{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:G3Y6T4OFO5IOT2JBBIHFOI3R2H","short_pith_number":"pith:G3Y6T4OF","canonical_record":{"source":{"id":"1311.2104","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-11-08T23:26:10Z","cross_cats_sorted":[],"title_canon_sha256":"4c6215cfa7ce2351c29e4ed7f7c8138c17070eae058a14e8ac32441f5f7db01a","abstract_canon_sha256":"18fa37155982521a3b1a2a7084fea01ac2252bbff02fa0e5c987a4fca4034943"},"schema_version":"1.0"},"canonical_sha256":"36f1e9f1c57750e9e9210a0e572371d1c51b0b1acd3b518f793dee5ee375f410","source":{"kind":"arxiv","id":"1311.2104","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.2104","created_at":"2026-05-18T00:41:13Z"},{"alias_kind":"arxiv_version","alias_value":"1311.2104v1","created_at":"2026-05-18T00:41:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.2104","created_at":"2026-05-18T00:41:13Z"},{"alias_kind":"pith_short_12","alias_value":"G3Y6T4OFO5IO","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"G3Y6T4OFO5IOT2JB","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"G3Y6T4OF","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:G3Y6T4OFO5IOT2JBBIHFOI3R2H","target":"record","payload":{"canonical_record":{"source":{"id":"1311.2104","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-11-08T23:26:10Z","cross_cats_sorted":[],"title_canon_sha256":"4c6215cfa7ce2351c29e4ed7f7c8138c17070eae058a14e8ac32441f5f7db01a","abstract_canon_sha256":"18fa37155982521a3b1a2a7084fea01ac2252bbff02fa0e5c987a4fca4034943"},"schema_version":"1.0"},"canonical_sha256":"36f1e9f1c57750e9e9210a0e572371d1c51b0b1acd3b518f793dee5ee375f410","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:13.395257Z","signature_b64":"F3LFI1YrizMf/GUmtSsLTXXnGda2bku0pH/FeJwqiF5VAClCEVyUniIWOEETvOT34woAMAGDOUsMNcWXRRsFAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36f1e9f1c57750e9e9210a0e572371d1c51b0b1acd3b518f793dee5ee375f410","last_reissued_at":"2026-05-18T00:41:13.394748Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:13.394748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.2104","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":"2026-05-18T00:41:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NzdC+14badrQxdxLiEEiSjYv6weGRPi5B/1Wxr8fkY3unpuXDM/AWQmoo8TRlMNrZ8Q5SXsKle5Z922E8aYSAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T09:50:05.335559Z"},"content_sha256":"cbc1d6ab9f4579ae009cfef1b32360607baad1522af18f6fe99ca9bf01bfbba0","schema_version":"1.0","event_id":"sha256:cbc1d6ab9f4579ae009cfef1b32360607baad1522af18f6fe99ca9bf01bfbba0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:G3Y6T4OFO5IOT2JBBIHFOI3R2H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sets of constant distance from a Jordan curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Jang-Mei Wu, Vyron Vellis","submitted_at":"2013-11-08T23:26:10Z","abstract_excerpt":"We study the $\\epsilon$-level sets of the signed distance function to a planar Jordan curve $\\Gamma$, and ask what properties of $\\Gamma$ ensure that the $\\epsilon$-level sets are Jordan curves, or uniform quasicircles, or uniform chord-arc curves for all sufficiently small $\\epsilon$. Sufficient conditions are given in term of a scaled invariant parameter for measuring the local deviation of subarcs from their chords. The chordal conditions given are sharp."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2104","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":"2026-05-18T00:41:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uDThAWUMImSPZqfPyiQkacIwu52Y0EUosoddYIy6nzYvJOGpzRc+1zE7cWgtFA7zPVzpgHsA08VPPZdikbpnAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T09:50:05.335916Z"},"content_sha256":"ac6822dade0f96e3d7aada042568a4d8d524a68ce7e537ce33fce8ea629fc479","schema_version":"1.0","event_id":"sha256:ac6822dade0f96e3d7aada042568a4d8d524a68ce7e537ce33fce8ea629fc479"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G3Y6T4OFO5IOT2JBBIHFOI3R2H/bundle.json","state_url":"https://pith.science