{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:Z5Y3GJX65QUJVZ5E5WWKCMJNY3","short_pith_number":"pith:Z5Y3GJX6","canonical_record":{"source":{"id":"2504.11593","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-04-15T20:12:40Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"14f203ac1f2b16abaef2d2b8fb0ae812d6e5a9d12d3fd9d40455537695fae6bb","abstract_canon_sha256":"9a7037eb869477fa63904306f8cefad5f05c5c6e7f20973f3925ae923fffea1e"},"schema_version":"1.0"},"canonical_sha256":"cf71b326feec289ae7a4edaca1312dc6e63523600e23ebc9d8d10fc4b3eb82ba","source":{"kind":"arxiv","id":"2504.11593","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.11593","created_at":"2026-07-05T10:49:37Z"},{"alias_kind":"arxiv_version","alias_value":"2504.11593v1","created_at":"2026-07-05T10:49:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.11593","created_at":"2026-07-05T10:49:37Z"},{"alias_kind":"pith_short_12","alias_value":"Z5Y3GJX65QUJ","created_at":"2026-07-05T10:49:37Z"},{"alias_kind":"pith_short_16","alias_value":"Z5Y3GJX65QUJVZ5E","created_at":"2026-07-05T10:49:37Z"},{"alias_kind":"pith_short_8","alias_value":"Z5Y3GJX6","created_at":"2026-07-05T10:49:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:Z5Y3GJX65QUJVZ5E5WWKCMJNY3","target":"record","payload":{"canonical_record":{"source":{"id":"2504.11593","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-04-15T20:12:40Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"14f203ac1f2b16abaef2d2b8fb0ae812d6e5a9d12d3fd9d40455537695fae6bb","abstract_canon_sha256":"9a7037eb869477fa63904306f8cefad5f05c5c6e7f20973f3925ae923fffea1e"},"schema_version":"1.0"},"canonical_sha256":"cf71b326feec289ae7a4edaca1312dc6e63523600e23ebc9d8d10fc4b3eb82ba","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:49:37.444974Z","signature_b64":"MDC8DTDEI49joRdNjutrNhRyT2wqnRgjiC9FkibDDXkFJXI2MAc3r5E36SEq0G4pe9b2fgnpIEIpHq/QvljLAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf71b326feec289ae7a4edaca1312dc6e63523600e23ebc9d8d10fc4b3eb82ba","last_reissued_at":"2026-07-05T10:49:37.444521Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:49:37.444521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2504.11593","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":"2026-07-05T10:49:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7CLMwu7C2Tdq2CojzkN/AkTYsuILgcWK/JT4ZkUGeOTpxSpbZRmgie6jAPjc4CompbqcgWJQ8e67VaYbs4zuBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T15:30:15.120562Z"},"content_sha256":"38ee716317f7068a1b4260d8b99ada1ec0fecdf698f3fcdd313069e0a7e15d40","schema_version":"1.0","event_id":"sha256:38ee716317f7068a1b4260d8b99ada1ec0fecdf698f3fcdd313069e0a7e15d40"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:Z5Y3GJX65QUJVZ5E5WWKCMJNY3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Zeros and exponential profiles of polynomials I: Limit distributions, finite free convolutions and repeated differentiation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.PR","authors_text":"Alexander Marynych, Jonas Jalowy, Zakhar Kabluchko","submitted_at":"2025-04-15T20:12:40Z","abstract_excerpt":"Given a sequence of polynomials $(P_n)_{n \\in \\mathbb{N}}$ with only nonpositive zeros, the aim of this article is to present a user-friendly approach for determining the limiting zero distribution of $P_n$ as $\\mathrm{deg}\\, P_n \\to \\infty$. The method is based on establishing an equivalence between the existence of a limiting empirical zero distribution $\\mu$ and the existence of an exponential profile $g$ associated with the coefficients of the polynomials $(P_n)_{n \\in \\mathbb{N}}$. The exponential profile $g$, which can be roughly described by $[z^k]P_n(z) \\approx \\exp(n g(k/n))$, offers "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.11593","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/2504.11593/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":"2026-07-05T10:49:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mB/DLo2se99Lw2BN49Pd9IO9zkRoFuDLALsirsmqoGGkTAlx4BpGhyPb9eQ+riDmODSMuM7sOZYxLuUM68FbDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T15:30:15.121065Z"},"content_sha256":"50566a25572436068d40715e3a9d6d56c71fedf58764ff9e653e817aea2ab66b","schema_version":"1.0","event_id":"sha256:50566a25572436068d40715e3a9d6d56c71fedf58764ff9e653e817aea2ab66b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z5Y3GJX65QUJVZ5E5WWKCMJNY3/bundle.json","state_url