{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1997:YCKQV6WGVLKODHRY42BDSIA54C","short_pith_number":"pith:YCKQV6WG","canonical_record":{"source":{"id":"math/9709211","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"1997-09-08T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"3a97f0ee3896728be366ce7ee03dac5739b43d4a34fe9f7e982e6bb31ddc0ce2","abstract_canon_sha256":"3ca928d3785c6f18e6dcc030b8707cb05837d53749711423efda33780e50308f"},"schema_version":"1.0"},"canonical_sha256":"c0950afac6aad4e19e38e68239201de09f85514b9fed769c3868f6cfdc15b71c","source":{"kind":"arxiv","id":"math/9709211","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9709211","created_at":"2026-05-18T04:41:16Z"},{"alias_kind":"arxiv_version","alias_value":"math/9709211v1","created_at":"2026-05-18T04:41:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9709211","created_at":"2026-05-18T04:41:16Z"},{"alias_kind":"pith_short_12","alias_value":"YCKQV6WGVLKO","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"YCKQV6WGVLKODHRY","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"YCKQV6WG","created_at":"2026-05-18T12:25:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1997:YCKQV6WGVLKODHRY42BDSIA54C","target":"record","payload":{"canonical_record":{"source":{"id":"math/9709211","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"1997-09-08T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"3a97f0ee3896728be366ce7ee03dac5739b43d4a34fe9f7e982e6bb31ddc0ce2","abstract_canon_sha256":"3ca928d3785c6f18e6dcc030b8707cb05837d53749711423efda33780e50308f"},"schema_version":"1.0"},"canonical_sha256":"c0950afac6aad4e19e38e68239201de09f85514b9fed769c3868f6cfdc15b71c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:16.600660Z","signature_b64":"F+YyozARTiVdajovnU7guf6Mgc1KwaQITdWjLg0rR+NIMXtZTdGNrbNfl1iEVXXNa3RdCmRrctFok/cz5E89CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0950afac6aad4e19e38e68239201de09f85514b9fed769c3868f6cfdc15b71c","last_reissued_at":"2026-05-18T04:41:16.600186Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:16.600186Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9709211","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":"2026-05-18T04:41:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CyX9yKskbB7ltXm5OD3lm/m2IuubDA4gHiGsLfmPJc6/qBIHUeTJE2nns64Tw1T6aw6I/F3ftiihdxeBoUJPCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:26:37.548520Z"},"content_sha256":"8677773cc0bc31942f9b38eda9a022734a1db731c036ed722d7c8ac6dd147450","schema_version":"1.0","event_id":"sha256:8677773cc0bc31942f9b38eda9a022734a1db731c036ed722d7c8ac6dd147450"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1997:YCKQV6WGVLKODHRY42BDSIA54C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distances between Banach spaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mikhail I. Ostrovskii, Nigel J. Kalton","submitted_at":"1997-09-08T00:00:00Z","abstract_excerpt":"The main object of the paper is to study the distance between Banach spaces introduced by Kadets. For Banach spaces $X$ and $Y$, the Kadets distance is defined to be the infimum of the Hausdorff distance $d(B_X,B_Y)$ between the respective closed unit balls over all isometric linear embeddings of $X$ and $Y$ into a common Banach space $Z.$ This is compared with the Gromov-Hausdorff distance which is defined to be the infimum of $d(B_X,B_Y)$ over all isometric embeddings into a common metric space $Z$. We prove continuity type results for the Kadets distance including a result that shows that t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9709211","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":"2026-05-18T04:41:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vo8KW7K/KFPcrxJSE7yqxzp+b6ZmdoNRo5Q3L0NghCX9YZpFYr9Zi92XdW1MuxLvH55fxowO8VZ5AeCub4jAAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:26:37.548975Z"},"content_sha256":"15f9f6c663c509c070dadf0f5ec53f9fceca23f4586eca22186804b95fc7f340","schema_version":"1.0","event_id":"sha256:15f9f6c663c509c070dadf0f5ec53f9fceca23f4586eca22186804b95fc7f340"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YCKQV6WGVLKODHRY42BDSIA54C/bundle.json","state_url":"https://pith.science/pith/YCKQV6WGVLKODHRY42BDSIA54C