{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:NYQEBSD2AP4SNZCLBHG2DTKIQT","short_pith_number":"pith:NYQEBSD2","canonical_record":{"source":{"id":"2204.12529","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2022-04-26T18:26:26Z","cross_cats_sorted":[],"title_canon_sha256":"2eeda7e5da4ea7a35330b959c5d438ade101eb1b6acd3b8fd2094132ff517e66","abstract_canon_sha256":"7edd662332c0111a8344efcbdbdff3bcf1adcf26f8071a46429d70cc54e90d71"},"schema_version":"1.0"},"canonical_sha256":"6e2040c87a03f926e44b09cda1cd4884c1043e6055010bf72385c15b5f1115f9","source":{"kind":"arxiv","id":"2204.12529","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2204.12529","created_at":"2026-07-05T04:18:19Z"},{"alias_kind":"arxiv_version","alias_value":"2204.12529v1","created_at":"2026-07-05T04:18:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.12529","created_at":"2026-07-05T04:18:19Z"},{"alias_kind":"pith_short_12","alias_value":"NYQEBSD2AP4S","created_at":"2026-07-05T04:18:19Z"},{"alias_kind":"pith_short_16","alias_value":"NYQEBSD2AP4SNZCL","created_at":"2026-07-05T04:18:19Z"},{"alias_kind":"pith_short_8","alias_value":"NYQEBSD2","created_at":"2026-07-05T04:18:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:NYQEBSD2AP4SNZCLBHG2DTKIQT","target":"record","payload":{"canonical_record":{"source":{"id":"2204.12529","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2022-04-26T18:26:26Z","cross_cats_sorted":[],"title_canon_sha256":"2eeda7e5da4ea7a35330b959c5d438ade101eb1b6acd3b8fd2094132ff517e66","abstract_canon_sha256":"7edd662332c0111a8344efcbdbdff3bcf1adcf26f8071a46429d70cc54e90d71"},"schema_version":"1.0"},"canonical_sha256":"6e2040c87a03f926e44b09cda1cd4884c1043e6055010bf72385c15b5f1115f9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:18:19.748452Z","signature_b64":"REvesyVGhLfJjXYp/+F9LS4Ax8zKtT9Ls1fuNUTa3zYin0qtDRAdIxPWe17kb4SEM3S2RD08VuHqilExfKwzCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e2040c87a03f926e44b09cda1cd4884c1043e6055010bf72385c15b5f1115f9","last_reissued_at":"2026-07-05T04:18:19.748068Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:18:19.748068Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2204.12529","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":"2026-07-05T04:18:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+tqXcvnnLeWh15PCwnoXbiD7LpWL3T7eCMWIeota+7Z7V27Cf1ZcDpe0iwm8JObjNWZEcXNezZeznSPaDDBEAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-26T23:47:14.751471Z"},"content_sha256":"bc548e028def00fb4e0843590a56ed9c2e1e62d44ab90c9e82fbf50a2e98c0a7","schema_version":"1.0","event_id":"sha256:bc548e028def00fb4e0843590a56ed9c2e1e62d44ab90c9e82fbf50a2e98c0a7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:NYQEBSD2AP4SNZCLBHG2DTKIQT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Infinite dimensional spaces in the set of strongly norm-attaining Lipschitz maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Abraham Rueda Zoca, Antonio Avil\\'es, Gonzalo Mart\\'inez-Cervantes, Pedro Tradacete","submitted_at":"2022-04-26T18:26:26Z","abstract_excerpt":"We prove that if $M$ is an infinite complete metric space then the set of strongly norm-attaining Lipschitz functions $\\SA(M)$ contains a linear subspace isomorphic to $c_0$. This solves an open question posed by V. Kadets and O. Rold\\'an."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.12529","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2204.12529/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T04:18:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+x7KR+vje/+Ap4D3nvunXop/Op/kjkxBHMIb8jzkKdyBgwwnX3liX8tnkx2w+66klDAAJZTBoKK2oYaQsu3QBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-26T23:47:14.751845Z"},"content_sha256":"a74a898df8d9501f55e1237e80e36344f8b902330f2bf23457ff303443c41bb7","schema_version":"1.0","event_id":"sha256:a74a898df8d9501f55e1237e80e36344f8b902330f2bf23457ff303443c41bb7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NYQEBSD2AP4SNZCLBHG2DTKIQT/bundle.json","state_url":"https://pith.science