{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:D2F3CDP5JC5LO2W6IVOCHNGATZ","short_pith_number":"pith:D2F3CDP5","canonical_record":{"source":{"id":"1406.3545","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-06-13T14:20:24Z","cross_cats_sorted":[],"title_canon_sha256":"3e15cdf8f2b8c7d8c68dff90cb4e754152731cfa99e9d085c6c2e4c337e764f4","abstract_canon_sha256":"b7228db6030f2f00cd970f5ea11aa7eab32ef7ad2f580f3cfa1ec2315f2c06ea"},"schema_version":"1.0"},"canonical_sha256":"1e8bb10dfd48bab76ade455c23b4c09e561d1456c9aa5c31524ca7f88a5005c3","source":{"kind":"arxiv","id":"1406.3545","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.3545","created_at":"2026-05-18T02:49:11Z"},{"alias_kind":"arxiv_version","alias_value":"1406.3545v2","created_at":"2026-05-18T02:49:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3545","created_at":"2026-05-18T02:49:11Z"},{"alias_kind":"pith_short_12","alias_value":"D2F3CDP5JC5L","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"D2F3CDP5JC5LO2W6","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"D2F3CDP5","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:D2F3CDP5JC5LO2W6IVOCHNGATZ","target":"record","payload":{"canonical_record":{"source":{"id":"1406.3545","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-06-13T14:20:24Z","cross_cats_sorted":[],"title_canon_sha256":"3e15cdf8f2b8c7d8c68dff90cb4e754152731cfa99e9d085c6c2e4c337e764f4","abstract_canon_sha256":"b7228db6030f2f00cd970f5ea11aa7eab32ef7ad2f580f3cfa1ec2315f2c06ea"},"schema_version":"1.0"},"canonical_sha256":"1e8bb10dfd48bab76ade455c23b4c09e561d1456c9aa5c31524ca7f88a5005c3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:11.440763Z","signature_b64":"qpO1ppVMfmIKmnP/S2tpVt+ThAyxIxh84HlgiWkO/D9r6CSPiH766XwlvfynqAmgcTwyv1AOPIbQETy9kT4YBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1e8bb10dfd48bab76ade455c23b4c09e561d1456c9aa5c31524ca7f88a5005c3","last_reissued_at":"2026-05-18T02:49:11.440327Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:11.440327Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.3545","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":"2026-05-18T02:49:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"65XLxNvq4cO7AKXbTLdeFfI35kcSD54aolHQgEVrl5MVLaUIz4AVq3yuGk0BNviHF5p571yXs+LLC3HdCj/lAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T01:38:19.822953Z"},"content_sha256":"34e4cfb7d4b8113dc1bf774b7ed62bd3e6fd1820665111ebabb063c7183ef365","schema_version":"1.0","event_id":"sha256:34e4cfb7d4b8113dc1bf774b7ed62bd3e6fd1820665111ebabb063c7183ef365"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:D2F3CDP5JC5LO2W6IVOCHNGATZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Shapes, fingerprints and rational lemniscates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Malik Younsi","submitted_at":"2014-06-13T14:20:24Z","abstract_excerpt":"It has been known since the work of A.A. Kirillov that any smooth Jordan curve in the plane can be represented by its so-called fingerprint, an orientation preserving smooth diffeomorphism of the unit circle onto itself. In this paper, we give a new, simple proof of a theorem of Ebenfelt, Khavinson and Shapiro stating that the fingerprint of a polynomial lemniscate of degree $n$ is given by the $n$-th root of a Blaschke product of degree $n$ and that conversely, any smooth diffeomorphism induced by such a map is the fingerprint of a polynomial lemniscate of the same degree. The proof is easily"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3545","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":"2026-05-18T02:49:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QJ6+jEUPrncStMEIyx9toMI9yPK4fVGLfe77TWMFtQOGZJgHXUbFV90Oirq+O5fB8woTeiwnTM9q4iK1bwHwCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T01:38:19.823289Z"},"content_sha256":"4c1e7933943797d636c0af90650534a5d90fa73a84cda9aa4baab934e735edf4","schema_version":"1.0","event_id":"sha256:4c1e7933943797d636c0af90650534a5d90fa73a84cda9aa4baab934e735edf4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D2F3CDP5JC5LO2W6IVOCHNGATZ/bundle.json","state_url":"https://pith.science