{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:DN2JQHLQULONLPCLAIP7CHHMIM","short_pith_number":"pith:DN2JQHLQ","canonical_record":{"source":{"id":"1404.5877","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-04-23T16:15:48Z","cross_cats_sorted":["cs.CG","math.FA"],"title_canon_sha256":"3cf2de8cec32c1af623f9a34243c2666af6ecf91f5f676742f87d6e48222e8e4","abstract_canon_sha256":"8a53a1a86c864f1fc229dd0a2908dd360369a5e7fd5d45f5378e320a03ec22a5"},"schema_version":"1.0"},"canonical_sha256":"1b74981d70a2dcd5bc4b021ff11cec431776b39829afe219a4001a0572ec47df","source":{"kind":"arxiv","id":"1404.5877","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5877","created_at":"2026-05-18T00:48:06Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5877v3","created_at":"2026-05-18T00:48:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5877","created_at":"2026-05-18T00:48:06Z"},{"alias_kind":"pith_short_12","alias_value":"DN2JQHLQULON","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DN2JQHLQULONLPCL","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DN2JQHLQ","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:DN2JQHLQULONLPCLAIP7CHHMIM","target":"record","payload":{"canonical_record":{"source":{"id":"1404.5877","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-04-23T16:15:48Z","cross_cats_sorted":["cs.CG","math.FA"],"title_canon_sha256":"3cf2de8cec32c1af623f9a34243c2666af6ecf91f5f676742f87d6e48222e8e4","abstract_canon_sha256":"8a53a1a86c864f1fc229dd0a2908dd360369a5e7fd5d45f5378e320a03ec22a5"},"schema_version":"1.0"},"canonical_sha256":"1b74981d70a2dcd5bc4b021ff11cec431776b39829afe219a4001a0572ec47df","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:06.019504Z","signature_b64":"SHawHzTQMGdgmZ82UUFQBuvE9pBWImcMMsxpayJcERn4HUYypKVf1a6vlIJNsWyFRHtXnTI7symbhXfzhDB/Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b74981d70a2dcd5bc4b021ff11cec431776b39829afe219a4001a0572ec47df","last_reissued_at":"2026-05-18T00:48:06.018898Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:06.018898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.5877","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":"2026-05-18T00:48:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7SYRv5dBLOo8jrlIOBcw7Oa2ObQxLC+0OfI1NVEvlLZfwFjcNUvC0DTnEdjwW1MNpLiwvO5mNSTpRcZ1l/JqBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T04:15:38.522391Z"},"content_sha256":"a339fe05b17155a9bcc4af6856b78ce0e0fc770fa93a5c1a7cb46cdf7fd157d9","schema_version":"1.0","event_id":"sha256:a339fe05b17155a9bcc4af6856b78ce0e0fc770fa93a5c1a7cb46cdf7fd157d9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:DN2JQHLQULONLPCLAIP7CHHMIM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Density not realizable as the Jacobian determinant of a bilipschitz map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","math.FA"],"primary_cat":"math.MG","authors_text":"Vojt\\v{e}ch Kalu\\v{z}a","submitted_at":"2014-04-23T16:15:48Z","abstract_excerpt":"Are every two separated nets in the plane bilipschitz equivalent? In the late 1990s, Burago and Kleiner and, independently, McMullen resolved this beautiful question negatively. Both solutions are based on a construction of a density function that is not realizable as the Jacobian determinant of a bilipschitz map. McMullen's construction is simpler than the Burago-Kleiner one, and we provide a full proof of its nonrealizability, which has not been available in the literature."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5877","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":"2026-05-18T00:48:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vjKs695Jle8a2QLtX7x18wTR9Sfiq7fgqoL1T8ENi0AwStO0rcONk/elVUfntbPcirSJEVhxfEhrH6U5tOEsAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T04:15:38.522744Z"},"content_sha256":"aaacb1effc17ed57f15ac9b3a8a6a1bb2aa22612d1f0c0be7337d36a6f060c1c","schema_version":"1.0","event_id":"sha256:aaacb1effc17ed57f15ac9b3a8a6a1bb2aa22612d1f0c0be7337d36a6f060c1c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DN2JQHLQULONLPCLAIP7CHHMIM/bundle.json","state_url":"https://pith.