{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1991:IN26JJVAXZNFFIGAMPM5WCQZBU","short_pith_number":"pith:IN26JJVA","schema_version":"1.0","canonical_sha256":"4375e4a6a0be5a52a0c063d9db0a190d181a2bcecede7d16860614db1cd045c8","source":{"kind":"arxiv","id":"math/9201282","version":1},"attestation_state":"computed","paper":{"title":"The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Mitsuhiro Shishikura","submitted_at":"1991-04-12T00:00:00Z","abstract_excerpt":"It is shown that the boundary of the Mandelbrot set $M$ has Hausdorff dimension two and that for a generic $c \\in \\bM$, the Julia set of $z \\mapsto z^2+c$ also has Hausdorff dimension two. The proof is based on the study of the bifurcation of parabolic periodic points."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/9201282","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DS","submitted_at":"1991-04-12T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"93a7d231de17ded5485d07d3a01dd1b1da9566749cc19935b203307ef72cb798","abstract_canon_sha256":"f1272077fd6ddf30084fad67990092ccd9d2b68a33554ed8e79423f29afca2d1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:54.559954Z","signature_b64":"RX/mXPfYTIziZuH0zFXXCI1KyvEx1jbam50JpMjskX70avdje+aVbLZO8vdl172OlQ1XKuOhIovpnH0ZrkV+DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4375e4a6a0be5a52a0c063d9db0a190d181a2bcecede7d16860614db1cd045c8","last_reissued_at":"2026-05-18T01:05:54.559549Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:54.559549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Mitsuhiro Shishikura","submitted_at":"1991-04-12T00:00:00Z","abstract_excerpt":"It is shown that the boundary of the Mandelbrot set $M$ has Hausdorff dimension two and that for a generic $c \\in \\bM$, the Julia set of $z \\mapsto z^2+c$ also has Hausdorff dimension two. The proof is based on the study of the bifurcation of parabolic periodic points."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9201282","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/9201282","created_at":"2026-05-18T01:05:54.559620+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9201282v1","created_at":"2026-05-18T01:05:54.559620+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9201282","created_at":"2026-05-18T01:05:54.559620+00:00"},{"alias_kind":"pith_short_12","alias_value":"IN26JJVAXZNF","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_16","alias_value":"IN26JJVAXZNFFIGA","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_8","alias_value":"IN26JJVA","created_at":"2026-05-18T12:25:47.102015+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IN26JJVAXZNFFIGAMPM5WCQZBU","json":"https://pith.science/pith/IN26JJVAXZNFFIGAMPM5WCQZBU.json","graph_json":"https://pith.science/api/pith-number/IN26JJVAXZNFFIGAMPM5WCQZBU/graph.json","events_json":"https://pith.science/api/pith-number/IN26JJVAXZNFFIGAMPM5WCQZBU/events.json","paper":"https://pith.science/paper/IN26JJVA"},"agent_actions":{"view_html":"https://pith.science/pith/IN26JJVAXZNFFIGAMPM5WCQZBU","download_json":"https://pith.science/pith/IN26JJVAXZNFFIGAMPM5WCQZBU.json","view_paper":"https://pith.science/paper/IN26JJVA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9201282&json=true","fetch_graph":"https://pith.science/api/pith-number/IN26JJVAXZNFFIGAMPM5WCQZBU/graph.json","fetch_events":"https://pith.science/api/pith-number/IN26JJVAXZNFFIGAMPM5WCQZBU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IN26JJVAXZNFFIGAMPM5WCQZBU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IN26JJVAXZNFFIGAMPM5WCQZBU/action/storage_attestation","attest_author":"https://pith.science/pith/IN26JJVAXZNFFIGAMPM5WCQZBU/action/author_attestation","sign_citation":"https://pith.science/pith/IN26JJVAXZNFFIGAMPM5WCQZBU/action/citation_signature","submit_replication":"https://pith.science/pith/IN26JJVAXZNFFIGAMPM5WCQZBU/action/replication_record"}},"created_at":"2026-05-18T01:05:54.559620+00:00","updated_at":"2026-05-18T01:05:54.559620+00:00"}