{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:IG3ORJN6BVYIOOFKCNIYAUODCR","short_pith_number":"pith:IG3ORJN6","canonical_record":{"source":{"id":"1202.2882","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-13T22:04:52Z","cross_cats_sorted":[],"title_canon_sha256":"b176939622d5c7c92cb13560b55c2e80e1a004eb60c89393ad3ad9dbebbfd8d2","abstract_canon_sha256":"76c8f665fee125cfd37de5d4e5426746770e6c7b1b26482d554fbf34ffdfb823"},"schema_version":"1.0"},"canonical_sha256":"41b6e8a5be0d708738aa13518051c3145124e835f6f668d25d3d825fb3fed3b6","source":{"kind":"arxiv","id":"1202.2882","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2882","created_at":"2026-05-18T03:25:33Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2882v4","created_at":"2026-05-18T03:25:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2882","created_at":"2026-05-18T03:25:33Z"},{"alias_kind":"pith_short_12","alias_value":"IG3ORJN6BVYI","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IG3ORJN6BVYIOOFK","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IG3ORJN6","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:IG3ORJN6BVYIOOFKCNIYAUODCR","target":"record","payload":{"canonical_record":{"source":{"id":"1202.2882","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-13T22:04:52Z","cross_cats_sorted":[],"title_canon_sha256":"b176939622d5c7c92cb13560b55c2e80e1a004eb60c89393ad3ad9dbebbfd8d2","abstract_canon_sha256":"76c8f665fee125cfd37de5d4e5426746770e6c7b1b26482d554fbf34ffdfb823"},"schema_version":"1.0"},"canonical_sha256":"41b6e8a5be0d708738aa13518051c3145124e835f6f668d25d3d825fb3fed3b6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:33.505206Z","signature_b64":"M/YpVlf2HHIbKiY9GbSihxofooGKpauD+1XKQ4owSWvlGJ6kWtRH/OVIjUnnsOBe6Ss/2VXfYSKtKTYjAHxYAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"41b6e8a5be0d708738aa13518051c3145124e835f6f668d25d3d825fb3fed3b6","last_reissued_at":"2026-05-18T03:25:33.504714Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:33.504714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.2882","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:25:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TLAdC2fD3l0YWZue5NdQ0pf5fOTllIMzCY0AiMZx2Xa+kdEsPrD81EdanAMpelWSJe2xlUHJXceGrqW9xJ3EDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T14:02:16.604203Z"},"content_sha256":"a8fcaa4e86eaebbfc833d9c53899555d8c23dc1df67b0dd650793d7649f42576","schema_version":"1.0","event_id":"sha256:a8fcaa4e86eaebbfc833d9c53899555d8c23dc1df67b0dd650793d7649f42576"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:IG3ORJN6BVYIOOFKCNIYAUODCR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the characterisation of honest times that avoid all stopping times","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Constantinos Kardaras","submitted_at":"2012-02-13T22:04:52Z","abstract_excerpt":"We present a short and self-contained proof of the following result: a random time is an honest time that avoids all stopping times if and only if it coincides with the (last) time of maximum of a nonnegative local martingale with zero terminal value and no jumps while at its running supremum, where the latter running supremum process is continuous. Illustrative examples involving local martingales with discontinuous paths are provided."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2882","kind":"arxiv","version":4},"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":"2026-05-18T03:25:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F7HtAnPtw3qsXtAVyGN1kIj6oEQomcqB77Nxqipr34taRWzZpwfhuLDKHl2+7NYO+K+zxcIQaOwNUCJmxCW2Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T14:02:16.604572Z"},"content_sha256":"cbc44dfbf20a1c784488b7c5629a9f116cce827bea3b2492af28f4b3c00ac735","schema_version":"1.0","event_id":"sha256:cbc44dfbf20a1c784488b7c5629a9f116cce827bea3b2492af28f4b3c00ac735"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IG3ORJN6BVYIOOFKCNIYAUODCR/bundle.json","state_url":"https://pith.science/pith