{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:4D4JEGXA2EDHGFYRRH2CSZIN3Z","short_pith_number":"pith:4D4JEGXA","canonical_record":{"source":{"id":"1009.5580","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-28T14:25:29Z","cross_cats_sorted":[],"title_canon_sha256":"94b81c664ed3f4f459b392cde473a8a66f7f5c6f7688e085ce458117f76fd225","abstract_canon_sha256":"31f9d902bc8eb58a68982e54115d23ea871b38c9daa7a314511da9f6be092ee5"},"schema_version":"1.0"},"canonical_sha256":"e0f8921ae0d10673171189f429650dde467dc0143c7245fb9bb661c4b718d638","source":{"kind":"arxiv","id":"1009.5580","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.5580","created_at":"2026-05-18T04:15:18Z"},{"alias_kind":"arxiv_version","alias_value":"1009.5580v2","created_at":"2026-05-18T04:15:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.5580","created_at":"2026-05-18T04:15:18Z"},{"alias_kind":"pith_short_12","alias_value":"4D4JEGXA2EDH","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"4D4JEGXA2EDHGFYR","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"4D4JEGXA","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:4D4JEGXA2EDHGFYRRH2CSZIN3Z","target":"record","payload":{"canonical_record":{"source":{"id":"1009.5580","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-28T14:25:29Z","cross_cats_sorted":[],"title_canon_sha256":"94b81c664ed3f4f459b392cde473a8a66f7f5c6f7688e085ce458117f76fd225","abstract_canon_sha256":"31f9d902bc8eb58a68982e54115d23ea871b38c9daa7a314511da9f6be092ee5"},"schema_version":"1.0"},"canonical_sha256":"e0f8921ae0d10673171189f429650dde467dc0143c7245fb9bb661c4b718d638","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:15:18.880064Z","signature_b64":"+9nUekDhidIy0ptQr4ehvQ/1MLv3iuWXOXiB0B+XhxdAXV/BpQkYiRVfidHuj+xgr3uwFpXvw6hxL6Uj/Yp6CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0f8921ae0d10673171189f429650dde467dc0143c7245fb9bb661c4b718d638","last_reissued_at":"2026-05-18T04:15:18.879289Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:15:18.879289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.5580","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:15:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O+65kueIxDGuXQlmPUAYDDIyAu7WFPLCIk5+wxpfvpGHdqAnrpCm2GM2XTI9rXAwPWuT5a/wbS9Jt8vEaXkxCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T16:05:50.634362Z"},"content_sha256":"1c4962dbb81f60e4971336002f963eedd9b567d7bea34ceed125963b4aabafcc","schema_version":"1.0","event_id":"sha256:1c4962dbb81f60e4971336002f963eedd9b567d7bea34ceed125963b4aabafcc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:4D4JEGXA2EDHGFYRRH2CSZIN3Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Small deviations for a family of smooth Gaussian processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Frank Aurzada, Fuchang Gao, Qi-Man Shao, Thomas K\\\"uhn, Wenbo V. Li","submitted_at":"2010-09-28T14:25:29Z","abstract_excerpt":"We study the small deviation probabilities of a family of very smooth self-similar Gaussian processes. The canonical process from the family has the same scaling property as standard Brownian motion and plays an important role in the study of zeros of random polynomials.\n  Our estimates are based on the entropy method, discovered in Kuelbs and Li (1992) and developed further in Li and Linde (1999), Gao (2004), and Aurzada et al. (2009). While there are several ways to obtain the result w.r.t. the $L_2$ norm, the main contribution of this paper concerns the result w.r.t. the supremum norm. In t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5580","kind":"arxiv","version":2},"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":"2026-05-18T04:15:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bIZlNA7FJQeovIkj224wpjrLekqYQxSrtyFRHg6WfftUrkOs8TRYz9q2sBCwL583W6Lx1Am96DIeMhInLatHDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T16:05:50.635084Z"},"content_sha256":"c3f261541a4983900a69a911b6736052f0e4c84b69be82fbc044b747a027fd77","schema_version":"1.0","event_id":"sha256:c3f261541a4983900a69a911b6736052f0e4c84b69be82fbc044b747a027fd77"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4D4JEGXA2EDHGFYRRH2CSZIN3Z/bundle.json","state_url":"https://pith.science/pith