{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:LHTHAW7S5NQ73BC6WSN6F6TM42","short_pith_number":"pith:LHTHAW7S","canonical_record":{"source":{"id":"1110.6886","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2011-10-31T18:22:24Z","cross_cats_sorted":["cs.IT","math.IT","stat.ML"],"title_canon_sha256":"5e1a60b34bdf0e70a817ed06e752ed1eb8450ebc8dd2d8a1481ee93a4812a3c5","abstract_canon_sha256":"dad45b8726b22c7e86d5f3d7c976d2219b3e13fbd2f4a490f898d2f6d7e6d9d7"},"schema_version":"1.0"},"canonical_sha256":"59e6705bf2eb61fd845eb49be2fa6ce6befbb1718d2acaa3d2210d3ba20c0c4d","source":{"kind":"arxiv","id":"1110.6886","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.6886","created_at":"2026-05-18T03:49:58Z"},{"alias_kind":"arxiv_version","alias_value":"1110.6886v3","created_at":"2026-05-18T03:49:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6886","created_at":"2026-05-18T03:49:58Z"},{"alias_kind":"pith_short_12","alias_value":"LHTHAW7S5NQ7","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LHTHAW7S5NQ73BC6","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LHTHAW7S","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:LHTHAW7S5NQ73BC6WSN6F6TM42","target":"record","payload":{"canonical_record":{"source":{"id":"1110.6886","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2011-10-31T18:22:24Z","cross_cats_sorted":["cs.IT","math.IT","stat.ML"],"title_canon_sha256":"5e1a60b34bdf0e70a817ed06e752ed1eb8450ebc8dd2d8a1481ee93a4812a3c5","abstract_canon_sha256":"dad45b8726b22c7e86d5f3d7c976d2219b3e13fbd2f4a490f898d2f6d7e6d9d7"},"schema_version":"1.0"},"canonical_sha256":"59e6705bf2eb61fd845eb49be2fa6ce6befbb1718d2acaa3d2210d3ba20c0c4d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:49:58.382875Z","signature_b64":"2Ld6gKwOTgyJpzL+S68vaLcqESidXH1c32lduir4mcYD64FtXms1DHu8UK2iyhcz7sJ3T9Ct9CNwheu91TQoBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59e6705bf2eb61fd845eb49be2fa6ce6befbb1718d2acaa3d2210d3ba20c0c4d","last_reissued_at":"2026-05-18T03:49:58.382355Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:49:58.382355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.6886","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:49:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k9YrQ50e0K/XLZAdhTno9n8wcauhuanjQXIjMdKeXeRmCBQQykBwA7W/tesQ+LZQe9hkq2f/gqzjfSurAkALCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T14:26:24.513712Z"},"content_sha256":"dfc934c892cdb099b47a4fcca18654920ab1e023531ffef7ffe35a9f3ad19d4a","schema_version":"1.0","event_id":"sha256:dfc934c892cdb099b47a4fcca18654920ab1e023531ffef7ffe35a9f3ad19d4a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:LHTHAW7S5NQ73BC6WSN6F6TM42","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"PAC-Bayesian Inequalities for Martingales","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","stat.ML"],"primary_cat":"cs.LG","authors_text":"Fran\\c{c}ois Laviolette, John Shawe-Taylor, Nicol\\`o Cesa-Bianchi, Peter Auer, Yevgeny Seldin","submitted_at":"2011-10-31T18:22:24Z","abstract_excerpt":"We present a set of high-probability inequalities that control the concentration of weighted averages of multiple (possibly uncountably many) simultaneously evolving and interdependent martingales. Our results extend the PAC-Bayesian analysis in learning theory from the i.i.d. setting to martingales opening the way for its application to importance weighted sampling, reinforcement learning, and other interactive learning domains, as well as many other domains in probability theory and statistics, where martingales are encountered.\n  We also present a comparison inequality that bounds the expec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6886","kind":"arxiv","version":3},"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":"2026-05-18T03:49:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"veLO58kSzqStXc6b8x3+cwkiZq0BvPN71FqFcfrbVXBlMqk9wVZ8yl4+YSjGdOHxgr1MkrueLYFfl/+IJl8MBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T14:26:24.514139Z"},"content_sha256":"f44a0ae945fc12652a494f5a724a2050a1bffeb938b0ad02c754580f944e1b60","schema_version":"1.0","event_id":"sha256:f44a0ae945fc12652a494f5a724a2050a1bffeb938b0ad02c754580f944e1b60"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LHTHAW7S5NQ73BC6WSN6F6TM42/bundle.json","state_url":"https://pith.science/pith