{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:EON7U47ROATZQMEBI5OX54NCJL","short_pith_number":"pith:EON7U47R","canonical_record":{"source":{"id":"1401.4698","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-19T16:48:43Z","cross_cats_sorted":["q-fin.PR"],"title_canon_sha256":"1c1110b79764d108f0cf1756641f30488fb7a1052d9673e2b8bb6e829eedc2d8","abstract_canon_sha256":"1cf22392e15d0c66d1d564212982ce8516d27575a4f7ff89236e18971dd25a99"},"schema_version":"1.0"},"canonical_sha256":"239bfa73f17027983081475d7ef1a24ad21081a018b2c955e8438fa5a4957c5c","source":{"kind":"arxiv","id":"1401.4698","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.4698","created_at":"2026-05-18T02:39:48Z"},{"alias_kind":"arxiv_version","alias_value":"1401.4698v2","created_at":"2026-05-18T02:39:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.4698","created_at":"2026-05-18T02:39:48Z"},{"alias_kind":"pith_short_12","alias_value":"EON7U47ROATZ","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"EON7U47ROATZQMEB","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"EON7U47R","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:EON7U47ROATZQMEBI5OX54NCJL","target":"record","payload":{"canonical_record":{"source":{"id":"1401.4698","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-19T16:48:43Z","cross_cats_sorted":["q-fin.PR"],"title_canon_sha256":"1c1110b79764d108f0cf1756641f30488fb7a1052d9673e2b8bb6e829eedc2d8","abstract_canon_sha256":"1cf22392e15d0c66d1d564212982ce8516d27575a4f7ff89236e18971dd25a99"},"schema_version":"1.0"},"canonical_sha256":"239bfa73f17027983081475d7ef1a24ad21081a018b2c955e8438fa5a4957c5c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:48.465237Z","signature_b64":"KdEYOYiwmzoJ9ZhWFKXzlHcGYJeRxwiqOm7WUuFBzi32v/ZDIsHXwkLgredKSULJxWv4fopIjCa46q9UGll1BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"239bfa73f17027983081475d7ef1a24ad21081a018b2c955e8438fa5a4957c5c","last_reissued_at":"2026-05-18T02:39:48.464637Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:48.464637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.4698","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":"2026-05-18T02:39:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jgd/USZG4UgDk0OZmLcumlQEcxnM3qus6h1ksHwl2Y4so15Q3d5lU6vY6v8CWHDBu83kr2/3OyBjnJLoB4CnBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T09:52:44.525404Z"},"content_sha256":"21b1785f3d69214e698b164f37a1671ba8e845622ed3b852ab588492d664b40e","schema_version":"1.0","event_id":"sha256:21b1785f3d69214e698b164f37a1671ba8e845622ed3b852ab588492d664b40e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:EON7U47ROATZQMEBI5OX54NCJL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Martingale Inequalities and Deterministic Counterparts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-fin.PR"],"primary_cat":"math.PR","authors_text":"Marcel Nutz, Mathias Beiglb\\\"ock","submitted_at":"2014-01-19T16:48:43Z","abstract_excerpt":"We study martingale inequalities from an analytic point of view and show that a general martingale inequality can be reduced to a pair of deterministic inequalities in a small number of variables. More precisely, the optimal bound in the martingale inequality is determined by a fixed point of a simple nonlinear operator involving a concave envelope. Our results yield an explanation for certain inequalities that arise in mathematical finance in the context of robust hedging."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4698","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":"2026-05-18T02:39:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zq3tJe9yXT+3k7rwn0xKkEEFZGFoUxRg5T+1VxEAp7sA1iqf2s5YfHT6q43cUbnM70hC/tmAR5C0RV61ciNQAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T09:52:44.525747Z"},"content_sha256":"6ea4b593ecef5ccb1efc96dce373e94e78383a836b0c40b3d83b81a191430560","schema_version":"1.0","event_id":"sha256:6ea4b593ecef5ccb1efc96dce373e94e78383a836b0c40b3d83b81a191430560"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EON7U47ROATZQMEBI5OX54NCJL/bundle.json","state_url":"https://pith.science