/pith/G3Y6T4OFO5IOT2JBBIHFOI3R2H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G3Y6T4OFO5IOT2JBBIHFOI3R2H/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":"2026-06-02T09:50:05Z","links":{"resolver":"https://pith.science/pith/G3Y6T4OFO5IOT2JBBIHFOI3R2H","bundle":"https://pith.science/pith/G3Y6T4OFO5IOT2JBBIHFOI3R2H/bundle.json","state":"https://pith.science/pith/G3Y6T4OFO5IOT2JBBIHFOI3R2H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G3Y6T4OFO5IOT2JBBIHFOI3R2H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:G3Y6T4OFO5IOT2JBBIHFOI3R2H","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":"18fa37155982521a3b1a2a7084fea01ac2252bbff02fa0e5c987a4fca4034943","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-11-08T23:26:10Z","title_canon_sha256":"4c6215cfa7ce2351c29e4ed7f7c8138c17070eae058a14e8ac32441f5f7db01a"},"schema_version":"1.0","source":{"id":"1311.2104","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.2104","created_at":"2026-05-18T00:41:13Z"},{"alias_kind":"arxiv_version","alias_value":"1311.2104v1","created_at":"2026-05-18T00:41:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.2104","created_at":"2026-05-18T00:41:13Z"},{"alias_kind":"pith_short_12","alias_value":"G3Y6T4OFO5IO","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"G3Y6T4OFO5IOT2JB","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"G3Y6T4OF","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:ac6822dade0f96e3d7aada042568a4d8d524a68ce7e537ce33fce8ea629fc479","target":"graph","created_at":"2026-05-18T00:41:13Z","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 study the $\\epsilon$-level sets of the signed distance function to a planar Jordan curve $\\Gamma$, and ask what properties of $\\Gamma$ ensure that the $\\epsilon$-level sets are Jordan curves, or uniform quasicircles, or uniform chord-arc curves for all sufficiently small $\\epsilon$. Sufficient conditions are given in term of a scaled invariant parameter for measuring the local deviation of subarcs from their chords. The chordal conditions given are sharp.","authors_text":"Jang-Mei Wu, Vyron Vellis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-11-08T23:26:10Z","title":"Sets of constant distance from a Jordan curve"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2104","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:cbc1d6ab9f4579ae009cfef1b32360607baad1522af18f6fe99ca9bf01bfbba0","target":"record","created_at":"2026-05-18T00:41:13Z","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":"18fa37155982521a3b1a2a7084fea01ac2252bbff02fa0e5c987a4fca4034943","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-11-08T23:26:10Z","title_canon_sha256":"4c6215cfa7ce2351c29e4ed7f7c8138c17070eae058a14e8ac32441f5f7db01a"},"schema_version":"1.0","source":{"id":"1311.2104","kind":"arxiv","version":1}},"canonical_sha256":"36f1e9f1c57750e9e9210a0e572371d1c51b0b1acd3b518f793dee5ee375f410","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36f1e9f1c57750e9e9210a0e572371d1c51b0b1acd3b518f793dee5ee375f410","first_computed_at":"2026-05-18T00:41:13.394748Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:13.394748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F3LFI1YrizMf/GUmtSsLTXXnGda2bku0pH/FeJwqiF5VAClCEVyUniIWOEETvOT34woAMAGDOUsMNcWXRRsFAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:13.395257Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.2104","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cbc1d6ab9f4579ae009cfef1b32360607baad1522af18f6fe99ca9bf01bfbba0","sha256:ac6822dade0f96e3d7aada042568a4d8d524a68ce7e537ce33fce8ea629fc479"],"state_sha256":"c3424999f487f43029f2c0c29d19d0c5bd790f245e16751b19484d1a4d1108bf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"StAL7oKq6KP58ZmcJXzwbX8s09Qmuxa85QQOatqLMbItubttLgAiFxW3N1l4USqATYNw42x8nfuyPs/B9a+xAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T09:50:05.337860Z","bundle_sha256":"fe5ec43083c0be11da34aafcd7576f1f58ad65fe9b63181050d61180f858d1d0"}}