{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:INEB5I3YF2H6ZV5YIEEMJ5PEO5","short_pith_number":"pith:INEB5I3Y","canonical_record":{"source":{"id":"2606.27272","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-06-25T16:51:43Z","cross_cats_sorted":[],"title_canon_sha256":"daae798e958cb8769f02d59c8b67b79dd9e17732d1bd7403ab7cc83c0955e2d2","abstract_canon_sha256":"897da71ccba974d50bcc3bb97d223e93a63aa5b2226132e7bfbe712171f18cbf"},"schema_version":"1.0"},"canonical_sha256":"43481ea3782e8fecd7b84108c4f5e47754056c29ff046e112619556e17b84fad","source":{"kind":"arxiv","id":"2606.27272","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.27272","created_at":"2026-06-26T01:16:17Z"},{"alias_kind":"arxiv_version","alias_value":"2606.27272v1","created_at":"2026-06-26T01:16:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.27272","created_at":"2026-06-26T01:16:17Z"},{"alias_kind":"pith_short_12","alias_value":"INEB5I3YF2H6","created_at":"2026-06-26T01:16:17Z"},{"alias_kind":"pith_short_16","alias_value":"INEB5I3YF2H6ZV5Y","created_at":"2026-06-26T01:16:17Z"},{"alias_kind":"pith_short_8","alias_value":"INEB5I3Y","created_at":"2026-06-26T01:16:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:INEB5I3YF2H6ZV5YIEEMJ5PEO5","target":"record","payload":{"canonical_record":{"source":{"id":"2606.27272","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-06-25T16:51:43Z","cross_cats_sorted":[],"title_canon_sha256":"daae798e958cb8769f02d59c8b67b79dd9e17732d1bd7403ab7cc83c0955e2d2","abstract_canon_sha256":"897da71ccba974d50bcc3bb97d223e93a63aa5b2226132e7bfbe712171f18cbf"},"schema_version":"1.0"},"canonical_sha256":"43481ea3782e8fecd7b84108c4f5e47754056c29ff046e112619556e17b84fad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-26T01:16:17.172406Z","signature_b64":"Kn9JIl4UqsBP4/0wA5ky9jUYEv4GKp4HZ8d4DO+rVloAKFIIEOsIuM1DNVG1/Qomkpl1pgwPr2st8vsQj8XcCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43481ea3782e8fecd7b84108c4f5e47754056c29ff046e112619556e17b84fad","last_reissued_at":"2026-06-26T01:16:17.172012Z","signature_status":"signed_v1","first_computed_at":"2026-06-26T01:16:17.172012Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.27272","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":"2026-06-26T01:16:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z9rsK2/9D/PfJ29WIbuAFCNammPDRIa6Q9aFR5NO6Q5P6sccQfHE89EkJnD6/7hxuCzwMNcmrNdDoS2O/bgzDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T11:57:40.386763Z"},"content_sha256":"d7346c0f902c562bb89dddd64e61562ccbef4979ea2fd02db7563a9d8a836d6a","schema_version":"1.0","event_id":"sha256:d7346c0f902c562bb89dddd64e61562ccbef4979ea2fd02db7563a9d8a836d6a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:INEB5I3YF2H6ZV5YIEEMJ5PEO5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"MLC for parabolically bounded primitive renormalization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alex Kapiamba, Jeremy Kahn, Mikhail Lyubich","submitted_at":"2026-06-25T16:51:43Z","abstract_excerpt":"We prove $\\textit{a priori}$ bounds and MLC (local connectivity of the Mandelbrot set $\\mathcal{M}$) for a class of infinitely renormalizable parameters whose renormalization type is primitive but can approach the cusp of $\\mathcal{M}$. To this end we develop and refine a variety of tools that allow us to control degeneration of renormalizations. They include the Thin-Thick Decomposition, the Value Calculus, the Wanderers Theorem, and the Wave Lemma."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27272","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.27272/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-26T01:16:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gfD0kOjAzXVXeVvfIpFm5x0KaSHDpB2d5dUQfJD4ZBUOwx8BzaNy+G1SOUEp5e7krPvqdXJiM+Pm4rHuAQmvCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T11:57:40.387133Z"},"content_sha256":"43e9d3c6c4da120b577de5934c3a042a84d0f84fff1ed85a111423665d83f4b6","schema_version":"1.0","event_id":"sha256:43e9d3c6c4da120b577de5934c3a042a84d0f84fff1ed85a111423665d83f4b6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/INEB5I3YF2H6ZV5YIEEMJ5PEO5/bundle.json","state_url":"https://pith.science/pith/INEB5I3YF2H6ZV5YIEEMJ5PEO5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/INEB5I3YF2H6ZV5YIEEMJ5PEO5/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":"2026-08-19T11:57:40Z","links":{"resolver":"https://pith.science/pith/INEB5I3YF2H6ZV5YIEEMJ5PEO5","bundle":"https://pith.science/pith/INEB5I3YF2H6ZV5YIEEMJ5PEO5/bundle.json","state":"https://pith.science/pith/INEB5I3YF2H6ZV5YIEEMJ5PEO5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/INEB5I3YF2H6ZV5YIEEMJ5PEO5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:INEB5I3YF2H6ZV5YIEEMJ5PEO5","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":"897da71ccba974d50bcc3bb97d223e93a63aa5b2226132e7bfbe712171f18cbf","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-06-25T16:51:43Z","title_canon_sha256":"daae798e958cb8769f02d59c8b67b79dd9e17732d1bd7403ab7cc83c0955e2d2"},"schema_version":"1.0","source":{"id":"2606.27272","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.27272","created_at":"2026-06-26T01:16:17Z"},{"alias_kind":"arxiv_version","alias_value":"2606.27272v1","created_at":"2026-06-26T01:16:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.27272","created_at":"2026-06-26T01:16:17Z"},{"alias_kind":"pith_short_12","alias_value":"INEB5I3YF2H6","created_at":"2026-06-26T01:16:17Z"},{"alias_kind":"pith_short_16","alias_value":"INEB5I3YF2H6ZV5Y","created_at":"2026-06-26T01:16:17Z"},{"alias_kind":"pith_short_8","alias_value":"INEB5I3Y","created_at":"2026-06-26T01:16:17Z"}],"graph_snapshots":[{"event_id":"sha256:43e9d3c6c4da120b577de5934c3a042a84d0f84fff1ed85a111423665d83f4b6","target":"graph","created_at":"2026-06-26T01:16:17Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.27272/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove $\\textit{a priori}$ bounds and MLC (local connectivity of the Mandelbrot set $\\mathcal{M}$) for a class of infinitely renormalizable parameters whose renormalization type is primitive but can approach the cusp of $\\mathcal{M}$. To this end we develop and refine a variety of tools that allow us to control degeneration of renormalizations. They include the Thin-Thick Decomposition, the Value Calculus, the Wanderers Theorem, and the Wave Lemma.","authors_text":"Alex Kapiamba, Jeremy Kahn, Mikhail Lyubich","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-06-25T16:51:43Z","title":"MLC for parabolically bounded primitive renormalization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27272","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:d7346c0f902c562bb89dddd64e61562ccbef4979ea2fd02db7563a9d8a836d6a","target":"record","created_at":"2026-06-26T01:16:17Z","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":"897da71ccba974d50bcc3bb97d223e93a63aa5b2226132e7bfbe712171f18cbf","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-06-25T16:51:43Z","title_canon_sha256":"daae798e958cb8769f02d59c8b67b79dd9e17732d1bd7403ab7cc83c0955e2d2"},"schema_version":"1.0","source":{"id":"2606.27272","kind":"arxiv","version":1}},"canonical_sha256":"43481ea3782e8fecd7b84108c4f5e47754056c29ff046e112619556e17b84fad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43481ea3782e8fecd7b84108c4f5e47754056c29ff046e112619556e17b84fad","first_computed_at":"2026-06-26T01:16:17.172012Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-26T01:16:17.172012Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Kn9JIl4UqsBP4/0wA5ky9jUYEv4GKp4HZ8d4DO+rVloAKFIIEOsIuM1DNVG1/Qomkpl1pgwPr2st8vsQj8XcCA==","signature_status":"signed_v1","signed_at":"2026-06-26T01:16:17.172406Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.27272","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7346c0f902c562bb89dddd64e61562ccbef4979ea2fd02db7563a9d8a836d6a","sha256:43e9d3c6c4da120b577de5934c3a042a84d0f84fff1ed85a111423665d83f4b6"],"state_sha256":"d271a5ec16a2f77103e463c8850a63330a8b55c303a8bbfb619ff434387d07b5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"euUIqPSSZKRvNv8bZCYIxDH8Jii7Q3u7/7rI55wQZz/83N2kGyj172pNqhI9EtU6Yj54/IRDQd0dNIIZo/Y1AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T11:57:40.389455Z","bundle_sha256":"fed1fa54ac477322aa89d31e111aa5d2f53918e6f657fd0bedc3b9501968f227"}}