":"https://pith.science/pith/Z5Y3GJX65QUJVZ5E5WWKCMJNY3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z5Y3GJX65QUJVZ5E5WWKCMJNY3/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":"2026-08-22T15:30:15Z","links":{"resolver":"https://pith.science/pith/Z5Y3GJX65QUJVZ5E5WWKCMJNY3","bundle":"https://pith.science/pith/Z5Y3GJX65QUJVZ5E5WWKCMJNY3/bundle.json","state":"https://pith.science/pith/Z5Y3GJX65QUJVZ5E5WWKCMJNY3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z5Y3GJX65QUJVZ5E5WWKCMJNY3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:Z5Y3GJX65QUJVZ5E5WWKCMJNY3","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":"9a7037eb869477fa63904306f8cefad5f05c5c6e7f20973f3925ae923fffea1e","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-04-15T20:12:40Z","title_canon_sha256":"14f203ac1f2b16abaef2d2b8fb0ae812d6e5a9d12d3fd9d40455537695fae6bb"},"schema_version":"1.0","source":{"id":"2504.11593","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.11593","created_at":"2026-07-05T10:49:37Z"},{"alias_kind":"arxiv_version","alias_value":"2504.11593v1","created_at":"2026-07-05T10:49:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.11593","created_at":"2026-07-05T10:49:37Z"},{"alias_kind":"pith_short_12","alias_value":"Z5Y3GJX65QUJ","created_at":"2026-07-05T10:49:37Z"},{"alias_kind":"pith_short_16","alias_value":"Z5Y3GJX65QUJVZ5E","created_at":"2026-07-05T10:49:37Z"},{"alias_kind":"pith_short_8","alias_value":"Z5Y3GJX6","created_at":"2026-07-05T10:49:37Z"}],"graph_snapshots":[{"event_id":"sha256:50566a25572436068d40715e3a9d6d56c71fedf58764ff9e653e817aea2ab66b","target":"graph","created_at":"2026-07-05T10:49:37Z","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/2504.11593/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given a sequence of polynomials $(P_n)_{n \\in \\mathbb{N}}$ with only nonpositive zeros, the aim of this article is to present a user-friendly approach for determining the limiting zero distribution of $P_n$ as $\\mathrm{deg}\\, P_n \\to \\infty$. The method is based on establishing an equivalence between the existence of a limiting empirical zero distribution $\\mu$ and the existence of an exponential profile $g$ associated with the coefficients of the polynomials $(P_n)_{n \\in \\mathbb{N}}$. The exponential profile $g$, which can be roughly described by $[z^k]P_n(z) \\approx \\exp(n g(k/n))$, offers ","authors_text":"Alexander Marynych, Jonas Jalowy, Zakhar Kabluchko","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-04-15T20:12:40Z","title":"Zeros and exponential profiles of polynomials I: Limit distributions, finite free convolutions and repeated differentiation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.11593","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":"sha256:38ee716317f7068a1b4260d8b99ada1ec0fecdf698f3fcdd313069e0a7e15d40","target":"record","created_at":"2026-07-05T10:49:37Z","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":"9a7037eb869477fa63904306f8cefad5f05c5c6e7f20973f3925ae923fffea1e","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-04-15T20:12:40Z","title_canon_sha256":"14f203ac1f2b16abaef2d2b8fb0ae812d6e5a9d12d3fd9d40455537695fae6bb"},"schema_version":"1.0","source":{"id":"2504.11593","kind":"arxiv","version":1}},"canonical_sha256":"cf71b326feec289ae7a4edaca1312dc6e63523600e23ebc9d8d10fc4b3eb82ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf71b326feec289ae7a4edaca1312dc6e63523600e23ebc9d8d10fc4b3eb82ba","first_computed_at":"2026-07-05T10:49:37.444521Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:49:37.444521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MDC8DTDEI49joRdNjutrNhRyT2wqnRgjiC9FkibDDXkFJXI2MAc3r5E36SEq0G4pe9b2fgnpIEIpHq/QvljLAw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:49:37.444974Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.11593","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:38ee716317f7068a1b4260d8b99ada1ec0fecdf698f3fcdd313069e0a7e15d40","sha256:50566a25572436068d40715e3a9d6d56c71fedf58764ff9e653e817aea2ab66b"],"state_sha256":"83a56f5117b0d505a2ffe6dda98a753ed04988b0a52ed64dfbf35d992fbd9397"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pSVVGZaRNeBJsreGbh+aguQXyjEbX1VhcgDhkMtGAVQwi2hL10T1qgGn1xTzw625RithC2ooLR2/UfFC2UaXBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T15:30:15.125117Z","bundle_sha256":"3490b1ebc12c1790c5ecddfa11ceff52b17f082cad764ffe888b3a5c3ddbfc8d"}}