{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:UJSBUBRRFKICHXGKQ6PGAFBDTZ","short_pith_number":"pith:UJSBUBRR","canonical_record":{"source":{"id":"2505.02723","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-05-05T15:24:24Z","cross_cats_sorted":["math.CA","math.CV"],"title_canon_sha256":"47275b53b0888699cb0875f2428b3e99c704459ea3624878946c705fac28f827","abstract_canon_sha256":"a32107c5df09a37baa41d24bbe28ecabfd73824bea049e31eeb71a6df6092fc3"},"schema_version":"1.0"},"canonical_sha256":"a2641a06312a9023dcca879e6014239e5d81a7feb57d646abb6bfe22f84bb2a7","source":{"kind":"arxiv","id":"2505.02723","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.02723","created_at":"2026-07-05T10:58:42Z"},{"alias_kind":"arxiv_version","alias_value":"2505.02723v1","created_at":"2026-07-05T10:58:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.02723","created_at":"2026-07-05T10:58:42Z"},{"alias_kind":"pith_short_12","alias_value":"UJSBUBRRFKIC","created_at":"2026-07-05T10:58:42Z"},{"alias_kind":"pith_short_16","alias_value":"UJSBUBRRFKICHXGK","created_at":"2026-07-05T10:58:42Z"},{"alias_kind":"pith_short_8","alias_value":"UJSBUBRR","created_at":"2026-07-05T10:58:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:UJSBUBRRFKICHXGKQ6PGAFBDTZ","target":"record","payload":{"canonical_record":{"source":{"id":"2505.02723","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-05-05T15:24:24Z","cross_cats_sorted":["math.CA","math.CV"],"title_canon_sha256":"47275b53b0888699cb0875f2428b3e99c704459ea3624878946c705fac28f827","abstract_canon_sha256":"a32107c5df09a37baa41d24bbe28ecabfd73824bea049e31eeb71a6df6092fc3"},"schema_version":"1.0"},"canonical_sha256":"a2641a06312a9023dcca879e6014239e5d81a7feb57d646abb6bfe22f84bb2a7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:58:42.019371Z","signature_b64":"6tzpmUpp8R0GLO+tXMlTbP3JYM1ySM/JgHl4I1bpO1Kx1DbWb2sua98OQ1k9AetAOL8Y8LmAn2NpXtK+DO6qAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2641a06312a9023dcca879e6014239e5d81a7feb57d646abb6bfe22f84bb2a7","last_reissued_at":"2026-07-05T10:58:42.018769Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:58:42.018769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.02723","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":"2026-07-05T10:58:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vCWjGCHskJoZvXcRRiN3sZ2jtPEUCrmQ+g3+7D9Dij2L92UzQNehnPAFVhDOs25/J7fu/KItyr1yM+j+0WBwAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T18:21:17.904637Z"},"content_sha256":"5b47b35ab9ea696cc96e67d1736eeb4dc90b910d0bf68d128290607b3d41088c","schema_version":"1.0","event_id":"sha256:5b47b35ab9ea696cc96e67d1736eeb4dc90b910d0bf68d128290607b3d41088c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:UJSBUBRRFKICHXGKQ6PGAFBDTZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Limit law for root separation in random polynomials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CA","math.CV"],"primary_cat":"math.PR","authors_text":"Marcus Michelen, Oren Yakir","submitted_at":"2025-05-05T15:24:24Z","abstract_excerpt":"Let $f_n$ be a random polynomial of degree $n\\ge 2$ whose coefficients are independent and identically distributed random variables. We study the separation distances between roots of $f_n$ and prove that the set of these distances, normalized by $n^{-5/4}$, converges in distribution as $n\\to \\infty$ to a non-homogeneous Poisson point process. As a corollary, we deduce that the minimal separation distance between roots of $f_n$, normalized by $n^{-5/4}$ has a non-trivial limit law. In the course of the proof, we establish a related result which may be of independent interest: a Taylor series w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.02723","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/2505.02723/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":"2026-07-05T10:58:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"An1Ur/jA8DZ8N85CfI7o12VKvaLZu6PLrjAStvkCUgSl7w43xDn+mcERaSe7MigGx0OrvDzwDefpP/moi2eWDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T18:21:17.905164Z"},"content_sha256":"88f9289fec7074b620af1f3ed0029347052a5b7a97afe0808d12017e41224b27","schema_version":"1.0","event_id":"sha256:88f9289fec7074b620af1f3ed0029347052a5b7a97afe0808d12017e41224b27"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UJSBUBRRFKICHXGKQ6PGAFBDTZ/bundle.json","state_url":"https://pith.science