{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:XG2NVN4JH2RLNTM2SOKOUGOSJQ","short_pith_number":"pith:XG2NVN4J","canonical_record":{"source":{"id":"1110.1599","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-07T18:14:20Z","cross_cats_sorted":[],"title_canon_sha256":"5124718499264acfe9760b92a4b7121281f69f62c1ce4457e0e095ca1ab616dc","abstract_canon_sha256":"578664b0ca6d4e653de57f34995e26ec2751f64880a4ecdd42dd4eb96a3ccb6c"},"schema_version":"1.0"},"canonical_sha256":"b9b4dab7893ea2b6cd9a9394ea19d24c3e608fbf37977e96217d92270cca2501","source":{"kind":"arxiv","id":"1110.1599","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.1599","created_at":"2026-05-18T03:11:33Z"},{"alias_kind":"arxiv_version","alias_value":"1110.1599v2","created_at":"2026-05-18T03:11:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1599","created_at":"2026-05-18T03:11:33Z"},{"alias_kind":"pith_short_12","alias_value":"XG2NVN4JH2RL","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"XG2NVN4JH2RLNTM2","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"XG2NVN4J","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:XG2NVN4JH2RLNTM2SOKOUGOSJQ","target":"record","payload":{"canonical_record":{"source":{"id":"1110.1599","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-07T18:14:20Z","cross_cats_sorted":[],"title_canon_sha256":"5124718499264acfe9760b92a4b7121281f69f62c1ce4457e0e095ca1ab616dc","abstract_canon_sha256":"578664b0ca6d4e653de57f34995e26ec2751f64880a4ecdd42dd4eb96a3ccb6c"},"schema_version":"1.0"},"canonical_sha256":"b9b4dab7893ea2b6cd9a9394ea19d24c3e608fbf37977e96217d92270cca2501","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:33.720449Z","signature_b64":"A47FotjIa3sA8xdIlpBDU4OCce9eEwuC7/PpwDMtqs+voje9i3DZy9YjG1nSy550yctP9ZihmANIsxUdlPTFCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9b4dab7893ea2b6cd9a9394ea19d24c3e608fbf37977e96217d92270cca2501","last_reissued_at":"2026-05-18T03:11:33.719777Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:33.719777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.1599","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":"2026-05-18T03:11:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IE/zSI3YDTSqS7GzqRs2c6NIQ+hpeET2qREuA7iDc8N0P/Yaj3IU/fLfatbO76HlaYK9MvaUNS5XkAl3lL2qDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:17:37.098123Z"},"content_sha256":"4ab067c70e4f1309b6e2bd48ea43f156c1eb8b920ae6e653d0cc6333597c9fe7","schema_version":"1.0","event_id":"sha256:4ab067c70e4f1309b6e2bd48ea43f156c1eb8b920ae6e653d0cc6333597c9fe7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:XG2NVN4JH2RLNTM2SOKOUGOSJQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Is the location of the supremum of a stationary process nearly uniformly distributed?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Gennady Samorodnitsky, Yi Shen","submitted_at":"2011-10-07T18:14:20Z","abstract_excerpt":"It is, perhaps, surprising that the location of the unique supremum of a stationary process on an interval can fail to be uniformly distributed over that interval. We show that this distribution is absolutely continuous in the interior of the interval and describe very specific conditions the density has to satisfy. We establish universal upper bounds on the density and demonstrate their optimality."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1599","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":"2026-05-18T03:11:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iHqUNReUT/W0/7+ENrxH63gpGkAZrh5V88fXQnrd49lN8OLz5KQy3abSmnZArsUY0f2Vp+xvOlY5WquOP12lAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:17:37.098492Z"},"content_sha256":"7b52137f9b9657c98247106de392d7ec1f39ae9456003ff85e87987e5f812a2a","schema_version":"1.0","event_id":"sha256:7b52137f9b9657c98247106de392d7ec1f39ae9456003ff85e87987e5f812a2a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XG2NVN4JH2RLNTM2SOKOUGOSJQ/bundle.json","state_url":"https://pith.science