{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:N4P25FN4ZDLYD4JRLLFOXXJPZ6","short_pith_number":"pith:N4P25FN4","canonical_record":{"source":{"id":"1004.0633","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-04-01T18:33:14Z","cross_cats_sorted":[],"title_canon_sha256":"68aa88aee864d124e689982f5d46c4852cf060f23f96df9007499ca6c0099c42","abstract_canon_sha256":"60c073d9cfffe91d08c5e1f8a55521221e9c9a0e7683e127896096829346fea6"},"schema_version":"1.0"},"canonical_sha256":"6f1fae95bcc8d781f1315acaebdd2fcf84d3eded961f0d16d89d46832e3e0bd3","source":{"kind":"arxiv","id":"1004.0633","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.0633","created_at":"2026-05-18T02:24:17Z"},{"alias_kind":"arxiv_version","alias_value":"1004.0633v1","created_at":"2026-05-18T02:24:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.0633","created_at":"2026-05-18T02:24:17Z"},{"alias_kind":"pith_short_12","alias_value":"N4P25FN4ZDLY","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"N4P25FN4ZDLYD4JR","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"N4P25FN4","created_at":"2026-05-18T12:26:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:N4P25FN4ZDLYD4JRLLFOXXJPZ6","target":"record","payload":{"canonical_record":{"source":{"id":"1004.0633","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-04-01T18:33:14Z","cross_cats_sorted":[],"title_canon_sha256":"68aa88aee864d124e689982f5d46c4852cf060f23f96df9007499ca6c0099c42","abstract_canon_sha256":"60c073d9cfffe91d08c5e1f8a55521221e9c9a0e7683e127896096829346fea6"},"schema_version":"1.0"},"canonical_sha256":"6f1fae95bcc8d781f1315acaebdd2fcf84d3eded961f0d16d89d46832e3e0bd3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:24:17.642848Z","signature_b64":"PGhcHgHML1NhLv2IXxoC4djUKPgLNdcXWQ0vfyUfRQ1dguSabwYGn/Zo5T8MRPmpQ3lF6bf58JqIG6H5DLulBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f1fae95bcc8d781f1315acaebdd2fcf84d3eded961f0d16d89d46832e3e0bd3","last_reissued_at":"2026-05-18T02:24:17.642242Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:24:17.642242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1004.0633","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":"2026-05-18T02:24:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lEzUaseH9BlgoYig8JZgepkSDErxshbmDxpHuZXGpI6mHh/FyXHQlyF4onYFICmQXNi9FIkCJdG+AYij1hv6BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:42:37.019980Z"},"content_sha256":"d69658987f116aebf8092bc336773b36708c3ca41e3ca45d269ca54beeeafe69","schema_version":"1.0","event_id":"sha256:d69658987f116aebf8092bc336773b36708c3ca41e3ca45d269ca54beeeafe69"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:N4P25FN4ZDLYD4JRLLFOXXJPZ6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Decoration Theorem for Mandelbrot and Multibrot Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Dzmitry Dudko","submitted_at":"2010-04-01T18:33:14Z","abstract_excerpt":"We prove the decoration theorem for the Mandelbrot set (and Multibrot sets) which says that when a \"little Mandelbrot set\" is removed from the Mandelbrot set, then most of the resulting connected components have small diameters."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0633","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":"2026-05-18T02:24:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sbpwLZ39Yafdk31CAqj0BmyLClYaJvraxnxZqJqBoTC/m/3tqfQv+9dKTFeJ/kgjrAYw2t+aLr2rymu0uQD3BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:42:37.020338Z"},"content_sha256":"83edbdb012bebf5f460aa3e06361e431df0160eddb211adf1c71d573314dab3e","schema_version":"1.0","event_id":"sha256:83edbdb012bebf5f460aa3e06361e431df0160eddb211adf1c71d573314dab3e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N4P25FN4ZDLYD4JRLLFOXXJPZ6/bundle.json","state_url