{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:I3UIGVHNEREIFRH7D5FVCV5H7X","short_pith_number":"pith:I3UIGVHN","canonical_record":{"source":{"id":"1403.0246","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-03-02T17:32:19Z","cross_cats_sorted":[],"title_canon_sha256":"16b2403372c2a63358e0f493aecfd6acc5937fd17c9d3d53af8e4b71e3910b3c","abstract_canon_sha256":"8292230ce9edf357031a4c8ec63a244b37e6d068abccdc94bf42613f78cf939f"},"schema_version":"1.0"},"canonical_sha256":"46e88354ed244882c4ff1f4b5157a7fdfe9cf1e7d024fcf8d38d946393a789c5","source":{"kind":"arxiv","id":"1403.0246","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.0246","created_at":"2026-05-18T02:57:25Z"},{"alias_kind":"arxiv_version","alias_value":"1403.0246v1","created_at":"2026-05-18T02:57:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.0246","created_at":"2026-05-18T02:57:25Z"},{"alias_kind":"pith_short_12","alias_value":"I3UIGVHNEREI","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"I3UIGVHNEREIFRH7","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"I3UIGVHN","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:I3UIGVHNEREIFRH7D5FVCV5H7X","target":"record","payload":{"canonical_record":{"source":{"id":"1403.0246","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-03-02T17:32:19Z","cross_cats_sorted":[],"title_canon_sha256":"16b2403372c2a63358e0f493aecfd6acc5937fd17c9d3d53af8e4b71e3910b3c","abstract_canon_sha256":"8292230ce9edf357031a4c8ec63a244b37e6d068abccdc94bf42613f78cf939f"},"schema_version":"1.0"},"canonical_sha256":"46e88354ed244882c4ff1f4b5157a7fdfe9cf1e7d024fcf8d38d946393a789c5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:25.351206Z","signature_b64":"Pvvn3X/K2a4i6TCv7wiPZZYBGVMYCL5U/rnz4SpqsSU62er4AhqQirVk0FtdQjfxJ+Ix0u5u69ae/IUu7FwKBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46e88354ed244882c4ff1f4b5157a7fdfe9cf1e7d024fcf8d38d946393a789c5","last_reissued_at":"2026-05-18T02:57:25.350441Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:25.350441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.0246","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":"2026-05-18T02:57:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JOobzLG6OwJ10YcADx7w0AD/YrAp8bgihSIvo2lSxr6nyxHcyUk9sAS4SKFPxjRg6GQyyNLjUZETYAQRkR30Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T03:54:03.528171Z"},"content_sha256":"367a27269c488e532ab32ca601f37be35322dfc16e87559fb75ac276f31d4274","schema_version":"1.0","event_id":"sha256:367a27269c488e532ab32ca601f37be35322dfc16e87559fb75ac276f31d4274"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:I3UIGVHNEREIFRH7D5FVCV5H7X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Magic mirrors, dense diameters, Baire category","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Imre B\\'ar\\'any, Mikl\\'os Laczkovich","submitted_at":"2014-03-02T17:32:19Z","abstract_excerpt":"An old result of Zamfirescu says that for most convex curves $C$ in the plane most points in $R^2$ lie on infinitely many normals to $C$, where most is meant in Baire category sense. We strengthen this result by showing that `infinitely many' can be replaced by `contiunuum many' in the statement. We present further theorems in the same spirit."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0246","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":"2026-05-18T02:57:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AVOAL6sNRXI8uo6wI2f7TgkoJiR6LJTFB3WfUUtX6DLzJSJSrHc+2egWPsGTqfsdQ9iA3CntWQsuGrUpul7lCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T03:54:03.528964Z"},"content_sha256":"1a87f3021eae912f19f2733f57152884dc9cb4672640cf5d866dc87abc9f845c","schema_version":"1.0","event_id":"sha256:1a87f3021eae912f19f2733f57152884dc9cb4672640cf5d866dc87abc9f845c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I3UIGVHNEREIFRH7D5FVCV5H7X/bundle.json","state_url":"https://pith.science