/pith/XG2NVN4JH2RLNTM2SOKOUGOSJQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XG2NVN4JH2RLNTM2SOKOUGOSJQ/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":"2026-05-31T04:17:37Z","links":{"resolver":"https://pith.science/pith/XG2NVN4JH2RLNTM2SOKOUGOSJQ","bundle":"https://pith.science/pith/XG2NVN4JH2RLNTM2SOKOUGOSJQ/bundle.json","state":"https://pith.science/pith/XG2NVN4JH2RLNTM2SOKOUGOSJQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XG2NVN4JH2RLNTM2SOKOUGOSJQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XG2NVN4JH2RLNTM2SOKOUGOSJQ","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":"578664b0ca6d4e653de57f34995e26ec2751f64880a4ecdd42dd4eb96a3ccb6c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-07T18:14:20Z","title_canon_sha256":"5124718499264acfe9760b92a4b7121281f69f62c1ce4457e0e095ca1ab616dc"},"schema_version":"1.0","source":{"id":"1110.1599","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.1599","created_at":"2026-05-18T03:11:33Z"},{"alias_kind":"arxiv_version","alias_value":"1110.1599v2","created_at":"2026-05-18T03:11:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1599","created_at":"2026-05-18T03:11:33Z"},{"alias_kind":"pith_short_12","alias_value":"XG2NVN4JH2RL","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"XG2NVN4JH2RLNTM2","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"XG2NVN4J","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:7b52137f9b9657c98247106de392d7ec1f39ae9456003ff85e87987e5f812a2a","target":"graph","created_at":"2026-05-18T03:11:33Z","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":"It is, perhaps, surprising that the location of the unique supremum of a stationary process on an interval can fail to be uniformly distributed over that interval. We show that this distribution is absolutely continuous in the interior of the interval and describe very specific conditions the density has to satisfy. We establish universal upper bounds on the density and demonstrate their optimality.","authors_text":"Gennady Samorodnitsky, Yi Shen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-07T18:14:20Z","title":"Is the location of the supremum of a stationary process nearly uniformly distributed?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1599","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":"sha256:4ab067c70e4f1309b6e2bd48ea43f156c1eb8b920ae6e653d0cc6333597c9fe7","target":"record","created_at":"2026-05-18T03:11:33Z","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":"578664b0ca6d4e653de57f34995e26ec2751f64880a4ecdd42dd4eb96a3ccb6c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-07T18:14:20Z","title_canon_sha256":"5124718499264acfe9760b92a4b7121281f69f62c1ce4457e0e095ca1ab616dc"},"schema_version":"1.0","source":{"id":"1110.1599","kind":"arxiv","version":2}},"canonical_sha256":"b9b4dab7893ea2b6cd9a9394ea19d24c3e608fbf37977e96217d92270cca2501","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9b4dab7893ea2b6cd9a9394ea19d24c3e608fbf37977e96217d92270cca2501","first_computed_at":"2026-05-18T03:11:33.719777Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:33.719777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A47FotjIa3sA8xdIlpBDU4OCce9eEwuC7/PpwDMtqs+voje9i3DZy9YjG1nSy550yctP9ZihmANIsxUdlPTFCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:33.720449Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.1599","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ab067c70e4f1309b6e2bd48ea43f156c1eb8b920ae6e653d0cc6333597c9fe7","sha256:7b52137f9b9657c98247106de392d7ec1f39ae9456003ff85e87987e5f812a2a"],"state_sha256":"e58080af12650a0d04f56a9fcf7949d02437def58ccafd8ec96e393dabe4edad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ncsPQDeBI5u+VD6lfF/va03PsIc9MX1NSDBlargo+LGNJ6Iu4ngFuF754oDrZkg709wKEbVKMkPahgiLMP4DDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T04:17:37.100713Z","bundle_sha256":"f6153d3f7d95d66b77799d46eb9104658264556ca59429f2da5d52258cef5ebc"}}