/pith/D2F3CDP5JC5LO2W6IVOCHNGATZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D2F3CDP5JC5LO2W6IVOCHNGATZ/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":"2026-06-22T01:38:19Z","links":{"resolver":"https://pith.science/pith/D2F3CDP5JC5LO2W6IVOCHNGATZ","bundle":"https://pith.science/pith/D2F3CDP5JC5LO2W6IVOCHNGATZ/bundle.json","state":"https://pith.science/pith/D2F3CDP5JC5LO2W6IVOCHNGATZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D2F3CDP5JC5LO2W6IVOCHNGATZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:D2F3CDP5JC5LO2W6IVOCHNGATZ","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":"b7228db6030f2f00cd970f5ea11aa7eab32ef7ad2f580f3cfa1ec2315f2c06ea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-06-13T14:20:24Z","title_canon_sha256":"3e15cdf8f2b8c7d8c68dff90cb4e754152731cfa99e9d085c6c2e4c337e764f4"},"schema_version":"1.0","source":{"id":"1406.3545","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.3545","created_at":"2026-05-18T02:49:11Z"},{"alias_kind":"arxiv_version","alias_value":"1406.3545v2","created_at":"2026-05-18T02:49:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3545","created_at":"2026-05-18T02:49:11Z"},{"alias_kind":"pith_short_12","alias_value":"D2F3CDP5JC5L","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"D2F3CDP5JC5LO2W6","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"D2F3CDP5","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:4c1e7933943797d636c0af90650534a5d90fa73a84cda9aa4baab934e735edf4","target":"graph","created_at":"2026-05-18T02:49:11Z","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 has been known since the work of A.A. Kirillov that any smooth Jordan curve in the plane can be represented by its so-called fingerprint, an orientation preserving smooth diffeomorphism of the unit circle onto itself. In this paper, we give a new, simple proof of a theorem of Ebenfelt, Khavinson and Shapiro stating that the fingerprint of a polynomial lemniscate of degree $n$ is given by the $n$-th root of a Blaschke product of degree $n$ and that conversely, any smooth diffeomorphism induced by such a map is the fingerprint of a polynomial lemniscate of the same degree. The proof is easily","authors_text":"Malik Younsi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-06-13T14:20:24Z","title":"Shapes, fingerprints and rational lemniscates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3545","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":"sha256:34e4cfb7d4b8113dc1bf774b7ed62bd3e6fd1820665111ebabb063c7183ef365","target":"record","created_at":"2026-05-18T02:49:11Z","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":"b7228db6030f2f00cd970f5ea11aa7eab32ef7ad2f580f3cfa1ec2315f2c06ea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-06-13T14:20:24Z","title_canon_sha256":"3e15cdf8f2b8c7d8c68dff90cb4e754152731cfa99e9d085c6c2e4c337e764f4"},"schema_version":"1.0","source":{"id":"1406.3545","kind":"arxiv","version":2}},"canonical_sha256":"1e8bb10dfd48bab76ade455c23b4c09e561d1456c9aa5c31524ca7f88a5005c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e8bb10dfd48bab76ade455c23b4c09e561d1456c9aa5c31524ca7f88a5005c3","first_computed_at":"2026-05-18T02:49:11.440327Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:11.440327Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qpO1ppVMfmIKmnP/S2tpVt+ThAyxIxh84HlgiWkO/D9r6CSPiH766XwlvfynqAmgcTwyv1AOPIbQETy9kT4YBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:11.440763Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.3545","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34e4cfb7d4b8113dc1bf774b7ed62bd3e6fd1820665111ebabb063c7183ef365","sha256:4c1e7933943797d636c0af90650534a5d90fa73a84cda9aa4baab934e735edf4"],"state_sha256":"3013e594e248febc224563aa9a66bf8e29918c68542c72f977d8474659784649"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w4C12nrUC434wVEBvBZUGGKfQUNbiYwSzskyYtgWpCutASucj7hk51Z4CirmNUXFRsIyQrWSJNj/qW31sWXtBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T01:38:19.825184Z","bundle_sha256":"e981375f3810b92510638512ccb50c339a40c4f81f6256ebb9faac673972866d"}}