/IG3ORJN6BVYIOOFKCNIYAUODCR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IG3ORJN6BVYIOOFKCNIYAUODCR/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":"2026-05-30T14:02:16Z","links":{"resolver":"https://pith.science/pith/IG3ORJN6BVYIOOFKCNIYAUODCR","bundle":"https://pith.science/pith/IG3ORJN6BVYIOOFKCNIYAUODCR/bundle.json","state":"https://pith.science/pith/IG3ORJN6BVYIOOFKCNIYAUODCR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IG3ORJN6BVYIOOFKCNIYAUODCR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:IG3ORJN6BVYIOOFKCNIYAUODCR","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":"76c8f665fee125cfd37de5d4e5426746770e6c7b1b26482d554fbf34ffdfb823","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-13T22:04:52Z","title_canon_sha256":"b176939622d5c7c92cb13560b55c2e80e1a004eb60c89393ad3ad9dbebbfd8d2"},"schema_version":"1.0","source":{"id":"1202.2882","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2882","created_at":"2026-05-18T03:25:33Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2882v4","created_at":"2026-05-18T03:25:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2882","created_at":"2026-05-18T03:25:33Z"},{"alias_kind":"pith_short_12","alias_value":"IG3ORJN6BVYI","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IG3ORJN6BVYIOOFK","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IG3ORJN6","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:cbc44dfbf20a1c784488b7c5629a9f116cce827bea3b2492af28f4b3c00ac735","target":"graph","created_at":"2026-05-18T03:25:33Z","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":"We present a short and self-contained proof of the following result: a random time is an honest time that avoids all stopping times if and only if it coincides with the (last) time of maximum of a nonnegative local martingale with zero terminal value and no jumps while at its running supremum, where the latter running supremum process is continuous. Illustrative examples involving local martingales with discontinuous paths are provided.","authors_text":"Constantinos Kardaras","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-13T22:04:52Z","title":"On the characterisation of honest times that avoid all stopping times"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2882","kind":"arxiv","version":4},"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:a8fcaa4e86eaebbfc833d9c53899555d8c23dc1df67b0dd650793d7649f42576","target":"record","created_at":"2026-05-18T03:25:33Z","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":"76c8f665fee125cfd37de5d4e5426746770e6c7b1b26482d554fbf34ffdfb823","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-13T22:04:52Z","title_canon_sha256":"b176939622d5c7c92cb13560b55c2e80e1a004eb60c89393ad3ad9dbebbfd8d2"},"schema_version":"1.0","source":{"id":"1202.2882","kind":"arxiv","version":4}},"canonical_sha256":"41b6e8a5be0d708738aa13518051c3145124e835f6f668d25d3d825fb3fed3b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41b6e8a5be0d708738aa13518051c3145124e835f6f668d25d3d825fb3fed3b6","first_computed_at":"2026-05-18T03:25:33.504714Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:33.504714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M/YpVlf2HHIbKiY9GbSihxofooGKpauD+1XKQ4owSWvlGJ6kWtRH/OVIjUnnsOBe6Ss/2VXfYSKtKTYjAHxYAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:33.505206Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.2882","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a8fcaa4e86eaebbfc833d9c53899555d8c23dc1df67b0dd650793d7649f42576","sha256:cbc44dfbf20a1c784488b7c5629a9f116cce827bea3b2492af28f4b3c00ac735"],"state_sha256":"95686df90441714939e55b7d7208e8397a5fdfd68c63d359bb6b0a5a987f4b2f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MmzARe66BfAUv4SPMKVS4wCMwDHuNNPNreo0FsHAqwu8bP1ZQKMVWbEDVlA6K2d6UlDyv3Z4p8zA/s/EOKN+DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T14:02:16.606687Z","bundle_sha256":"457e94ca885cc7256c8f26dff34e9507004fb7ac978c6375d93b7e3aa83fbf62"}}