{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:EFJBNYGRYPAPFTEMHXCAZYCLCN","short_pith_number":"pith:EFJBNYGR","canonical_record":{"source":{"id":"1111.1627","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-11-07T16:09:50Z","cross_cats_sorted":[],"title_canon_sha256":"8b0e3bfc5b98d8c3a7bde34fb3139b6ea6c95acc77e44a1ab77df7984ec7bc3f","abstract_canon_sha256":"92a3bd6937d47fbfe2e342e5825f117d55413cabe0b51055a4a3a92948a2bc07"},"schema_version":"1.0"},"canonical_sha256":"215216e0d1c3c0f2cc8c3dc40ce04b13777a71593106494421ba717758538bc4","source":{"kind":"arxiv","id":"1111.1627","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.1627","created_at":"2026-05-18T03:56:10Z"},{"alias_kind":"arxiv_version","alias_value":"1111.1627v2","created_at":"2026-05-18T03:56:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.1627","created_at":"2026-05-18T03:56:10Z"},{"alias_kind":"pith_short_12","alias_value":"EFJBNYGRYPAP","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"EFJBNYGRYPAPFTEM","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"EFJBNYGR","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:EFJBNYGRYPAPFTEMHXCAZYCLCN","target":"record","payload":{"canonical_record":{"source":{"id":"1111.1627","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-11-07T16:09:50Z","cross_cats_sorted":[],"title_canon_sha256":"8b0e3bfc5b98d8c3a7bde34fb3139b6ea6c95acc77e44a1ab77df7984ec7bc3f","abstract_canon_sha256":"92a3bd6937d47fbfe2e342e5825f117d55413cabe0b51055a4a3a92948a2bc07"},"schema_version":"1.0"},"canonical_sha256":"215216e0d1c3c0f2cc8c3dc40ce04b13777a71593106494421ba717758538bc4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:10.568826Z","signature_b64":"jrqgF1/r8h2Kgu6QaKI24ID6w3ozw5++MvDpww+0nXf6GQOJDn6fetuvd12eHy8nnrn/3DYUl0sPgfO9++iaDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"215216e0d1c3c0f2cc8c3dc40ce04b13777a71593106494421ba717758538bc4","last_reissued_at":"2026-05-18T03:56:10.567925Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:10.567925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.1627","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":"2026-05-18T03:56:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qDJV5zUNTtX8XG4gGFFgEDLb4kEC1TQ9xVxZJu70eHwA/2NgV9RgL8rAv/ULeT8vmmw9qh9hvj+X6aQVij17Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T10:20:09.835935Z"},"content_sha256":"b81fb18acf3e8560c24b5db99d241b4a3289b7c1bef2e2a1e3fb087fb5f4a36d","schema_version":"1.0","event_id":"sha256:b81fb18acf3e8560c24b5db99d241b4a3289b7c1bef2e2a1e3fb087fb5f4a36d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:EFJBNYGRYPAPFTEMHXCAZYCLCN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Two infinite versions of nonlinear Dvoretzky's theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Kei Funano","submitted_at":"2011-11-07T16:09:50Z","abstract_excerpt":"We investigate nonlinear Dvoretzky's theorem for countably infinite metric spaces and analytic sets whose Hausdorff dimension are infinite."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1627","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":"2026-05-18T03:56:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h8wxh5ElJJuQwFF2SoOlJ1WEy8d/SPIqYJwsKPUXNcN1s6hNlNggiLICrzFzexupDJ2s41725knyXZgIEilsDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T10:20:09.836261Z"},"content_sha256":"7f28b01ec2f9996c6ed21a96f8013bfbad46ede9d7601b76dfca31b7c089eb62","schema_version":"1.0","event_id":"sha256:7f28b01ec2f9996c6ed21a96f8013bfbad46ede9d7601b76dfca31b7c089eb62"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EFJBNYGRYPAPFTEMHXCAZYCLCN/bundle.json","state_url":"https://pith.science