{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:NPZMVQJEGEGGXZHPV32RURIFJH","short_pith_number":"pith:NPZMVQJE","canonical_record":{"source":{"id":"1704.06961","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-04-23T18:54:40Z","cross_cats_sorted":[],"title_canon_sha256":"0afe2d0afb3079ecef859a957051951fb302eff2513952a909ff40ea734e9124","abstract_canon_sha256":"8cceb55b4ad7233a5c2b45f0cc4272a9fdf8f9ecf76e112c1aeab6f754124db2"},"schema_version":"1.0"},"canonical_sha256":"6bf2cac124310c6be4efaef51a450549da12d66f3cde29f9cff73b381dfc2830","source":{"kind":"arxiv","id":"1704.06961","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.06961","created_at":"2026-05-18T00:10:52Z"},{"alias_kind":"arxiv_version","alias_value":"1704.06961v3","created_at":"2026-05-18T00:10:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06961","created_at":"2026-05-18T00:10:52Z"},{"alias_kind":"pith_short_12","alias_value":"NPZMVQJEGEGG","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NPZMVQJEGEGGXZHP","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NPZMVQJE","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:NPZMVQJEGEGGXZHPV32RURIFJH","target":"record","payload":{"canonical_record":{"source":{"id":"1704.06961","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-04-23T18:54:40Z","cross_cats_sorted":[],"title_canon_sha256":"0afe2d0afb3079ecef859a957051951fb302eff2513952a909ff40ea734e9124","abstract_canon_sha256":"8cceb55b4ad7233a5c2b45f0cc4272a9fdf8f9ecf76e112c1aeab6f754124db2"},"schema_version":"1.0"},"canonical_sha256":"6bf2cac124310c6be4efaef51a450549da12d66f3cde29f9cff73b381dfc2830","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:52.305731Z","signature_b64":"EHY90QvFVJ2FCBMxsjp8PonSFPY26t32B+mouGuopja1lhf7yqHJFJbGCnVFGkeR1Xhcr4tD0qQ+szw2rjbEBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6bf2cac124310c6be4efaef51a450549da12d66f3cde29f9cff73b381dfc2830","last_reissued_at":"2026-05-18T00:10:52.305056Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:52.305056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.06961","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:10:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lpFxDXVmbO6bGil9q6rYl0M0h0veBH5TIefqKbz0fwQdUkZXkwtZDLFZKccfhdbRpFneZ2CdW/PkGvOx4RagDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T20:06:39.321030Z"},"content_sha256":"e63733dbab1302d2835500529fe9696c6033c8a57e2036d769c210b36d9b41d3","schema_version":"1.0","event_id":"sha256:e63733dbab1302d2835500529fe9696c6033c8a57e2036d769c210b36d9b41d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:NPZMVQJEGEGGXZHPV32RURIFJH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-expansive bijections between unit balls of Banach spaces (A technical version with some boring proofs included)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Olesia Zavarzina","submitted_at":"2017-04-23T18:54:40Z","abstract_excerpt":"It is known that if $M$ is a finite-dimensional Banach space, or a strictly convex space, or the space $\\ell_1$, then every non-expansive bijection $F: B_M \\to B_M$ is an isometry. We extend these results to non-expansive bijections $F: B_E \\to B_M$ between unit balls of two different Banach spaces. Namely, if $E$ is an arbitrary Banach space and $M$ is finite-dimensional or strictly convex, or the space $\\ell_1$ then every non-expansive bijection $F: B_E \\to B_M$ is an isometry."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06961","kind":"arxiv","version":3},"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":"2026-05-18T00:10:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FQbNAJvefaYNluvNk5Fapx+wTqOdOtjpsxNEmU7bupHrOwuGCcPPYMQCaXjnqK+N9wHWyMT6N3Pnvb41Ow8RAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T20:06:39.321714Z"},"content_sha256":"9a907a3fc1ed4908068454dbc4c4bed2c3372395a730e3f078b292bff88042da","schema_version":"1.0","event_id":"sha256:9a907a3fc1ed4908068454dbc4c4bed2c3372395a730e3f078b292bff88042da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NPZMVQJEGEGGXZHPV32RURIFJH/bundle.json","state_url":"https://pith.science/pith