{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1995:EMNWF6DIHNQVW4DFKLOLBG2MEG","short_pith_number":"pith:EMNWF6DI","canonical_record":{"source":{"id":"math/9511208","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DS","submitted_at":"1995-11-02T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"e3ffe7422807110f95b50058941ed43ed68b2c8e85d10ec7717959eaf884d55b","abstract_canon_sha256":"79da92942cc4644b1145ad671dd1f58fe5d24ca38f741a563878db21cfb8b60d"},"schema_version":"1.0"},"canonical_sha256":"231b62f8683b615b706552dcb09b4c2190bf357aa02d3e0894f0c7d4aff5904a","source":{"kind":"arxiv","id":"math/9511208","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9511208","created_at":"2026-05-18T01:05:48Z"},{"alias_kind":"arxiv_version","alias_value":"math/9511208v1","created_at":"2026-05-18T01:05:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9511208","created_at":"2026-05-18T01:05:48Z"},{"alias_kind":"pith_short_12","alias_value":"EMNWF6DIHNQV","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"EMNWF6DIHNQVW4DF","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"EMNWF6DI","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1995:EMNWF6DIHNQVW4DFKLOLBG2MEG","target":"record","payload":{"canonical_record":{"source":{"id":"math/9511208","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DS","submitted_at":"1995-11-02T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"e3ffe7422807110f95b50058941ed43ed68b2c8e85d10ec7717959eaf884d55b","abstract_canon_sha256":"79da92942cc4644b1145ad671dd1f58fe5d24ca38f741a563878db21cfb8b60d"},"schema_version":"1.0"},"canonical_sha256":"231b62f8683b615b706552dcb09b4c2190bf357aa02d3e0894f0c7d4aff5904a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:48.142875Z","signature_b64":"e8jsF1q6kSPG14Xw1F+UCqmbajSjQG1KrZEvib4OVHRDNVieqXwbrXlwmRrWsO2w1zeKU5d3x/+A8qHXpL+bCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"231b62f8683b615b706552dcb09b4c2190bf357aa02d3e0894f0c7d4aff5904a","last_reissued_at":"2026-05-18T01:05:48.142366Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:48.142366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9511208","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":"2026-05-18T01:05:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"epPGR083izw10Wb3k4eP4UgerMilTNfK2Byw2Eb8hXDtY8FD3KEIopER0XzZdylN8UWMiU8LKfWC1cqLUKixDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T22:36:41.491188Z"},"content_sha256":"d82207c2e55b2531f29d8b6ce23d51c61fae59cb88b94004905a23f555a68cb6","schema_version":"1.0","event_id":"sha256:d82207c2e55b2531f29d8b6ce23d51c61fae59cb88b94004905a23f555a68cb6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1995:EMNWF6DIHNQVW4DFKLOLBG2MEG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Renormalization Method and Quadratic-Like Maps","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Yunping Jiang","submitted_at":"1995-11-02T00:00:00Z","abstract_excerpt":"The renormalization of a quadratic-like map is studied. The three-dimensional Yoccoz puzzle for an infinitely renormalizable quadratic-like map is discussed. For an unbranched quadratic-like map having the {\\sl a priori} complex bounds, the local connectivity of its Julia set is proved by using the three-dimensional Yoccoz puzzle. The generalized version of Sullivan's sector theorem is discussed and is used to prove his result that the Feigenbaum quadratic polynomial has the {\\sl a priori} complex bounds and is unbranched. A dense subset on the boundary of the Mandelbrot set is constructed so "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9511208","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":"2026-05-18T01:05:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ps+zZMLDRYF0dy37gTVGi9G4PcSC4bZ9jB94BilBgq/hEG5qzpv4yBK+zbQud7+6MWiNNVZ14sGMeLTArv7DAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T22:36:41.491574Z"},"content_sha256":"46291b95dfd0b5607e983c99877627e994bb0181e0ade51a234b27c750932365","schema_version":"1.0","event_id":"sha256:46291b95dfd0b5607e983c99877627e994bb0181e0ade51a234b27c750932365"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EMNWF6DIHNQVW4DFKLOLBG2MEG/bundle.json","state_url":"https://pith.science/pith/EMNWF6