{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:S2HFHZJK4ZBUEXICSHOPQMJ6TJ","short_pith_number":"pith:S2HFHZJK","canonical_record":{"source":{"id":"1302.3202","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-13T19:56:36Z","cross_cats_sorted":[],"title_canon_sha256":"606963dfcdf3a69422e0cb0f0b07740fa74196430d55b62c753afb148ee27505","abstract_canon_sha256":"f3cfbe4bc095d484f159ba4cca245a2e4d201fe7feb03041e3f6806687b7a7bd"},"schema_version":"1.0"},"canonical_sha256":"968e53e52ae643425d0291dcf8313e9a524a4da373e4ca4145bb87f8351fad9c","source":{"kind":"arxiv","id":"1302.3202","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.3202","created_at":"2026-05-18T03:33:48Z"},{"alias_kind":"arxiv_version","alias_value":"1302.3202v1","created_at":"2026-05-18T03:33:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.3202","created_at":"2026-05-18T03:33:48Z"},{"alias_kind":"pith_short_12","alias_value":"S2HFHZJK4ZBU","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"S2HFHZJK4ZBUEXIC","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"S2HFHZJK","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:S2HFHZJK4ZBUEXICSHOPQMJ6TJ","target":"record","payload":{"canonical_record":{"source":{"id":"1302.3202","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-13T19:56:36Z","cross_cats_sorted":[],"title_canon_sha256":"606963dfcdf3a69422e0cb0f0b07740fa74196430d55b62c753afb148ee27505","abstract_canon_sha256":"f3cfbe4bc095d484f159ba4cca245a2e4d201fe7feb03041e3f6806687b7a7bd"},"schema_version":"1.0"},"canonical_sha256":"968e53e52ae643425d0291dcf8313e9a524a4da373e4ca4145bb87f8351fad9c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:33:48.409957Z","signature_b64":"RL2c/ZwVfhT/25iWGymduykhVwl7QJYAt8p3STygqSFDu4n4iR+fquTf/JD4CCrrYK1PeQ4PyWtDtZnotxl0BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"968e53e52ae643425d0291dcf8313e9a524a4da373e4ca4145bb87f8351fad9c","last_reissued_at":"2026-05-18T03:33:48.409359Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:33:48.409359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.3202","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":"2026-05-18T03:33:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4uSHNujc2U5iPW9Etf4WexLyf8t8BBDbwFl2epPJXG2R/qJaV3sz3bPjoSgwlzEpyXY4cRk33eyvtHH0I+irBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T06:08:14.541916Z"},"content_sha256":"0bf37baba18b71e68924f7c99d9f6fbb6029fbfedaf9b2cd99efb2dadf6f2b0d","schema_version":"1.0","event_id":"sha256:0bf37baba18b71e68924f7c99d9f6fbb6029fbfedaf9b2cd99efb2dadf6f2b0d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:S2HFHZJK4ZBUEXICSHOPQMJ6TJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Simplification of the majorizing measures method, with development","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"E.Ostrovsky, L.Sirota","submitted_at":"2013-02-13T19:56:36Z","abstract_excerpt":"We update, specify, review and develop in this article the classical majorizing measures method for investigation of the local structure of random fields, belonging to X.Fernique and M.Talagrand in order to simplify and improve the constant values.\n  Our considerations based on the generalization of the L.Arnold and P.Imkeller generalization of classical Garsia-Rodemich-Rumsey inequality."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3202","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":""},"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":"2026-05-18T03:33:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T03ofzTKdzMc7Y92YulRdYT9rAGJJbO6xzF65ZBT+3CTE/hw4EheQu60RxOZ0gu0upwTroZEs9e/fG7My5lPBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T06:08:14.542258Z"},"content_sha256":"c10341ebdf40697f48e168cafbf174eb78296684d0272586f9c94a5458c61ff8","schema_version":"1.0","event_id":"sha256:c10341ebdf40697f48e168cafbf174eb78296684d0272586f9c94a5458c61ff8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S2HFHZJK4ZBUEXICSHOPQMJ6TJ/bundle