{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:JZR6PEEPSJU4243DOCERVVERAA","short_pith_number":"pith:JZR6PEEP","canonical_record":{"source":{"id":"1509.08280","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2015-09-28T11:37:04Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"a59cfe9f47abcf62f56d6d7f44db491f733d3905b4637b3d1b65109c15f9544e","abstract_canon_sha256":"b45ad05c8f97d892786e67334e4e4a8ef0b91d851e6dc9fe09e7c2d74aad34b0"},"schema_version":"1.0"},"canonical_sha256":"4e63e7908f9269cd736370891ad4910038511c542e9f2503c75af0942a15de54","source":{"kind":"arxiv","id":"1509.08280","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.08280","created_at":"2026-05-18T00:49:42Z"},{"alias_kind":"arxiv_version","alias_value":"1509.08280v3","created_at":"2026-05-18T00:49:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.08280","created_at":"2026-05-18T00:49:42Z"},{"alias_kind":"pith_short_12","alias_value":"JZR6PEEPSJU4","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JZR6PEEPSJU4243D","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JZR6PEEP","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:JZR6PEEPSJU4243DOCERVVERAA","target":"record","payload":{"canonical_record":{"source":{"id":"1509.08280","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2015-09-28T11:37:04Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"a59cfe9f47abcf62f56d6d7f44db491f733d3905b4637b3d1b65109c15f9544e","abstract_canon_sha256":"b45ad05c8f97d892786e67334e4e4a8ef0b91d851e6dc9fe09e7c2d74aad34b0"},"schema_version":"1.0"},"canonical_sha256":"4e63e7908f9269cd736370891ad4910038511c542e9f2503c75af0942a15de54","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:42.650200Z","signature_b64":"MPRbzaGcWwGYHmRgE2sJ6Od2FCC40M7btU55yVgBIyetnnEztmGQHfy5z8GgGoBEBqpTXxCSuVzi92ylZH2ZBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e63e7908f9269cd736370891ad4910038511c542e9f2503c75af0942a15de54","last_reissued_at":"2026-05-18T00:49:42.649717Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:42.649717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.08280","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":"2026-05-18T00:49:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V3H6iaCee6Qfb8Oh3Gmjnsy3uvAa8ztsl47s1ZsHfJxEISu0A2z6bmTjSwYetgEAh8rYyhcNhKXHojeLafUpCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T05:00:45.895402Z"},"content_sha256":"ba63d37804018fb53be1938c24ce8cdae6403cb26d5282d5e51fb3fea45f0713","schema_version":"1.0","event_id":"sha256:ba63d37804018fb53be1938c24ce8cdae6403cb26d5282d5e51fb3fea45f0713"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:JZR6PEEPSJU4243DOCERVVERAA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sticky processes, local and true martingales","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"q-fin.MF","authors_text":"Hasanjan Sayit, Mikl\\'os R\\'asonyi","submitted_at":"2015-09-28T11:37:04Z","abstract_excerpt":"We prove that for a so-called sticky process $S$ there exists an equivalent probability $Q$ and a $Q$-martingale $\\tilde{S}$ that is arbitrarily close to $S$ in $L^p(Q)$ norm. For continuous $S$, $\\tilde{S}$ can be chosen arbitrarily close to $S$ in supremum norm. In the case where $S$ is a local martingale we may choose $Q$ arbitrarily close to the original probability in the total variation norm. We provide examples to illustrate the power of our results and present applications in mathematical finance."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08280","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":"2026-05-18T00:49:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iqdUAd2MM1p6IP3Zvsrhol8hhInGA300wg3NXanuYYQFkgluVYajPPPEYgOZhqwqtND9tE102PLdLnl4v9sjAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T05:00:45.895750Z"},"content_sha256":"795886edf155bcb964dac0157aebf667dd1ca34ed648b89b3acca871237fb82e","schema_version":"1.0","event_id":"sha256:795886edf155bcb964dac0157aebf667dd1ca34ed648b89b3acca871237fb82e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JZR6PEEPSJU4243DOCERVVERAA/bundle.json","state_