DIHNQVW4DFKLOLBG2MEG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EMNWF6DIHNQVW4DFKLOLBG2MEG/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":"2026-06-30T22:36:41Z","links":{"resolver":"https://pith.science/pith/EMNWF6DIHNQVW4DFKLOLBG2MEG","bundle":"https://pith.science/pith/EMNWF6DIHNQVW4DFKLOLBG2MEG/bundle.json","state":"https://pith.science/pith/EMNWF6DIHNQVW4DFKLOLBG2MEG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EMNWF6DIHNQVW4DFKLOLBG2MEG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1995:EMNWF6DIHNQVW4DFKLOLBG2MEG","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":"79da92942cc4644b1145ad671dd1f58fe5d24ca38f741a563878db21cfb8b60d","cross_cats_sorted":[],"license":"","primary_cat":"math.DS","submitted_at":"1995-11-02T00:00:00Z","title_canon_sha256":"e3ffe7422807110f95b50058941ed43ed68b2c8e85d10ec7717959eaf884d55b"},"schema_version":"1.0","source":{"id":"math/9511208","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9511208","created_at":"2026-05-18T01:05:48Z"},{"alias_kind":"arxiv_version","alias_value":"math/9511208v1","created_at":"2026-05-18T01:05:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9511208","created_at":"2026-05-18T01:05:48Z"},{"alias_kind":"pith_short_12","alias_value":"EMNWF6DIHNQV","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"EMNWF6DIHNQVW4DF","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"EMNWF6DI","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:46291b95dfd0b5607e983c99877627e994bb0181e0ade51a234b27c750932365","target":"graph","created_at":"2026-05-18T01:05:48Z","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":"The renormalization of a quadratic-like map is studied. The three-dimensional Yoccoz puzzle for an infinitely renormalizable quadratic-like map is discussed. For an unbranched quadratic-like map having the {\\sl a priori} complex bounds, the local connectivity of its Julia set is proved by using the three-dimensional Yoccoz puzzle. The generalized version of Sullivan's sector theorem is discussed and is used to prove his result that the Feigenbaum quadratic polynomial has the {\\sl a priori} complex bounds and is unbranched. A dense subset on the boundary of the Mandelbrot set is constructed so ","authors_text":"Yunping Jiang","cross_cats":[],"headline":"","license":"","primary_cat":"math.DS","submitted_at":"1995-11-02T00:00:00Z","title":"The Renormalization Method and Quadratic-Like Maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9511208","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:d82207c2e55b2531f29d8b6ce23d51c61fae59cb88b94004905a23f555a68cb6","target":"record","created_at":"2026-05-18T01:05:48Z","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":"79da92942cc4644b1145ad671dd1f58fe5d24ca38f741a563878db21cfb8b60d","cross_cats_sorted":[],"license":"","primary_cat":"math.DS","submitted_at":"1995-11-02T00:00:00Z","title_canon_sha256":"e3ffe7422807110f95b50058941ed43ed68b2c8e85d10ec7717959eaf884d55b"},"schema_version":"1.0","source":{"id":"math/9511208","kind":"arxiv","version":1}},"canonical_sha256":"231b62f8683b615b706552dcb09b4c2190bf357aa02d3e0894f0c7d4aff5904a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"231b62f8683b615b706552dcb09b4c2190bf357aa02d3e0894f0c7d4aff5904a","first_computed_at":"2026-05-18T01:05:48.142366Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:48.142366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e8jsF1q6kSPG14Xw1F+UCqmbajSjQG1KrZEvib4OVHRDNVieqXwbrXlwmRrWsO2w1zeKU5d3x/+A8qHXpL+bCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:48.142875Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9511208","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d82207c2e55b2531f29d8b6ce23d51c61fae59cb88b94004905a23f555a68cb6","sha256:46291b95dfd0b5607e983c99877627e994bb0181e0ade51a234b27c750932365"],"state_sha256":"8f8a498f63054d88481f8ec6941009ae10e605cab70184d1bd55d3e11e66e2f6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mpq5vndHgFTXM5HqB/xoQ+SrJSvaZgedJPFVdVUXoL/vaoQnG2lNbZ8hVD0LWtYIntVFlu5QoGofVymBg5arAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T22:36:41.493772Z","bundle_sha256":"07f60ccec15b52500b026185af105714fb93ffbdf88e5272907d614160a6969d"}}