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YCKQV6WGVLKODHRY42BDSIA54C/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":"2026-05-25T21:26:37Z","links":{"resolver":"https://pith.science/pith/YCKQV6WGVLKODHRY42BDSIA54C","bundle":"https://pith.science/pith/YCKQV6WGVLKODHRY42BDSIA54C/bundle.json","state":"https://pith.science/pith/YCKQV6WGVLKODHRY42BDSIA54C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YCKQV6WGVLKODHRY42BDSIA54C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1997:YCKQV6WGVLKODHRY42BDSIA54C","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":"3ca928d3785c6f18e6dcc030b8707cb05837d53749711423efda33780e50308f","cross_cats_sorted":[],"license":"","primary_cat":"math.FA","submitted_at":"1997-09-08T00:00:00Z","title_canon_sha256":"3a97f0ee3896728be366ce7ee03dac5739b43d4a34fe9f7e982e6bb31ddc0ce2"},"schema_version":"1.0","source":{"id":"math/9709211","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9709211","created_at":"2026-05-18T04:41:16Z"},{"alias_kind":"arxiv_version","alias_value":"math/9709211v1","created_at":"2026-05-18T04:41:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9709211","created_at":"2026-05-18T04:41:16Z"},{"alias_kind":"pith_short_12","alias_value":"YCKQV6WGVLKO","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"YCKQV6WGVLKODHRY","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"YCKQV6WG","created_at":"2026-05-18T12:25:48Z"}],"graph_snapshots":[{"event_id":"sha256:15f9f6c663c509c070dadf0f5ec53f9fceca23f4586eca22186804b95fc7f340","target":"graph","created_at":"2026-05-18T04:41:16Z","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":"The main object of the paper is to study the distance between Banach spaces introduced by Kadets. For Banach spaces $X$ and $Y$, the Kadets distance is defined to be the infimum of the Hausdorff distance $d(B_X,B_Y)$ between the respective closed unit balls over all isometric linear embeddings of $X$ and $Y$ into a common Banach space $Z.$ This is compared with the Gromov-Hausdorff distance which is defined to be the infimum of $d(B_X,B_Y)$ over all isometric embeddings into a common metric space $Z$. We prove continuity type results for the Kadets distance including a result that shows that t","authors_text":"Mikhail I. Ostrovskii, Nigel J. Kalton","cross_cats":[],"headline":"","license":"","primary_cat":"math.FA","submitted_at":"1997-09-08T00:00:00Z","title":"Distances between Banach spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9709211","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":"sha256:8677773cc0bc31942f9b38eda9a022734a1db731c036ed722d7c8ac6dd147450","target":"record","created_at":"2026-05-18T04:41:16Z","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":"3ca928d3785c6f18e6dcc030b8707cb05837d53749711423efda33780e50308f","cross_cats_sorted":[],"license":"","primary_cat":"math.FA","submitted_at":"1997-09-08T00:00:00Z","title_canon_sha256":"3a97f0ee3896728be366ce7ee03dac5739b43d4a34fe9f7e982e6bb31ddc0ce2"},"schema_version":"1.0","source":{"id":"math/9709211","kind":"arxiv","version":1}},"canonical_sha256":"c0950afac6aad4e19e38e68239201de09f85514b9fed769c3868f6cfdc15b71c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0950afac6aad4e19e38e68239201de09f85514b9fed769c3868f6cfdc15b71c","first_computed_at":"2026-05-18T04:41:16.600186Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:16.600186Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F+YyozARTiVdajovnU7guf6Mgc1KwaQITdWjLg0rR+NIMXtZTdGNrbNfl1iEVXXNa3RdCmRrctFok/cz5E89CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:16.600660Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9709211","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8677773cc0bc31942f9b38eda9a022734a1db731c036ed722d7c8ac6dd147450","sha256:15f9f6c663c509c070dadf0f5ec53f9fceca23f4586eca22186804b95fc7f340"],"state_sha256":"17df061ef69000599a04b17d6d164a2649becb57f6d9172374439edd502b9198"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YpB13ATWJqo4syAsN9VG4++EKjpk5OjGZFIuGCv16Wsx8KSYg/5lEiMxG/d/qNwT5ruUdPAxrssbb2HYvmc1Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T21:26:37.551513Z","bundle_sha256":"b6a5179159e2eb450268ed1191cb55cc11f321f3f7e6b97385e2c53793a5ab01"}}