/NPZMVQJEGEGGXZHPV32RURIFJH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NPZMVQJEGEGGXZHPV32RURIFJH/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":"2026-06-07T20:06:39Z","links":{"resolver":"https://pith.science/pith/NPZMVQJEGEGGXZHPV32RURIFJH","bundle":"https://pith.science/pith/NPZMVQJEGEGGXZHPV32RURIFJH/bundle.json","state":"https://pith.science/pith/NPZMVQJEGEGGXZHPV32RURIFJH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NPZMVQJEGEGGXZHPV32RURIFJH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NPZMVQJEGEGGXZHPV32RURIFJH","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":"8cceb55b4ad7233a5c2b45f0cc4272a9fdf8f9ecf76e112c1aeab6f754124db2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-04-23T18:54:40Z","title_canon_sha256":"0afe2d0afb3079ecef859a957051951fb302eff2513952a909ff40ea734e9124"},"schema_version":"1.0","source":{"id":"1704.06961","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.06961","created_at":"2026-05-18T00:10:52Z"},{"alias_kind":"arxiv_version","alias_value":"1704.06961v3","created_at":"2026-05-18T00:10:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06961","created_at":"2026-05-18T00:10:52Z"},{"alias_kind":"pith_short_12","alias_value":"NPZMVQJEGEGG","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NPZMVQJEGEGGXZHP","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NPZMVQJE","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:9a907a3fc1ed4908068454dbc4c4bed2c3372395a730e3f078b292bff88042da","target":"graph","created_at":"2026-05-18T00:10:52Z","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":"It is known that if $M$ is a finite-dimensional Banach space, or a strictly convex space, or the space $\\ell_1$, then every non-expansive bijection $F: B_M \\to B_M$ is an isometry. We extend these results to non-expansive bijections $F: B_E \\to B_M$ between unit balls of two different Banach spaces. Namely, if $E$ is an arbitrary Banach space and $M$ is finite-dimensional or strictly convex, or the space $\\ell_1$ then every non-expansive bijection $F: B_E \\to B_M$ is an isometry.","authors_text":"Olesia Zavarzina","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-04-23T18:54:40Z","title":"Non-expansive bijections between unit balls of Banach spaces (A technical version with some boring proofs included)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06961","kind":"arxiv","version":3},"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:e63733dbab1302d2835500529fe9696c6033c8a57e2036d769c210b36d9b41d3","target":"record","created_at":"2026-05-18T00:10:52Z","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":"8cceb55b4ad7233a5c2b45f0cc4272a9fdf8f9ecf76e112c1aeab6f754124db2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-04-23T18:54:40Z","title_canon_sha256":"0afe2d0afb3079ecef859a957051951fb302eff2513952a909ff40ea734e9124"},"schema_version":"1.0","source":{"id":"1704.06961","kind":"arxiv","version":3}},"canonical_sha256":"6bf2cac124310c6be4efaef51a450549da12d66f3cde29f9cff73b381dfc2830","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6bf2cac124310c6be4efaef51a450549da12d66f3cde29f9cff73b381dfc2830","first_computed_at":"2026-05-18T00:10:52.305056Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:52.305056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EHY90QvFVJ2FCBMxsjp8PonSFPY26t32B+mouGuopja1lhf7yqHJFJbGCnVFGkeR1Xhcr4tD0qQ+szw2rjbEBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:52.305731Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.06961","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e63733dbab1302d2835500529fe9696c6033c8a57e2036d769c210b36d9b41d3","sha256:9a907a3fc1ed4908068454dbc4c4bed2c3372395a730e3f078b292bff88042da"],"state_sha256":"5586ee59da40bd2bc5b6672340d07bcb54e7ed20f59bb8dc4598b19f4662be5b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"evCqcL/ThfpidPHW+WZR1Xsa+d4EQXIM/DqUq+idPkMXOKuQNIffgFm/WFemyH1/CaDbnEK8RSPulx0SVUXZBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T20:06:39.325414Z","bundle_sha256":"6ca7ad9a82ee22cc6cd680b3371bec7617fde0f744ab747d26ef5406d301fb2a"}}