/pith/EFJBNYGRYPAPFTEMHXCAZYCLCN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EFJBNYGRYPAPFTEMHXCAZYCLCN/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":"2026-06-09T10:20:09Z","links":{"resolver":"https://pith.science/pith/EFJBNYGRYPAPFTEMHXCAZYCLCN","bundle":"https://pith.science/pith/EFJBNYGRYPAPFTEMHXCAZYCLCN/bundle.json","state":"https://pith.science/pith/EFJBNYGRYPAPFTEMHXCAZYCLCN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EFJBNYGRYPAPFTEMHXCAZYCLCN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:EFJBNYGRYPAPFTEMHXCAZYCLCN","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":"92a3bd6937d47fbfe2e342e5825f117d55413cabe0b51055a4a3a92948a2bc07","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-11-07T16:09:50Z","title_canon_sha256":"8b0e3bfc5b98d8c3a7bde34fb3139b6ea6c95acc77e44a1ab77df7984ec7bc3f"},"schema_version":"1.0","source":{"id":"1111.1627","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.1627","created_at":"2026-05-18T03:56:10Z"},{"alias_kind":"arxiv_version","alias_value":"1111.1627v2","created_at":"2026-05-18T03:56:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.1627","created_at":"2026-05-18T03:56:10Z"},{"alias_kind":"pith_short_12","alias_value":"EFJBNYGRYPAP","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"EFJBNYGRYPAPFTEM","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"EFJBNYGR","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:7f28b01ec2f9996c6ed21a96f8013bfbad46ede9d7601b76dfca31b7c089eb62","target":"graph","created_at":"2026-05-18T03:56:10Z","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 investigate nonlinear Dvoretzky's theorem for countably infinite metric spaces and analytic sets whose Hausdorff dimension are infinite.","authors_text":"Kei Funano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-11-07T16:09:50Z","title":"Two infinite versions of nonlinear Dvoretzky's theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1627","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:b81fb18acf3e8560c24b5db99d241b4a3289b7c1bef2e2a1e3fb087fb5f4a36d","target":"record","created_at":"2026-05-18T03:56:10Z","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":"92a3bd6937d47fbfe2e342e5825f117d55413cabe0b51055a4a3a92948a2bc07","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-11-07T16:09:50Z","title_canon_sha256":"8b0e3bfc5b98d8c3a7bde34fb3139b6ea6c95acc77e44a1ab77df7984ec7bc3f"},"schema_version":"1.0","source":{"id":"1111.1627","kind":"arxiv","version":2}},"canonical_sha256":"215216e0d1c3c0f2cc8c3dc40ce04b13777a71593106494421ba717758538bc4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"215216e0d1c3c0f2cc8c3dc40ce04b13777a71593106494421ba717758538bc4","first_computed_at":"2026-05-18T03:56:10.567925Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:10.567925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jrqgF1/r8h2Kgu6QaKI24ID6w3ozw5++MvDpww+0nXf6GQOJDn6fetuvd12eHy8nnrn/3DYUl0sPgfO9++iaDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:10.568826Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.1627","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b81fb18acf3e8560c24b5db99d241b4a3289b7c1bef2e2a1e3fb087fb5f4a36d","sha256:7f28b01ec2f9996c6ed21a96f8013bfbad46ede9d7601b76dfca31b7c089eb62"],"state_sha256":"4d84b480489ce3de75725fb1a4acc4ebc7d44f1c5da8828090a0437ca9ba607c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e/nrAzcqQCAy1yfMnKnJVn56EshJyFpBgdPPscLMUPDJsEOltNiQWmjy2Mspnnf8bhQxb01rV7gwcfta1xHiAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T10:20:09.838004Z","bundle_sha256":"6fa26da27d158f1f8a57b11fb0b8a36e5b060926460af9bead4d79d21feaec24"}}