/pith/UJSBUBRRFKICHXGKQ6PGAFBDTZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UJSBUBRRFKICHXGKQ6PGAFBDTZ/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":"2026-08-08T18:21:17Z","links":{"resolver":"https://pith.science/pith/UJSBUBRRFKICHXGKQ6PGAFBDTZ","bundle":"https://pith.science/pith/UJSBUBRRFKICHXGKQ6PGAFBDTZ/bundle.json","state":"https://pith.science/pith/UJSBUBRRFKICHXGKQ6PGAFBDTZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UJSBUBRRFKICHXGKQ6PGAFBDTZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:UJSBUBRRFKICHXGKQ6PGAFBDTZ","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":"a32107c5df09a37baa41d24bbe28ecabfd73824bea049e31eeb71a6df6092fc3","cross_cats_sorted":["math.CA","math.CV"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-05-05T15:24:24Z","title_canon_sha256":"47275b53b0888699cb0875f2428b3e99c704459ea3624878946c705fac28f827"},"schema_version":"1.0","source":{"id":"2505.02723","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.02723","created_at":"2026-07-05T10:58:42Z"},{"alias_kind":"arxiv_version","alias_value":"2505.02723v1","created_at":"2026-07-05T10:58:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.02723","created_at":"2026-07-05T10:58:42Z"},{"alias_kind":"pith_short_12","alias_value":"UJSBUBRRFKIC","created_at":"2026-07-05T10:58:42Z"},{"alias_kind":"pith_short_16","alias_value":"UJSBUBRRFKICHXGK","created_at":"2026-07-05T10:58:42Z"},{"alias_kind":"pith_short_8","alias_value":"UJSBUBRR","created_at":"2026-07-05T10:58:42Z"}],"graph_snapshots":[{"event_id":"sha256:88f9289fec7074b620af1f3ed0029347052a5b7a97afe0808d12017e41224b27","target":"graph","created_at":"2026-07-05T10:58:42Z","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/2505.02723/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $f_n$ be a random polynomial of degree $n\\ge 2$ whose coefficients are independent and identically distributed random variables. We study the separation distances between roots of $f_n$ and prove that the set of these distances, normalized by $n^{-5/4}$, converges in distribution as $n\\to \\infty$ to a non-homogeneous Poisson point process. As a corollary, we deduce that the minimal separation distance between roots of $f_n$, normalized by $n^{-5/4}$ has a non-trivial limit law. In the course of the proof, we establish a related result which may be of independent interest: a Taylor series w","authors_text":"Marcus Michelen, Oren Yakir","cross_cats":["math.CA","math.CV"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-05-05T15:24:24Z","title":"Limit law for root separation in random polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.02723","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":"sha256:5b47b35ab9ea696cc96e67d1736eeb4dc90b910d0bf68d128290607b3d41088c","target":"record","created_at":"2026-07-05T10:58:42Z","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":"a32107c5df09a37baa41d24bbe28ecabfd73824bea049e31eeb71a6df6092fc3","cross_cats_sorted":["math.CA","math.CV"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-05-05T15:24:24Z","title_canon_sha256":"47275b53b0888699cb0875f2428b3e99c704459ea3624878946c705fac28f827"},"schema_version":"1.0","source":{"id":"2505.02723","kind":"arxiv","version":1}},"canonical_sha256":"a2641a06312a9023dcca879e6014239e5d81a7feb57d646abb6bfe22f84bb2a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2641a06312a9023dcca879e6014239e5d81a7feb57d646abb6bfe22f84bb2a7","first_computed_at":"2026-07-05T10:58:42.018769Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:58:42.018769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6tzpmUpp8R0GLO+tXMlTbP3JYM1ySM/JgHl4I1bpO1Kx1DbWb2sua98OQ1k9AetAOL8Y8LmAn2NpXtK+DO6qAA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:58:42.019371Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.02723","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b47b35ab9ea696cc96e67d1736eeb4dc90b910d0bf68d128290607b3d41088c","sha256:88f9289fec7074b620af1f3ed0029347052a5b7a97afe0808d12017e41224b27"],"state_sha256":"7c0883c02c0da62e0825de06a30e4b8082f962f31289c1bc4207a08c9cb5a773"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JiqjFHom9sbLR9eMHjby/KF0AkWmCdCEak+jA+QEATyPChFsCzE1vFhNHhow96Rp9I02VN0+oEJZgSkMnnwwBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T18:21:17.911166Z","bundle_sha256":"257c8d9c983e329f9ee94f6153be83d7364376ea0b692d9382a6afec4fe71a65"}}