/4D4JEGXA2EDHGFYRRH2CSZIN3Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4D4JEGXA2EDHGFYRRH2CSZIN3Z/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":"2026-05-31T16:05:50Z","links":{"resolver":"https://pith.science/pith/4D4JEGXA2EDHGFYRRH2CSZIN3Z","bundle":"https://pith.science/pith/4D4JEGXA2EDHGFYRRH2CSZIN3Z/bundle.json","state":"https://pith.science/pith/4D4JEGXA2EDHGFYRRH2CSZIN3Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4D4JEGXA2EDHGFYRRH2CSZIN3Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:4D4JEGXA2EDHGFYRRH2CSZIN3Z","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":"31f9d902bc8eb58a68982e54115d23ea871b38c9daa7a314511da9f6be092ee5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-28T14:25:29Z","title_canon_sha256":"94b81c664ed3f4f459b392cde473a8a66f7f5c6f7688e085ce458117f76fd225"},"schema_version":"1.0","source":{"id":"1009.5580","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.5580","created_at":"2026-05-18T04:15:18Z"},{"alias_kind":"arxiv_version","alias_value":"1009.5580v2","created_at":"2026-05-18T04:15:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.5580","created_at":"2026-05-18T04:15:18Z"},{"alias_kind":"pith_short_12","alias_value":"4D4JEGXA2EDH","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"4D4JEGXA2EDHGFYR","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"4D4JEGXA","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:c3f261541a4983900a69a911b6736052f0e4c84b69be82fbc044b747a027fd77","target":"graph","created_at":"2026-05-18T04:15:18Z","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":"We study the small deviation probabilities of a family of very smooth self-similar Gaussian processes. The canonical process from the family has the same scaling property as standard Brownian motion and plays an important role in the study of zeros of random polynomials.\n  Our estimates are based on the entropy method, discovered in Kuelbs and Li (1992) and developed further in Li and Linde (1999), Gao (2004), and Aurzada et al. (2009). While there are several ways to obtain the result w.r.t. the $L_2$ norm, the main contribution of this paper concerns the result w.r.t. the supremum norm. In t","authors_text":"Frank Aurzada, Fuchang Gao, Qi-Man Shao, Thomas K\\\"uhn, Wenbo V. Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-28T14:25:29Z","title":"Small deviations for a family of smooth Gaussian processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5580","kind":"arxiv","version":2},"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":"sha256:1c4962dbb81f60e4971336002f963eedd9b567d7bea34ceed125963b4aabafcc","target":"record","created_at":"2026-05-18T04:15:18Z","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":"31f9d902bc8eb58a68982e54115d23ea871b38c9daa7a314511da9f6be092ee5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-28T14:25:29Z","title_canon_sha256":"94b81c664ed3f4f459b392cde473a8a66f7f5c6f7688e085ce458117f76fd225"},"schema_version":"1.0","source":{"id":"1009.5580","kind":"arxiv","version":2}},"canonical_sha256":"e0f8921ae0d10673171189f429650dde467dc0143c7245fb9bb661c4b718d638","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e0f8921ae0d10673171189f429650dde467dc0143c7245fb9bb661c4b718d638","first_computed_at":"2026-05-18T04:15:18.879289Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:15:18.879289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+9nUekDhidIy0ptQr4ehvQ/1MLv3iuWXOXiB0B+XhxdAXV/BpQkYiRVfidHuj+xgr3uwFpXvw6hxL6Uj/Yp6CA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:15:18.880064Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.5580","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c4962dbb81f60e4971336002f963eedd9b567d7bea34ceed125963b4aabafcc","sha256:c3f261541a4983900a69a911b6736052f0e4c84b69be82fbc044b747a027fd77"],"state_sha256":"1b146b66749114269340b36c3f44cec5edc67920a6b6b6495cc711280e320671"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V+493DdGi7qyu1Avjs+XtrJN7qyHXOUA5eXE33lqGRYXw9n4q7cAbKxFWpLks4oyKmwuLag0NTwXcs0hGlRyAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T16:05:50.638800Z","bundle_sha256":"76f997fc6e7e2560b5080955ed400c759ae5390e70a383d7d29a2860d6933704"}}