/pith/EON7U47ROATZQMEBI5OX54NCJL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EON7U47ROATZQMEBI5OX54NCJL/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":"2026-06-03T09:52:44Z","links":{"resolver":"https://pith.science/pith/EON7U47ROATZQMEBI5OX54NCJL","bundle":"https://pith.science/pith/EON7U47ROATZQMEBI5OX54NCJL/bundle.json","state":"https://pith.science/pith/EON7U47ROATZQMEBI5OX54NCJL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EON7U47ROATZQMEBI5OX54NCJL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:EON7U47ROATZQMEBI5OX54NCJL","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":"1cf22392e15d0c66d1d564212982ce8516d27575a4f7ff89236e18971dd25a99","cross_cats_sorted":["q-fin.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-19T16:48:43Z","title_canon_sha256":"1c1110b79764d108f0cf1756641f30488fb7a1052d9673e2b8bb6e829eedc2d8"},"schema_version":"1.0","source":{"id":"1401.4698","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.4698","created_at":"2026-05-18T02:39:48Z"},{"alias_kind":"arxiv_version","alias_value":"1401.4698v2","created_at":"2026-05-18T02:39:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.4698","created_at":"2026-05-18T02:39:48Z"},{"alias_kind":"pith_short_12","alias_value":"EON7U47ROATZ","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"EON7U47ROATZQMEB","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"EON7U47R","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:6ea4b593ecef5ccb1efc96dce373e94e78383a836b0c40b3d83b81a191430560","target":"graph","created_at":"2026-05-18T02:39:48Z","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 study martingale inequalities from an analytic point of view and show that a general martingale inequality can be reduced to a pair of deterministic inequalities in a small number of variables. More precisely, the optimal bound in the martingale inequality is determined by a fixed point of a simple nonlinear operator involving a concave envelope. Our results yield an explanation for certain inequalities that arise in mathematical finance in the context of robust hedging.","authors_text":"Marcel Nutz, Mathias Beiglb\\\"ock","cross_cats":["q-fin.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-19T16:48:43Z","title":"Martingale Inequalities and Deterministic Counterparts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4698","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":"sha256:21b1785f3d69214e698b164f37a1671ba8e845622ed3b852ab588492d664b40e","target":"record","created_at":"2026-05-18T02:39:48Z","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":"1cf22392e15d0c66d1d564212982ce8516d27575a4f7ff89236e18971dd25a99","cross_cats_sorted":["q-fin.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-19T16:48:43Z","title_canon_sha256":"1c1110b79764d108f0cf1756641f30488fb7a1052d9673e2b8bb6e829eedc2d8"},"schema_version":"1.0","source":{"id":"1401.4698","kind":"arxiv","version":2}},"canonical_sha256":"239bfa73f17027983081475d7ef1a24ad21081a018b2c955e8438fa5a4957c5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"239bfa73f17027983081475d7ef1a24ad21081a018b2c955e8438fa5a4957c5c","first_computed_at":"2026-05-18T02:39:48.464637Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:48.464637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KdEYOYiwmzoJ9ZhWFKXzlHcGYJeRxwiqOm7WUuFBzi32v/ZDIsHXwkLgredKSULJxWv4fopIjCa46q9UGll1BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:48.465237Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.4698","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21b1785f3d69214e698b164f37a1671ba8e845622ed3b852ab588492d664b40e","sha256:6ea4b593ecef5ccb1efc96dce373e94e78383a836b0c40b3d83b81a191430560"],"state_sha256":"5b0da571826fb308c3ff96482ff519e9c5a4c211cb5ae27e51efa0f7cd8d078e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h8c0JsKlpPxk17daTSxt5/3k2f+AXLwIWirpnjvynx7rKKyzsB7bduM6yPTeoaON+4M3oqTtdhqPJAQKBV0ZBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T09:52:44.527667Z","bundle_sha256":"34bd0b9e45f51ecc2f94c665299468ba758b17e08f68103de5200711a2d841db"}}