/pith/NYQEBSD2AP4SNZCLBHG2DTKIQT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NYQEBSD2AP4SNZCLBHG2DTKIQT/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":"2026-07-26T23:47:14Z","links":{"resolver":"https://pith.science/pith/NYQEBSD2AP4SNZCLBHG2DTKIQT","bundle":"https://pith.science/pith/NYQEBSD2AP4SNZCLBHG2DTKIQT/bundle.json","state":"https://pith.science/pith/NYQEBSD2AP4SNZCLBHG2DTKIQT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NYQEBSD2AP4SNZCLBHG2DTKIQT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:NYQEBSD2AP4SNZCLBHG2DTKIQT","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":"7edd662332c0111a8344efcbdbdff3bcf1adcf26f8071a46429d70cc54e90d71","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2022-04-26T18:26:26Z","title_canon_sha256":"2eeda7e5da4ea7a35330b959c5d438ade101eb1b6acd3b8fd2094132ff517e66"},"schema_version":"1.0","source":{"id":"2204.12529","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2204.12529","created_at":"2026-07-05T04:18:19Z"},{"alias_kind":"arxiv_version","alias_value":"2204.12529v1","created_at":"2026-07-05T04:18:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.12529","created_at":"2026-07-05T04:18:19Z"},{"alias_kind":"pith_short_12","alias_value":"NYQEBSD2AP4S","created_at":"2026-07-05T04:18:19Z"},{"alias_kind":"pith_short_16","alias_value":"NYQEBSD2AP4SNZCL","created_at":"2026-07-05T04:18:19Z"},{"alias_kind":"pith_short_8","alias_value":"NYQEBSD2","created_at":"2026-07-05T04:18:19Z"}],"graph_snapshots":[{"event_id":"sha256:a74a898df8d9501f55e1237e80e36344f8b902330f2bf23457ff303443c41bb7","target":"graph","created_at":"2026-07-05T04:18:19Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2204.12529/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that if $M$ is an infinite complete metric space then the set of strongly norm-attaining Lipschitz functions $\\SA(M)$ contains a linear subspace isomorphic to $c_0$. This solves an open question posed by V. Kadets and O. Rold\\'an.","authors_text":"Abraham Rueda Zoca, Antonio Avil\\'es, Gonzalo Mart\\'inez-Cervantes, Pedro Tradacete","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2022-04-26T18:26:26Z","title":"Infinite dimensional spaces in the set of strongly norm-attaining Lipschitz maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.12529","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:bc548e028def00fb4e0843590a56ed9c2e1e62d44ab90c9e82fbf50a2e98c0a7","target":"record","created_at":"2026-07-05T04:18:19Z","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":"7edd662332c0111a8344efcbdbdff3bcf1adcf26f8071a46429d70cc54e90d71","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2022-04-26T18:26:26Z","title_canon_sha256":"2eeda7e5da4ea7a35330b959c5d438ade101eb1b6acd3b8fd2094132ff517e66"},"schema_version":"1.0","source":{"id":"2204.12529","kind":"arxiv","version":1}},"canonical_sha256":"6e2040c87a03f926e44b09cda1cd4884c1043e6055010bf72385c15b5f1115f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e2040c87a03f926e44b09cda1cd4884c1043e6055010bf72385c15b5f1115f9","first_computed_at":"2026-07-05T04:18:19.748068Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:18:19.748068Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"REvesyVGhLfJjXYp/+F9LS4Ax8zKtT9Ls1fuNUTa3zYin0qtDRAdIxPWe17kb4SEM3S2RD08VuHqilExfKwzCg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:18:19.748452Z","signed_message":"canonical_sha256_bytes"},"source_id":"2204.12529","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc548e028def00fb4e0843590a56ed9c2e1e62d44ab90c9e82fbf50a2e98c0a7","sha256:a74a898df8d9501f55e1237e80e36344f8b902330f2bf23457ff303443c41bb7"],"state_sha256":"fbd6373b85312f9161c2233e2899183c2ce6064e4e33b581013e88bb2d355f8e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WYnhOQNQTAchjISCEPTLc7/xTo1CNSIQbH2aV9D13VaCIwZwtxLdk8hBe9ROILYIEb9PP174c57HdfpRU31cDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-26T23:47:14.753901Z","bundle_sha256":"f711b8ddbd2068b123ead9f1f9e0116c1ee1378e0d9094cbe808640f37902168"}}