{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:XTRPAHGVW2KJCGUFVRZF7UDVQW","short_pith_number":"pith:XTRPAHGV","canonical_record":{"source":{"id":"1208.2382","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-08-11T19:47:58Z","cross_cats_sorted":[],"title_canon_sha256":"a18c2150d993c16716f5e207da9331265b17266941b5c4fc85d3f1a20b33bd19","abstract_canon_sha256":"3607d1213f5960f4840fbcb3a019b801055bbaece288b3c282323f6785cc02d0"},"schema_version":"1.0"},"canonical_sha256":"bce2f01cd5b694911a85ac725fd07585b576a39affa8f5788451ffb094ddd415","source":{"kind":"arxiv","id":"1208.2382","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.2382","created_at":"2026-05-18T02:29:45Z"},{"alias_kind":"arxiv_version","alias_value":"1208.2382v4","created_at":"2026-05-18T02:29:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.2382","created_at":"2026-05-18T02:29:45Z"},{"alias_kind":"pith_short_12","alias_value":"XTRPAHGVW2KJ","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XTRPAHGVW2KJCGUF","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XTRPAHGV","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:XTRPAHGVW2KJCGUFVRZF7UDVQW","target":"record","payload":{"canonical_record":{"source":{"id":"1208.2382","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-08-11T19:47:58Z","cross_cats_sorted":[],"title_canon_sha256":"a18c2150d993c16716f5e207da9331265b17266941b5c4fc85d3f1a20b33bd19","abstract_canon_sha256":"3607d1213f5960f4840fbcb3a019b801055bbaece288b3c282323f6785cc02d0"},"schema_version":"1.0"},"canonical_sha256":"bce2f01cd5b694911a85ac725fd07585b576a39affa8f5788451ffb094ddd415","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:45.830858Z","signature_b64":"Qowt45tqmKLXvXEWurDa+5oL1XdESNwknesMst0wNRybCRKBQhzaWT2gjOlRBfK8sfPtFXrUWrUvQWBbnVybCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bce2f01cd5b694911a85ac725fd07585b576a39affa8f5788451ffb094ddd415","last_reissued_at":"2026-05-18T02:29:45.830489Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:45.830489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.2382","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:29:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0SxxojzShijR0OjeIezE5vqFhZ9+JOlKwCJnlgaf0eizJiBj9QvJ3ClzVSAJJTSKwC2EWfgMjkPwuCxVxYyNAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:55:38.760718Z"},"content_sha256":"00f96e240c89525a9efcd74edfc255b4e6886713d86c1e0b662c700882dd3177","schema_version":"1.0","event_id":"sha256:00f96e240c89525a9efcd74edfc255b4e6886713d86c1e0b662c700882dd3177"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:XTRPAHGVW2KJCGUFVRZF7UDVQW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"No zero-crossings for random polynomials and the heat equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Amir Dembo, Sumit Mukherjee","submitted_at":"2012-08-11T19:47:58Z","abstract_excerpt":"Consider random polynomial $\\sum_{i=0}^na_ix^i$ of independent mean-zero normal coefficients $a_i$, whose variance is a regularly varying function (in $i$) of order $\\alpha$. We derive general criteria for continuity of persistence exponents for centered Gaussian processes, and use these to show that such polynomial has no roots in $[0,1]$ with probability $n^{-b_{\\alpha}+o(1)}$, and no roots in $(1,\\infty)$ with probability $n^{-b_0+o(1)}$, hence for $n$ even, it has no real roots with probability $n^{-2b_{\\alpha}-2b_0+o(1)}$. Here, $b_{\\alpha}=0$ when $\\alpha\\le-1$ and otherwise $b_{\\alpha}\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2382","kind":"arxiv","version":4},"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":"2026-05-18T02:29:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jz0d0CbEaiX+jmjHvSFuQ1PDZnZD3LKj/j9EYPgPGghdzvIOAWxEc1dvZ9lYcVfKTSsrJBObcRaI0eZo+LL0BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:55:38.761146Z"},"content_sha256":"caa7c417e67f08deef883b1adf6a4adda7846c65f052f215c79fbdc47f96ba9e","schema_version":"1.0","event_id":"sha256:caa7c417e67f08deef883b1adf6a4adda7846c65f052f215c79fbdc47f96ba9e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XTRPAHGVW2KJCGUFVRZF7UDVQW/bundle.json","state_url":"https://pith.science/pith/XTRPAHGVW2KJCGUFVRZF7UDVQW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XTRPAHGVW2KJCGUFVRZF7UDVQW/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":"2026-05-31T02:55:38Z","links":{"resolver":"https://pith.science/pith/XTRPAHGVW2KJCGUFVRZF7UDVQW","bundle":"https://pith.science/pith/XTRPAHGVW2KJCGUFVRZF7UDVQW/bundle.json","state":"https://pith.science/pith/XTRPAHGVW2KJCGUFVRZF7UDVQW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XTRPAHGVW2KJCGUFVRZF7UDVQW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:XTRPAHGVW2KJCGUFVRZF7UDVQW","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":"3607d1213f5960f4840fbcb3a019b801055bbaece288b3c282323f6785cc02d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-08-11T19:47:58Z","title_canon_sha256":"a18c2150d993c16716f5e207da9331265b17266941b5c4fc85d3f1a20b33bd19"},"schema_version":"1.0","source":{"id":"1208.2382","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.2382","created_at":"2026-05-18T02:29:45Z"},{"alias_kind":"arxiv_version","alias_value":"1208.2382v4","created_at":"2026-05-18T02:29:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.2382","created_at":"2026-05-18T02:29:45Z"},{"alias_kind":"pith_short_12","alias_value":"XTRPAHGVW2KJ","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XTRPAHGVW2KJCGUF","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XTRPAHGV","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:caa7c417e67f08deef883b1adf6a4adda7846c65f052f215c79fbdc47f96ba9e","target":"graph","created_at":"2026-05-18T02:29:45Z","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":"Consider random polynomial $\\sum_{i=0}^na_ix^i$ of independent mean-zero normal coefficients $a_i$, whose variance is a regularly varying function (in $i$) of order $\\alpha$. We derive general criteria for continuity of persistence exponents for centered Gaussian processes, and use these to show that such polynomial has no roots in $[0,1]$ with probability $n^{-b_{\\alpha}+o(1)}$, and no roots in $(1,\\infty)$ with probability $n^{-b_0+o(1)}$, hence for $n$ even, it has no real roots with probability $n^{-2b_{\\alpha}-2b_0+o(1)}$. Here, $b_{\\alpha}=0$ when $\\alpha\\le-1$ and otherwise $b_{\\alpha}\\","authors_text":"Amir Dembo, Sumit Mukherjee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-08-11T19:47:58Z","title":"No zero-crossings for random polynomials and the heat equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2382","kind":"arxiv","version":4},"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":"sha256:00f96e240c89525a9efcd74edfc255b4e6886713d86c1e0b662c700882dd3177","target":"record","created_at":"2026-05-18T02:29:45Z","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":"3607d1213f5960f4840fbcb3a019b801055bbaece288b3c282323f6785cc02d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-08-11T19:47:58Z","title_canon_sha256":"a18c2150d993c16716f5e207da9331265b17266941b5c4fc85d3f1a20b33bd19"},"schema_version":"1.0","source":{"id":"1208.2382","kind":"arxiv","version":4}},"canonical_sha256":"bce2f01cd5b694911a85ac725fd07585b576a39affa8f5788451ffb094ddd415","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bce2f01cd5b694911a85ac725fd07585b576a39affa8f5788451ffb094ddd415","first_computed_at":"2026-05-18T02:29:45.830489Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:45.830489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qowt45tqmKLXvXEWurDa+5oL1XdESNwknesMst0wNRybCRKBQhzaWT2gjOlRBfK8sfPtFXrUWrUvQWBbnVybCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:45.830858Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.2382","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00f96e240c89525a9efcd74edfc255b4e6886713d86c1e0b662c700882dd3177","sha256:caa7c417e67f08deef883b1adf6a4adda7846c65f052f215c79fbdc47f96ba9e"],"state_sha256":"52e3781e729224a71fb39823b7ec4653b1e5a54ca3603d302bf87ffa6a8a873f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2jhNn6lom+SA+zfc+VAqAt+u3WsBvbHUOd/7oKxbyFDDuc0zAvzP1ujy6k/X1fduhsRwE842Sq0kT3g18ZveCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T02:55:38.763844Z","bundle_sha256":"e93749e35cef3f3c03d19c823c6d1fd08a024b37e318c6c5a29762afc2b86379"}}