url":"https://pith.science/pith/JZR6PEEPSJU4243DOCERVVERAA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JZR6PEEPSJU4243DOCERVVERAA/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":"2026-05-28T05:00:45Z","links":{"resolver":"https://pith.science/pith/JZR6PEEPSJU4243DOCERVVERAA","bundle":"https://pith.science/pith/JZR6PEEPSJU4243DOCERVVERAA/bundle.json","state":"https://pith.science/pith/JZR6PEEPSJU4243DOCERVVERAA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JZR6PEEPSJU4243DOCERVVERAA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JZR6PEEPSJU4243DOCERVVERAA","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":"b45ad05c8f97d892786e67334e4e4a8ef0b91d851e6dc9fe09e7c2d74aad34b0","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2015-09-28T11:37:04Z","title_canon_sha256":"a59cfe9f47abcf62f56d6d7f44db491f733d3905b4637b3d1b65109c15f9544e"},"schema_version":"1.0","source":{"id":"1509.08280","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.08280","created_at":"2026-05-18T00:49:42Z"},{"alias_kind":"arxiv_version","alias_value":"1509.08280v3","created_at":"2026-05-18T00:49:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.08280","created_at":"2026-05-18T00:49:42Z"},{"alias_kind":"pith_short_12","alias_value":"JZR6PEEPSJU4","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JZR6PEEPSJU4243D","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JZR6PEEP","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:795886edf155bcb964dac0157aebf667dd1ca34ed648b89b3acca871237fb82e","target":"graph","created_at":"2026-05-18T00:49:42Z","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 prove that for a so-called sticky process $S$ there exists an equivalent probability $Q$ and a $Q$-martingale $\\tilde{S}$ that is arbitrarily close to $S$ in $L^p(Q)$ norm. For continuous $S$, $\\tilde{S}$ can be chosen arbitrarily close to $S$ in supremum norm. In the case where $S$ is a local martingale we may choose $Q$ arbitrarily close to the original probability in the total variation norm. We provide examples to illustrate the power of our results and present applications in mathematical finance.","authors_text":"Hasanjan Sayit, Mikl\\'os R\\'asonyi","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2015-09-28T11:37:04Z","title":"Sticky processes, local and true martingales"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08280","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:ba63d37804018fb53be1938c24ce8cdae6403cb26d5282d5e51fb3fea45f0713","target":"record","created_at":"2026-05-18T00:49:42Z","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":"b45ad05c8f97d892786e67334e4e4a8ef0b91d851e6dc9fe09e7c2d74aad34b0","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2015-09-28T11:37:04Z","title_canon_sha256":"a59cfe9f47abcf62f56d6d7f44db491f733d3905b4637b3d1b65109c15f9544e"},"schema_version":"1.0","source":{"id":"1509.08280","kind":"arxiv","version":3}},"canonical_sha256":"4e63e7908f9269cd736370891ad4910038511c542e9f2503c75af0942a15de54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e63e7908f9269cd736370891ad4910038511c542e9f2503c75af0942a15de54","first_computed_at":"2026-05-18T00:49:42.649717Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:42.649717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MPRbzaGcWwGYHmRgE2sJ6Od2FCC40M7btU55yVgBIyetnnEztmGQHfy5z8GgGoBEBqpTXxCSuVzi92ylZH2ZBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:42.650200Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.08280","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba63d37804018fb53be1938c24ce8cdae6403cb26d5282d5e51fb3fea45f0713","sha256:795886edf155bcb964dac0157aebf667dd1ca34ed648b89b3acca871237fb82e"],"state_sha256":"b42aa7179b5cfd7fbef25978788a6fcb60de609314d48982c68dd99c7134bcc5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pjzh30vtPlbKhNz96E7dVh/lammGBX1ZuREPYgOKCJzRwXQqUsdyMzIYkXO3tsQOwye44RG5BA+X1ARees0oBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T05:00:45.897742Z","bundle_sha256":"a3596c8fe6c8eadd2f755abb1ea91bef9ead97a9ea80f15addf4ec92cdf97e21"}}