/LHTHAW7S5NQ73BC6WSN6F6TM42/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LHTHAW7S5NQ73BC6WSN6F6TM42/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":"2026-05-25T14:26:24Z","links":{"resolver":"https://pith.science/pith/LHTHAW7S5NQ73BC6WSN6F6TM42","bundle":"https://pith.science/pith/LHTHAW7S5NQ73BC6WSN6F6TM42/bundle.json","state":"https://pith.science/pith/LHTHAW7S5NQ73BC6WSN6F6TM42/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LHTHAW7S5NQ73BC6WSN6F6TM42/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:LHTHAW7S5NQ73BC6WSN6F6TM42","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":"dad45b8726b22c7e86d5f3d7c976d2219b3e13fbd2f4a490f898d2f6d7e6d9d7","cross_cats_sorted":["cs.IT","math.IT","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2011-10-31T18:22:24Z","title_canon_sha256":"5e1a60b34bdf0e70a817ed06e752ed1eb8450ebc8dd2d8a1481ee93a4812a3c5"},"schema_version":"1.0","source":{"id":"1110.6886","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.6886","created_at":"2026-05-18T03:49:58Z"},{"alias_kind":"arxiv_version","alias_value":"1110.6886v3","created_at":"2026-05-18T03:49:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6886","created_at":"2026-05-18T03:49:58Z"},{"alias_kind":"pith_short_12","alias_value":"LHTHAW7S5NQ7","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LHTHAW7S5NQ73BC6","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LHTHAW7S","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:f44a0ae945fc12652a494f5a724a2050a1bffeb938b0ad02c754580f944e1b60","target":"graph","created_at":"2026-05-18T03:49:58Z","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 present a set of high-probability inequalities that control the concentration of weighted averages of multiple (possibly uncountably many) simultaneously evolving and interdependent martingales. Our results extend the PAC-Bayesian analysis in learning theory from the i.i.d. setting to martingales opening the way for its application to importance weighted sampling, reinforcement learning, and other interactive learning domains, as well as many other domains in probability theory and statistics, where martingales are encountered.\n  We also present a comparison inequality that bounds the expec","authors_text":"Fran\\c{c}ois Laviolette, John Shawe-Taylor, Nicol\\`o Cesa-Bianchi, Peter Auer, Yevgeny Seldin","cross_cats":["cs.IT","math.IT","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2011-10-31T18:22:24Z","title":"PAC-Bayesian Inequalities for Martingales"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6886","kind":"arxiv","version":3},"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:dfc934c892cdb099b47a4fcca18654920ab1e023531ffef7ffe35a9f3ad19d4a","target":"record","created_at":"2026-05-18T03:49:58Z","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":"dad45b8726b22c7e86d5f3d7c976d2219b3e13fbd2f4a490f898d2f6d7e6d9d7","cross_cats_sorted":["cs.IT","math.IT","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2011-10-31T18:22:24Z","title_canon_sha256":"5e1a60b34bdf0e70a817ed06e752ed1eb8450ebc8dd2d8a1481ee93a4812a3c5"},"schema_version":"1.0","source":{"id":"1110.6886","kind":"arxiv","version":3}},"canonical_sha256":"59e6705bf2eb61fd845eb49be2fa6ce6befbb1718d2acaa3d2210d3ba20c0c4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59e6705bf2eb61fd845eb49be2fa6ce6befbb1718d2acaa3d2210d3ba20c0c4d","first_computed_at":"2026-05-18T03:49:58.382355Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:58.382355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2Ld6gKwOTgyJpzL+S68vaLcqESidXH1c32lduir4mcYD64FtXms1DHu8UK2iyhcz7sJ3T9Ct9CNwheu91TQoBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:58.382875Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.6886","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dfc934c892cdb099b47a4fcca18654920ab1e023531ffef7ffe35a9f3ad19d4a","sha256:f44a0ae945fc12652a494f5a724a2050a1bffeb938b0ad02c754580f944e1b60"],"state_sha256":"ce68e2898e9109f3705c6e635aaa6025575fa8b7b20e0ea2da99898bc0b9955c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RtdjEdctBC1iP41HgqZWuAC+KFEXptU9MQIO58xTEotu7x6dbJgiQeVWVFYqIYWkq7mQuFtiWit+Ia7mu3XgDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T14:26:24.517146Z","bundle_sha256":"835ed4524af4db82795366a121a8f41ff86ab07d56f0ce6b91bde944cf0d7296"}}