science/pith/DN2JQHLQULONLPCLAIP7CHHMIM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DN2JQHLQULONLPCLAIP7CHHMIM/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":"2026-06-20T04:15:38Z","links":{"resolver":"https://pith.science/pith/DN2JQHLQULONLPCLAIP7CHHMIM","bundle":"https://pith.science/pith/DN2JQHLQULONLPCLAIP7CHHMIM/bundle.json","state":"https://pith.science/pith/DN2JQHLQULONLPCLAIP7CHHMIM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DN2JQHLQULONLPCLAIP7CHHMIM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DN2JQHLQULONLPCLAIP7CHHMIM","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":"8a53a1a86c864f1fc229dd0a2908dd360369a5e7fd5d45f5378e320a03ec22a5","cross_cats_sorted":["cs.CG","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-04-23T16:15:48Z","title_canon_sha256":"3cf2de8cec32c1af623f9a34243c2666af6ecf91f5f676742f87d6e48222e8e4"},"schema_version":"1.0","source":{"id":"1404.5877","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5877","created_at":"2026-05-18T00:48:06Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5877v3","created_at":"2026-05-18T00:48:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5877","created_at":"2026-05-18T00:48:06Z"},{"alias_kind":"pith_short_12","alias_value":"DN2JQHLQULON","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DN2JQHLQULONLPCL","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DN2JQHLQ","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:aaacb1effc17ed57f15ac9b3a8a6a1bb2aa22612d1f0c0be7337d36a6f060c1c","target":"graph","created_at":"2026-05-18T00:48:06Z","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":"Are every two separated nets in the plane bilipschitz equivalent? In the late 1990s, Burago and Kleiner and, independently, McMullen resolved this beautiful question negatively. Both solutions are based on a construction of a density function that is not realizable as the Jacobian determinant of a bilipschitz map. McMullen's construction is simpler than the Burago-Kleiner one, and we provide a full proof of its nonrealizability, which has not been available in the literature.","authors_text":"Vojt\\v{e}ch Kalu\\v{z}a","cross_cats":["cs.CG","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-04-23T16:15:48Z","title":"Density not realizable as the Jacobian determinant of a bilipschitz map"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5877","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:a339fe05b17155a9bcc4af6856b78ce0e0fc770fa93a5c1a7cb46cdf7fd157d9","target":"record","created_at":"2026-05-18T00:48:06Z","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":"8a53a1a86c864f1fc229dd0a2908dd360369a5e7fd5d45f5378e320a03ec22a5","cross_cats_sorted":["cs.CG","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-04-23T16:15:48Z","title_canon_sha256":"3cf2de8cec32c1af623f9a34243c2666af6ecf91f5f676742f87d6e48222e8e4"},"schema_version":"1.0","source":{"id":"1404.5877","kind":"arxiv","version":3}},"canonical_sha256":"1b74981d70a2dcd5bc4b021ff11cec431776b39829afe219a4001a0572ec47df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b74981d70a2dcd5bc4b021ff11cec431776b39829afe219a4001a0572ec47df","first_computed_at":"2026-05-18T00:48:06.018898Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:06.018898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SHawHzTQMGdgmZ82UUFQBuvE9pBWImcMMsxpayJcERn4HUYypKVf1a6vlIJNsWyFRHtXnTI7symbhXfzhDB/Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:06.019504Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.5877","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a339fe05b17155a9bcc4af6856b78ce0e0fc770fa93a5c1a7cb46cdf7fd157d9","sha256:aaacb1effc17ed57f15ac9b3a8a6a1bb2aa22612d1f0c0be7337d36a6f060c1c"],"state_sha256":"f6579d9a2ce8907d560bde76fc685f535f03f4b7ff09834f01774a2e87b628c4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eDeCLztIbRbN4pmPMA1UegQo/7nlDhGtUbPRjU4eer9CUmKjVisEE7Us59se+UphTbln0ACtTPx/kekn0ivQDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T04:15:38.524700Z","bundle_sha256":"487dea73fb02dcf0be1cc849fcd36c646bb189a4d40bebcfe677fa3ee2ca6414"}}