":"https://pith.science/pith/N4P25FN4ZDLYD4JRLLFOXXJPZ6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N4P25FN4ZDLYD4JRLLFOXXJPZ6/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":"2026-06-02T04:42:37Z","links":{"resolver":"https://pith.science/pith/N4P25FN4ZDLYD4JRLLFOXXJPZ6","bundle":"https://pith.science/pith/N4P25FN4ZDLYD4JRLLFOXXJPZ6/bundle.json","state":"https://pith.science/pith/N4P25FN4ZDLYD4JRLLFOXXJPZ6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N4P25FN4ZDLYD4JRLLFOXXJPZ6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:N4P25FN4ZDLYD4JRLLFOXXJPZ6","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":"60c073d9cfffe91d08c5e1f8a55521221e9c9a0e7683e127896096829346fea6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-04-01T18:33:14Z","title_canon_sha256":"68aa88aee864d124e689982f5d46c4852cf060f23f96df9007499ca6c0099c42"},"schema_version":"1.0","source":{"id":"1004.0633","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.0633","created_at":"2026-05-18T02:24:17Z"},{"alias_kind":"arxiv_version","alias_value":"1004.0633v1","created_at":"2026-05-18T02:24:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.0633","created_at":"2026-05-18T02:24:17Z"},{"alias_kind":"pith_short_12","alias_value":"N4P25FN4ZDLY","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"N4P25FN4ZDLYD4JR","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"N4P25FN4","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:83edbdb012bebf5f460aa3e06361e431df0160eddb211adf1c71d573314dab3e","target":"graph","created_at":"2026-05-18T02:24:17Z","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 prove the decoration theorem for the Mandelbrot set (and Multibrot sets) which says that when a \"little Mandelbrot set\" is removed from the Mandelbrot set, then most of the resulting connected components have small diameters.","authors_text":"Dzmitry Dudko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-04-01T18:33:14Z","title":"The Decoration Theorem for Mandelbrot and Multibrot Sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0633","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:d69658987f116aebf8092bc336773b36708c3ca41e3ca45d269ca54beeeafe69","target":"record","created_at":"2026-05-18T02:24:17Z","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":"60c073d9cfffe91d08c5e1f8a55521221e9c9a0e7683e127896096829346fea6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-04-01T18:33:14Z","title_canon_sha256":"68aa88aee864d124e689982f5d46c4852cf060f23f96df9007499ca6c0099c42"},"schema_version":"1.0","source":{"id":"1004.0633","kind":"arxiv","version":1}},"canonical_sha256":"6f1fae95bcc8d781f1315acaebdd2fcf84d3eded961f0d16d89d46832e3e0bd3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f1fae95bcc8d781f1315acaebdd2fcf84d3eded961f0d16d89d46832e3e0bd3","first_computed_at":"2026-05-18T02:24:17.642242Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:17.642242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PGhcHgHML1NhLv2IXxoC4djUKPgLNdcXWQ0vfyUfRQ1dguSabwYGn/Zo5T8MRPmpQ3lF6bf58JqIG6H5DLulBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:17.642848Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.0633","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d69658987f116aebf8092bc336773b36708c3ca41e3ca45d269ca54beeeafe69","sha256:83edbdb012bebf5f460aa3e06361e431df0160eddb211adf1c71d573314dab3e"],"state_sha256":"c46e81a59ba0d1fee4174c791557af3f54ba3292dc0f363024d85c5fc4758c39"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gPDmCwV3MySpveIYHM5GEWLo6+rmGw+JMd2Ow5gj5Rwm3vsYj5TzelD8eOxC8uOCGq4D5TDWfropD8MSFj10Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T04:42:37.022206Z","bundle_sha256":"12eaa1e296a05a11f8fe1f3784bdb4e08b0dbed81ee21d9734fc29fae77ba1ac"}}