{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:4HPMZ2PR26FXXNKQYMBPGNK47H","short_pith_number":"pith:4HPMZ2PR","canonical_record":{"source":{"id":"1609.00935","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-04T13:49:29Z","cross_cats_sorted":[],"title_canon_sha256":"d7bd64b0d4518def4e182f179b0892bc65c014e003aad671fca0e0d2dd7ca690","abstract_canon_sha256":"28c98dcfb135159e66246503c3c5658272d3821517282a8c14c582e017351019"},"schema_version":"1.0"},"canonical_sha256":"e1decce9f1d78b7bb550c302f3355cf9cd25cc7638a4f28cd872278797ebe96c","source":{"kind":"arxiv","id":"1609.00935","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.00935","created_at":"2026-05-18T00:43:09Z"},{"alias_kind":"arxiv_version","alias_value":"1609.00935v2","created_at":"2026-05-18T00:43:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.00935","created_at":"2026-05-18T00:43:09Z"},{"alias_kind":"pith_short_12","alias_value":"4HPMZ2PR26FX","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4HPMZ2PR26FXXNKQ","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4HPMZ2PR","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:4HPMZ2PR26FXXNKQYMBPGNK47H","target":"record","payload":{"canonical_record":{"source":{"id":"1609.00935","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-04T13:49:29Z","cross_cats_sorted":[],"title_canon_sha256":"d7bd64b0d4518def4e182f179b0892bc65c014e003aad671fca0e0d2dd7ca690","abstract_canon_sha256":"28c98dcfb135159e66246503c3c5658272d3821517282a8c14c582e017351019"},"schema_version":"1.0"},"canonical_sha256":"e1decce9f1d78b7bb550c302f3355cf9cd25cc7638a4f28cd872278797ebe96c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:09.198170Z","signature_b64":"Ppk2pumpVWvRliynqwv13rW3w38HwpXmO7dA+VAX8g3j1H1pieLTw/XwYsJYVjuJJJKWjQgga/Lkb2JvQMd+Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1decce9f1d78b7bb550c302f3355cf9cd25cc7638a4f28cd872278797ebe96c","last_reissued_at":"2026-05-18T00:43:09.197584Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:09.197584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.00935","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":"2026-05-18T00:43:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PCvl2v8EcJm6fEPv6x8FVzSbyF6SrfLC7AdloxIO2Vx3i7NTErszIEzu+i1WeTq99nDfIosYFh4FWZ3Z/alTBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T00:31:15.015234Z"},"content_sha256":"bff816125f315c9f0512c8faaa7d9fa808c62c27ae998c95a95fd4659dd46cbc","schema_version":"1.0","event_id":"sha256:bff816125f315c9f0512c8faaa7d9fa808c62c27ae998c95a95fd4659dd46cbc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:4HPMZ2PR26FXXNKQYMBPGNK47H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Strict local martingales: examples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Xue-Mei Li","submitted_at":"2016-09-04T13:49:29Z","abstract_excerpt":"We show that a continuous local martingale is a strict local martingale if its supremum process is not in $ L_\\alpha$ for a positive number $\\alpha $ smaller than $1$. Using this we construct a family of strict local martingales."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00935","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":"2026-05-18T00:43:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lzFvIK4dWMtWSRuoMaXCjZnscFKviXr7nF0jiEMNQ5BddKqr3zefvQxIHQq+J2NcnGeHgMFu+tC7J4/7auhLDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T00:31:15.015702Z"},"content_sha256":"e9835ea4845979b8769ca8683615a3a4c4bcbc9307c9f67cdbe92b5c85b29780","schema_version":"1.0","event_id":"sha256:e9835ea4845979b8769ca8683615a3a4c4bcbc9307c9f67cdbe92b5c85b29780"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4HPMZ2PR26FXXNKQYMBPGNK47H/bundle.json","state_url":"https://pith.science/pith/4HPMZ2PR26FXXNKQYMBPGNK47H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4HPMZ2PR26FXXNKQYMBPGNK47H/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":"2026-05-27T00:31:15Z","links":{"resolver":"https://pith.science/pith/4HPMZ2PR26FXXNKQYMBPGNK47H","bundle":"https://pith.science/pith/4HPMZ2PR26FXXNKQYMBPGNK47H/bundle.json","state":"https://pith.science/pith/4HPMZ2PR26FXXNKQYMBPGNK47H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4HPMZ2PR26FXXNKQYMBPGNK47H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4HPMZ2PR26FXXNKQYMBPGNK47H","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":"28c98dcfb135159e66246503c3c5658272d3821517282a8c14c582e017351019","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-04T13:49:29Z","title_canon_sha256":"d7bd64b0d4518def4e182f179b0892bc65c014e003aad671fca0e0d2dd7ca690"},"schema_version":"1.0","source":{"id":"1609.00935","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.00935","created_at":"2026-05-18T00:43:09Z"},{"alias_kind":"arxiv_version","alias_value":"1609.00935v2","created_at":"2026-05-18T00:43:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.00935","created_at":"2026-05-18T00:43:09Z"},{"alias_kind":"pith_short_12","alias_value":"4HPMZ2PR26FX","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4HPMZ2PR26FXXNKQ","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4HPMZ2PR","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:e9835ea4845979b8769ca8683615a3a4c4bcbc9307c9f67cdbe92b5c85b29780","target":"graph","created_at":"2026-05-18T00:43:09Z","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 show that a continuous local martingale is a strict local martingale if its supremum process is not in $ L_\\alpha$ for a positive number $\\alpha $ smaller than $1$. Using this we construct a family of strict local martingales.","authors_text":"Xue-Mei Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-04T13:49:29Z","title":"Strict local martingales: examples"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00935","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:bff816125f315c9f0512c8faaa7d9fa808c62c27ae998c95a95fd4659dd46cbc","target":"record","created_at":"2026-05-18T00:43:09Z","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":"28c98dcfb135159e66246503c3c5658272d3821517282a8c14c582e017351019","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-04T13:49:29Z","title_canon_sha256":"d7bd64b0d4518def4e182f179b0892bc65c014e003aad671fca0e0d2dd7ca690"},"schema_version":"1.0","source":{"id":"1609.00935","kind":"arxiv","version":2}},"canonical_sha256":"e1decce9f1d78b7bb550c302f3355cf9cd25cc7638a4f28cd872278797ebe96c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1decce9f1d78b7bb550c302f3355cf9cd25cc7638a4f28cd872278797ebe96c","first_computed_at":"2026-05-18T00:43:09.197584Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:09.197584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ppk2pumpVWvRliynqwv13rW3w38HwpXmO7dA+VAX8g3j1H1pieLTw/XwYsJYVjuJJJKWjQgga/Lkb2JvQMd+Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:09.198170Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.00935","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bff816125f315c9f0512c8faaa7d9fa808c62c27ae998c95a95fd4659dd46cbc","sha256:e9835ea4845979b8769ca8683615a3a4c4bcbc9307c9f67cdbe92b5c85b29780"],"state_sha256":"1ea5b9bf9d02d904db5b5e487d2c28bbbb06226066b24d339e013dc9dcb48dd5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d+0xt37GmJJjKN1/bedprzx9NxR6lL2KCiuN/35qB7jj1vnHvtQ+pfFFgOLOmwpuBMprabO3BdL8AWV9XmJoAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T00:31:15.018247Z","bundle_sha256":"7e6d1b83578f3e3c4958b1dd1e834a0af7b667dbc56866ff7597553aac23c4de"}}