/pith/I3UIGVHNEREIFRH7D5FVCV5H7X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I3UIGVHNEREIFRH7D5FVCV5H7X/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":"2026-05-30T03:54:03Z","links":{"resolver":"https://pith.science/pith/I3UIGVHNEREIFRH7D5FVCV5H7X","bundle":"https://pith.science/pith/I3UIGVHNEREIFRH7D5FVCV5H7X/bundle.json","state":"https://pith.science/pith/I3UIGVHNEREIFRH7D5FVCV5H7X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I3UIGVHNEREIFRH7D5FVCV5H7X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:I3UIGVHNEREIFRH7D5FVCV5H7X","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":"8292230ce9edf357031a4c8ec63a244b37e6d068abccdc94bf42613f78cf939f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-03-02T17:32:19Z","title_canon_sha256":"16b2403372c2a63358e0f493aecfd6acc5937fd17c9d3d53af8e4b71e3910b3c"},"schema_version":"1.0","source":{"id":"1403.0246","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.0246","created_at":"2026-05-18T02:57:25Z"},{"alias_kind":"arxiv_version","alias_value":"1403.0246v1","created_at":"2026-05-18T02:57:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.0246","created_at":"2026-05-18T02:57:25Z"},{"alias_kind":"pith_short_12","alias_value":"I3UIGVHNEREI","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"I3UIGVHNEREIFRH7","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"I3UIGVHN","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:1a87f3021eae912f19f2733f57152884dc9cb4672640cf5d866dc87abc9f845c","target":"graph","created_at":"2026-05-18T02:57:25Z","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":"An old result of Zamfirescu says that for most convex curves $C$ in the plane most points in $R^2$ lie on infinitely many normals to $C$, where most is meant in Baire category sense. We strengthen this result by showing that `infinitely many' can be replaced by `contiunuum many' in the statement. We present further theorems in the same spirit.","authors_text":"Imre B\\'ar\\'any, Mikl\\'os Laczkovich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-03-02T17:32:19Z","title":"Magic mirrors, dense diameters, Baire category"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0246","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":"sha256:367a27269c488e532ab32ca601f37be35322dfc16e87559fb75ac276f31d4274","target":"record","created_at":"2026-05-18T02:57:25Z","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":"8292230ce9edf357031a4c8ec63a244b37e6d068abccdc94bf42613f78cf939f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-03-02T17:32:19Z","title_canon_sha256":"16b2403372c2a63358e0f493aecfd6acc5937fd17c9d3d53af8e4b71e3910b3c"},"schema_version":"1.0","source":{"id":"1403.0246","kind":"arxiv","version":1}},"canonical_sha256":"46e88354ed244882c4ff1f4b5157a7fdfe9cf1e7d024fcf8d38d946393a789c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46e88354ed244882c4ff1f4b5157a7fdfe9cf1e7d024fcf8d38d946393a789c5","first_computed_at":"2026-05-18T02:57:25.350441Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:25.350441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pvvn3X/K2a4i6TCv7wiPZZYBGVMYCL5U/rnz4SpqsSU62er4AhqQirVk0FtdQjfxJ+Ix0u5u69ae/IUu7FwKBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:25.351206Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.0246","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:367a27269c488e532ab32ca601f37be35322dfc16e87559fb75ac276f31d4274","sha256:1a87f3021eae912f19f2733f57152884dc9cb4672640cf5d866dc87abc9f845c"],"state_sha256":"2dcb5c0ce60abd9933dd2e979d5df4f7732544b510a7140c15962c046b73f25c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+YRh9gSFab/L8c/TrU8FW9wkP0C/F1xPd4yjLog6viPugXiZRCAtSrzU0CvX/UJy5pPH35KkWMkzwJ0P2slKAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T03:54:03.532553Z","bundle_sha256":"6c763afbb9309206a4ed21abdf89b0bc1f540ba6b3fb1d9b7239c8a7c9d69403"}}