.json","state_url":"https://pith.science/pith/S2HFHZJK4ZBUEXICSHOPQMJ6TJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S2HFHZJK4ZBUEXICSHOPQMJ6TJ/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":"2026-06-23T06:08:14Z","links":{"resolver":"https://pith.science/pith/S2HFHZJK4ZBUEXICSHOPQMJ6TJ","bundle":"https://pith.science/pith/S2HFHZJK4ZBUEXICSHOPQMJ6TJ/bundle.json","state":"https://pith.science/pith/S2HFHZJK4ZBUEXICSHOPQMJ6TJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S2HFHZJK4ZBUEXICSHOPQMJ6TJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:S2HFHZJK4ZBUEXICSHOPQMJ6TJ","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":"f3cfbe4bc095d484f159ba4cca245a2e4d201fe7feb03041e3f6806687b7a7bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-13T19:56:36Z","title_canon_sha256":"606963dfcdf3a69422e0cb0f0b07740fa74196430d55b62c753afb148ee27505"},"schema_version":"1.0","source":{"id":"1302.3202","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.3202","created_at":"2026-05-18T03:33:48Z"},{"alias_kind":"arxiv_version","alias_value":"1302.3202v1","created_at":"2026-05-18T03:33:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.3202","created_at":"2026-05-18T03:33:48Z"},{"alias_kind":"pith_short_12","alias_value":"S2HFHZJK4ZBU","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"S2HFHZJK4ZBUEXIC","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"S2HFHZJK","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:c10341ebdf40697f48e168cafbf174eb78296684d0272586f9c94a5458c61ff8","target":"graph","created_at":"2026-05-18T03:33:48Z","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 update, specify, review and develop in this article the classical majorizing measures method for investigation of the local structure of random fields, belonging to X.Fernique and M.Talagrand in order to simplify and improve the constant values.\n  Our considerations based on the generalization of the L.Arnold and P.Imkeller generalization of classical Garsia-Rodemich-Rumsey inequality.","authors_text":"E.Ostrovsky, L.Sirota","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-13T19:56:36Z","title":"Simplification of the majorizing measures method, with development"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3202","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":"sha256:0bf37baba18b71e68924f7c99d9f6fbb6029fbfedaf9b2cd99efb2dadf6f2b0d","target":"record","created_at":"2026-05-18T03:33:48Z","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":"f3cfbe4bc095d484f159ba4cca245a2e4d201fe7feb03041e3f6806687b7a7bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-13T19:56:36Z","title_canon_sha256":"606963dfcdf3a69422e0cb0f0b07740fa74196430d55b62c753afb148ee27505"},"schema_version":"1.0","source":{"id":"1302.3202","kind":"arxiv","version":1}},"canonical_sha256":"968e53e52ae643425d0291dcf8313e9a524a4da373e4ca4145bb87f8351fad9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"968e53e52ae643425d0291dcf8313e9a524a4da373e4ca4145bb87f8351fad9c","first_computed_at":"2026-05-18T03:33:48.409359Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:48.409359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RL2c/ZwVfhT/25iWGymduykhVwl7QJYAt8p3STygqSFDu4n4iR+fquTf/JD4CCrrYK1PeQ4PyWtDtZnotxl0BA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:48.409957Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.3202","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0bf37baba18b71e68924f7c99d9f6fbb6029fbfedaf9b2cd99efb2dadf6f2b0d","sha256:c10341ebdf40697f48e168cafbf174eb78296684d0272586f9c94a5458c61ff8"],"state_sha256":"163875cbb7018d526331cade2f5bf8328c5740e0e093902d0bcddce5b165a93d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RmuFo/tQDWEr190H045y5HKv3g4gjzyzvoxFhsE9QSbS7fhw9MrGG+LFmP9E7kG/r5LjhouvavUN5CZpk5D9BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T06:08:14.544220Z","bundle_sha256":"996844fa0a64aa467b4102cd3ded7f3c2603ae73fb8b5e2c9fc36f3c50bee5fe"}}