"36667521ff39dec37c91db88ffea1cf47c2dae8907b7fa076d55e2fecffd1343","abstract_canon_sha256":"db9480fc2f4ffb7a19420ab23a5f56ab4f6e2f9d29bc284dd45e31396a95012c"},"schema_version":"1.0"},"canonical_sha256":"f63ca2700cb4a1f762da7bcfec819e85e6247d67e6bd6295489348615bf63254","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:07.802129Z","signature_b64":"0EeI33TzX9oe44xVUQxvd5RrkRDDYKGSNPsOxoMgdxHgJIm4o6fUn/qHHV6C6dxgrpJ8zQuSoG1Z8zxQTH99Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f63ca2700cb4a1f762da7bcfec819e85e6247d67e6bd6295489348615bf63254","last_reissued_at":"2026-05-18T00:38:07.801668Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:07.801668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.03823","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":"2026-05-18T00:38:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8ni24dRbdIpPb3vZZgppGV/lL4XZJ0LU5KivxJB+UIifnT8BjA441LO9QP8xKVKk+zFAHbuKRSuwxN9GG+7/AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:09:04.224260Z"},"content_sha256":"550ea1b23b46c632f9b4ae935ee845a9fa387be57ebc2472a153b917ef12064e","schema_version":"1.0","event_id":"sha256:550ea1b23b46c632f9b4ae935ee845a9fa387be57ebc2472a153b917ef12064e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:6Y6KE4AMWSQ7OYW2PPH6ZAM6QX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"1-complemented subspaces of Banach spaces of universal disposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jes\\'us M. F. Castillo, Yolanda Moreno","submitted_at":"2017-08-12T21:24:25Z","abstract_excerpt":"We first unify all notions of partial injectivity appearing in the literature ---(universal) separable injectivity, (universal) $\\aleph$-injectivity --- in the notion of $(\\alpha, \\beta)$-injectivity ($(\\alpha, \\beta)_\\lambda$-injectivity if the parameter $\\lambda$ has to be specified). Then, extend the notion of space of universal disposition to space of universal $(\\alpha, \\beta)$-disposition. Finally, we characterize the $1$-complemented subspaces of spaces of universal $(\\alpha, \\beta)$-disposition as precisely the spaces $(\\alpha, \\beta)_1$-injective."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03823","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":"2026-05-18T00:38:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kRQPU2Lob5692elLdCovKLs6+CMfNawsMYjOAOb/4hc9qV4sV6O5rq3DbEmgd26ESF/5P9orM3dMGyKT1TUYDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:09:04.224853Z"},"content_sha256":"739ff2898be67d5b80b5468e7bca63a3850cf9d880adbfc9be0f2b802f15c199","schema_version":"1.0","event_id":"sha256:739ff2898be67d5b80b5468e7bca63a3850cf9d880adbfc9be0f2b802f15c199"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6Y6KE4AMWSQ7OYW2PPH6ZAM6QX/bundle.json","state_url":"https://pith.science/pith/6Y6KE4AMWSQ7OYW2PPH6ZAM6QX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6Y6KE4AMWSQ7OYW2PPH6ZAM6QX/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":"2026-05-28T21:09:04Z","links":{"resolver":"https://pith.science/pith/6Y6KE4AMWSQ7OYW2PPH6ZAM6QX","bundle":"https://pith.science/pith/6Y6KE4AMWSQ7OYW2PPH6ZAM6QX/bundle.json","state":"https://pith.science/pith/6Y6KE4AMWSQ7OYW2PPH6ZAM6QX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6Y6KE4AMWSQ7OYW2PPH6ZAM6QX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6Y6KE4AMWSQ7OYW2PPH6ZAM6QX","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":"db9480fc2f4ffb7a19420ab23a5f56ab4f6e2f9d29bc284dd45e31396a95012c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-08-12T21:24:25Z","title_canon_sha256":"36667521ff39dec37c91db88ffea1cf47c2dae8907b7fa076d55e2fecffd1343"},"schema_version":"1.0","source":{"id":"1708.03823","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.03823","created_at":"2026-05-18T00:38:07Z"},{"alias_kind":"arxiv_version","alias_value":"1708.03823v1","created_at":"2026-05-18T00:38:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.03823","created_at":"2026-05-18T00:38:07Z"},{"alias_kind":"pith_short_12","alias_value":"6Y6KE4AMWSQ7","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6Y6KE4AMWSQ7OYW2","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6Y6KE4AM","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:739ff2898be67d5b80b5468e7bca63a3850cf9d880adbfc9be0f2b802f15c199","target":"graph","created_at":"2026-05-18T00:38:07Z","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 first unify all notions of partial injectivity appearing in the literature ---(universal) separable injectivity, (universal) $\\aleph$-injectivity --- in the notion of $(\\alpha, \\beta)$-injectivity ($(\\alpha, \\beta)_\\lambda$-injectivity if the parameter $\\lambda$ has to be specified). Then, extend the notion of space of universal disposition to space of universal $(\\alpha, \\beta)$-disposition. Finally, we characterize the $1$-complemented subspaces of spaces of universal $(\\alpha, \\beta)$-disposition as precisely the spaces $(\\alpha, \\beta)_1$-injective.","authors_text":"Jes\\'us M. F. Castillo, Yolanda Moreno","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-08-12T21:24:25Z","title":"1-complemented subspaces of Banach spaces of universal disposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03823","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":"sha256:550ea1b23b46c632f9b4ae935ee845a9fa387be57ebc2472a153b917ef12064e","target":"record","created_at":"2026-05-18T00:38:07Z","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":"db9480fc2f4ffb7a19420ab23a5f56ab4f6e2f9d29bc284dd45e31396a95012c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-08-12T21:24:25Z","title_canon_sha256":"36667521ff39dec37c91db88ffea1cf47c2dae8907b7fa076d55e2fecffd1343"},"schema_version":"1.0","source":{"id":"1708.03823","kind":"arxiv","version":1}},"canonical_sha256":"f63ca2700cb4a1f762da7bcfec819e85e6247d67e6bd6295489348615bf63254","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f63ca2700cb4a1f762da7bcfec819e85e6247d67e6bd6295489348615bf63254","first_computed_at":"2026-05-18T00:38:07.801668Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:07.801668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0EeI33TzX9oe44xVUQxvd5RrkRDDYKGSNPsOxoMgdxHgJIm4o6fUn/qHHV6C6dxgrpJ8zQuSoG1Z8zxQTH99Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:07.802129Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.03823","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:550ea1b23b46c632f9b4ae935ee845a9fa387be57ebc2472a153b917ef12064e","sha256:739ff2898be67d5b80b5468e7bca63a3850cf9d880adbfc9be0f2b802f15c199"],"state_sha256":"de032520a1a76c4d8319fe2508d0c8cc2978279915ec088ddfb56dc762491326"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0zewemD9ZJ2ZswzdPLT0Xzza8MjRJDzpaCxLSfuSPLHMGUPDDfbJMweECk9PeZyaQe+UWr/v/uXYwaYPv1KXAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T21:09:04.227888Z","bundle_sha256":"d7eed10de261657dda007801f2e4fe55bd6169c19a453070f83f11cbb6a0f2e1"}}