{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:Z6ANZZVMYOJB7SBH7EIPKPQZKC","short_pith_number":"pith:Z6ANZZVM","canonical_record":{"source":{"id":"2508.18575","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-08-26T00:38:46Z","cross_cats_sorted":["math.CO","math.OA"],"title_canon_sha256":"f40c0d5edf5610f85aa163df79f60146f747241cf35810fa72bb36167fedfc5a","abstract_canon_sha256":"fef9636b94f02fb772b2ef6df50a3af66908073a9620573eaf511a0a0839ef5e"},"schema_version":"1.0"},"canonical_sha256":"cf80dce6acc3921fc827f910f53e195099cdcea5c966b534bbd3c7f67d27f432","source":{"kind":"arxiv","id":"2508.18575","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.18575","created_at":"2026-07-05T11:59:27Z"},{"alias_kind":"arxiv_version","alias_value":"2508.18575v1","created_at":"2026-07-05T11:59:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.18575","created_at":"2026-07-05T11:59:27Z"},{"alias_kind":"pith_short_12","alias_value":"Z6ANZZVMYOJB","created_at":"2026-07-05T11:59:27Z"},{"alias_kind":"pith_short_16","alias_value":"Z6ANZZVMYOJB7SBH","created_at":"2026-07-05T11:59:27Z"},{"alias_kind":"pith_short_8","alias_value":"Z6ANZZVM","created_at":"2026-07-05T11:59:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:Z6ANZZVMYOJB7SBH7EIPKPQZKC","target":"record","payload":{"canonical_record":{"source":{"id":"2508.18575","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-08-26T00:38:46Z","cross_cats_sorted":["math.CO","math.OA"],"title_canon_sha256":"f40c0d5edf5610f85aa163df79f60146f747241cf35810fa72bb36167fedfc5a","abstract_canon_sha256":"fef9636b94f02fb772b2ef6df50a3af66908073a9620573eaf511a0a0839ef5e"},"schema_version":"1.0"},"canonical_sha256":"cf80dce6acc3921fc827f910f53e195099cdcea5c966b534bbd3c7f67d27f432","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:59:27.008448Z","signature_b64":"gP2FowpZu4LOG6MoG1Y817aNpktnWruFGPsA1GxHm1Wnr24eMpZUi9Ad+08jR7J3k6MjKsrF9Kx6+YCVNQb7Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf80dce6acc3921fc827f910f53e195099cdcea5c966b534bbd3c7f67d27f432","last_reissued_at":"2026-07-05T11:59:27.008006Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:59:27.008006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2508.18575","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":"2026-07-05T11:59:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nc4sHiWqLjht7Ll37zWh3Kp4M59ccYdC904OcXOv1AE+9DTDF1THQK49108QRbYDzN3gAQZCZ/u9GnFH0HOKBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T14:52:30.330583Z"},"content_sha256":"90f4eb9e2dc5e940671fd526a796ca94e8d5448e46eeda5bb49b345689f34d98","schema_version":"1.0","event_id":"sha256:90f4eb9e2dc5e940671fd526a796ca94e8d5448e46eeda5bb49b345689f34d98"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:Z6ANZZVMYOJB7SBH7EIPKPQZKC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic root distribution of polynomials under repeated polar differentiation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.OA"],"primary_cat":"math.PR","authors_text":"Daniel Perales, Zhiyuan Yang","submitted_at":"2025-08-26T00:38:46Z","abstract_excerpt":"Given a sequence of real rooted polynomials $\\{p_n\\}_{n\\geq 1}$ with a fixed asymptotic root distribution, we study the asymptotic root distribution of the repeated polar derivatives of this sequence. This limiting distribution can be seen as the result of fractional free convolution and pushforward maps along M\\\"obius transforms for distributions. This new family of operations on measures forms a semigroup and satisfy some other nice properties. Using the fact that polar derivatives commute with one another, we obtain a non-trivial commutation relation between these new operations. We also st"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.18575","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/2508.18575/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":"2026-07-05T11:59:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G8jlGN221fNeqU/9los4qQKQC9TLPicikcBPcbpLWoApBWK2AhU9snxqCtrls+FOIR5x2VNf0Q905Ffv1ARjAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T14:52:30.331496Z"},"content_sha256":"880ba8a90696023cfc890bcf5f2abfa1f078f100fcbbc25513b376e3b893ee01","schema_version":"1.0","event_id":"sha256:880ba8a90696023cfc890bcf5f2abfa1f078f100fcbbc25513b376e3b893ee01"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z6ANZZVMYOJB7SBH7EIPKPQZKC/bundle.json","state_url":"https://pith.science/pith/Z6ANZZVMYOJB7SBH7EIPKPQZKC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z6ANZZVMYOJB7SBH7EIPKPQZKC/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":"2026-08-17T14:52:30Z","links":{"resolver":"https://pith.science/pith/Z6ANZZVMYOJB7SBH7EIPKPQZKC","bundle":"https://pith.science/pith/Z6ANZZVMYOJB7SBH7EIPKPQZKC/bundle.json","state":"https://pith.science/pith/Z6ANZZVMYOJB7SBH7EIPKPQZKC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z6ANZZVMYOJB7SBH7EIPKPQZKC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:Z6ANZZVMYOJB7SBH7EIPKPQZKC","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":"fef9636b94f02fb772b2ef6df50a3af66908073a9620573eaf511a0a0839ef5e","cross_cats_sorted":["math.CO","math.OA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-08-26T00:38:46Z","title_canon_sha256":"f40c0d5edf5610f85aa163df79f60146f747241cf35810fa72bb36167fedfc5a"},"schema_version":"1.0","source":{"id":"2508.18575","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.18575","created_at":"2026-07-05T11:59:27Z"},{"alias_kind":"arxiv_version","alias_value":"2508.18575v1","created_at":"2026-07-05T11:59:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.18575","created_at":"2026-07-05T11:59:27Z"},{"alias_kind":"pith_short_12","alias_value":"Z6ANZZVMYOJB","created_at":"2026-07-05T11:59:27Z"},{"alias_kind":"pith_short_16","alias_value":"Z6ANZZVMYOJB7SBH","created_at":"2026-07-05T11:59:27Z"},{"alias_kind":"pith_short_8","alias_value":"Z6ANZZVM","created_at":"2026-07-05T11:59:27Z"}],"graph_snapshots":[{"event_id":"sha256:880ba8a90696023cfc890bcf5f2abfa1f078f100fcbbc25513b376e3b893ee01","target":"graph","created_at":"2026-07-05T11:59:27Z","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/2508.18575/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given a sequence of real rooted polynomials $\\{p_n\\}_{n\\geq 1}$ with a fixed asymptotic root distribution, we study the asymptotic root distribution of the repeated polar derivatives of this sequence. This limiting distribution can be seen as the result of fractional free convolution and pushforward maps along M\\\"obius transforms for distributions. This new family of operations on measures forms a semigroup and satisfy some other nice properties. Using the fact that polar derivatives commute with one another, we obtain a non-trivial commutation relation between these new operations. We also st","authors_text":"Daniel Perales, Zhiyuan Yang","cross_cats":["math.CO","math.OA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-08-26T00:38:46Z","title":"Asymptotic root distribution of polynomials under repeated polar differentiation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.18575","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":"sha256:90f4eb9e2dc5e940671fd526a796ca94e8d5448e46eeda5bb49b345689f34d98","target":"record","created_at":"2026-07-05T11:59:27Z","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":"fef9636b94f02fb772b2ef6df50a3af66908073a9620573eaf511a0a0839ef5e","cross_cats_sorted":["math.CO","math.OA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-08-26T00:38:46Z","title_canon_sha256":"f40c0d5edf5610f85aa163df79f60146f747241cf35810fa72bb36167fedfc5a"},"schema_version":"1.0","source":{"id":"2508.18575","kind":"arxiv","version":1}},"canonical_sha256":"cf80dce6acc3921fc827f910f53e195099cdcea5c966b534bbd3c7f67d27f432","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf80dce6acc3921fc827f910f53e195099cdcea5c966b534bbd3c7f67d27f432","first_computed_at":"2026-07-05T11:59:27.008006Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:59:27.008006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gP2FowpZu4LOG6MoG1Y817aNpktnWruFGPsA1GxHm1Wnr24eMpZUi9Ad+08jR7J3k6MjKsrF9Kx6+YCVNQb7Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:59:27.008448Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.18575","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90f4eb9e2dc5e940671fd526a796ca94e8d5448e46eeda5bb49b345689f34d98","sha256:880ba8a90696023cfc890bcf5f2abfa1f078f100fcbbc25513b376e3b893ee01"],"state_sha256":"2e64f3b6824880235ef1144aaabff91f0190b99acc7a0fa449ff4e62d6bd5433"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FConL1SAxXS514/PXiU7K5ZCZ1qLLPwsiV5qcxPgenXuqFvF3zXj0YD0o7ebKO5XZo1v87v7FDXQQZU1ePhCCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T14:52:30.338033Z","bundle_sha256":"82fbd8843aafcea1bcb9248f7c2612ca47d5e1dd6a29ae7921c108c819881a6f"}}