{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:SSJVBJN4CI5XVOGOPTLANZCS2B","short_pith_number":"pith:SSJVBJN4","canonical_record":{"source":{"id":"1604.08947","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-29T19:59:44Z","cross_cats_sorted":[],"title_canon_sha256":"a13fcb14a276b313830ce7772d22853dc3504f3f6ba6bab002a782d3f2c9c901","abstract_canon_sha256":"d0d203e28e12745e894675e1bb57ecb1fe7aa2ee93dc42bef019517a69967c49"},"schema_version":"1.0"},"canonical_sha256":"949350a5bc123b7ab8ce7cd606e452d0600840c0e22b56d91d4bc7037d344b67","source":{"kind":"arxiv","id":"1604.08947","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.08947","created_at":"2026-05-18T00:35:18Z"},{"alias_kind":"arxiv_version","alias_value":"1604.08947v2","created_at":"2026-05-18T00:35:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.08947","created_at":"2026-05-18T00:35:18Z"},{"alias_kind":"pith_short_12","alias_value":"SSJVBJN4CI5X","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SSJVBJN4CI5XVOGO","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SSJVBJN4","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:SSJVBJN4CI5XVOGOPTLANZCS2B","target":"record","payload":{"canonical_record":{"source":{"id":"1604.08947","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-29T19:59:44Z","cross_cats_sorted":[],"title_canon_sha256":"a13fcb14a276b313830ce7772d22853dc3504f3f6ba6bab002a782d3f2c9c901","abstract_canon_sha256":"d0d203e28e12745e894675e1bb57ecb1fe7aa2ee93dc42bef019517a69967c49"},"schema_version":"1.0"},"canonical_sha256":"949350a5bc123b7ab8ce7cd606e452d0600840c0e22b56d91d4bc7037d344b67","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:18.670821Z","signature_b64":"+vviLB6ikqS0hIqSO9l03i91SLSeB9NJWdLwHDi+vU5acfRTHIu8322TieRJ+Y2Ujim8QlVr5tCg44Rs9TQdBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"949350a5bc123b7ab8ce7cd606e452d0600840c0e22b56d91d4bc7037d344b67","last_reissued_at":"2026-05-18T00:35:18.670425Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:18.670425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.08947","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":"2026-05-18T00:35:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RVNVN4756UMjzdB1IQeNw5YIF23YZtSbR2r1A3aqt37VZ8Cyy+cgeba19i0RfoVJNod6A5SIJtd8qfE9++q4Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T18:47:30.502583Z"},"content_sha256":"1f264c29d7f15f2fa3a39548c7be11e135c57daaf04f2b1c5b32700396d84023","schema_version":"1.0","event_id":"sha256:1f264c29d7f15f2fa3a39548c7be11e135c57daaf04f2b1c5b32700396d84023"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:SSJVBJN4CI5XVOGOPTLANZCS2B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"L\\'evy area with a drift as a renormalization limit of Markov chains on periodic graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Damien Simon, Olga Lopusanschi","submitted_at":"2016-04-29T19:59:44Z","abstract_excerpt":"A careful look at rough path topology applied to Brownian motion reveals new possible properties of the well-known L\\'evy area, in particular the presence of an intrinsic drift of this area. Using renormalization limit of Markov chains on periodic graphs, we present a construction of such a non-trivial drift and give an explicit formula for it. Several examples for which explicit computations are made are included."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.08947","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":"2026-05-18T00:35:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dYtRD8NAyfAo6Q+W+wDufANC1Ae1xcJo58dtHI/Cwfq7D5gVlIKg8ECj6Ni0AjjjRk3lak2M0AAQ4rlsioNxDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T18:47:30.502965Z"},"content_sha256":"b12fa63562f0cbfcd01c47899d06a53ef7bdce6503521c97e03f077009abc927","schema_version":"1.0","event_id":"sha256:b12fa63562f0cbfcd01c47899d06a53ef7bdce6503521c97e03f077009abc927"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SSJVBJN4CI5XVOGOPTLANZCS2B/bundle.json","state_url":"https://pith.science/pith/SSJVBJN4CI5XVOGOPTLANZCS2B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SSJVBJN4CI5XVOGOPTLANZCS2B/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":"2026-06-11T18:47:30Z","links":{"resolver":"https://pith.science/pith/SSJVBJN4CI5XVOGOPTLANZCS2B","bundle":"https://pith.science/pith/SSJVBJN4CI5XVOGOPTLANZCS2B/bundle.json","state":"https://pith.science/pith/SSJVBJN4CI5XVOGOPTLANZCS2B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SSJVBJN4CI5XVOGOPTLANZCS2B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SSJVBJN4CI5XVOGOPTLANZCS2B","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":"d0d203e28e12745e894675e1bb57ecb1fe7aa2ee93dc42bef019517a69967c49","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-29T19:59:44Z","title_canon_sha256":"a13fcb14a276b313830ce7772d22853dc3504f3f6ba6bab002a782d3f2c9c901"},"schema_version":"1.0","source":{"id":"1604.08947","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.08947","created_at":"2026-05-18T00:35:18Z"},{"alias_kind":"arxiv_version","alias_value":"1604.08947v2","created_at":"2026-05-18T00:35:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.08947","created_at":"2026-05-18T00:35:18Z"},{"alias_kind":"pith_short_12","alias_value":"SSJVBJN4CI5X","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SSJVBJN4CI5XVOGO","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SSJVBJN4","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:b12fa63562f0cbfcd01c47899d06a53ef7bdce6503521c97e03f077009abc927","target":"graph","created_at":"2026-05-18T00:35:18Z","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":"A careful look at rough path topology applied to Brownian motion reveals new possible properties of the well-known L\\'evy area, in particular the presence of an intrinsic drift of this area. Using renormalization limit of Markov chains on periodic graphs, we present a construction of such a non-trivial drift and give an explicit formula for it. Several examples for which explicit computations are made are included.","authors_text":"Damien Simon, Olga Lopusanschi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-29T19:59:44Z","title":"L\\'evy area with a drift as a renormalization limit of Markov chains on periodic graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.08947","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":"sha256:1f264c29d7f15f2fa3a39548c7be11e135c57daaf04f2b1c5b32700396d84023","target":"record","created_at":"2026-05-18T00:35:18Z","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":"d0d203e28e12745e894675e1bb57ecb1fe7aa2ee93dc42bef019517a69967c49","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-29T19:59:44Z","title_canon_sha256":"a13fcb14a276b313830ce7772d22853dc3504f3f6ba6bab002a782d3f2c9c901"},"schema_version":"1.0","source":{"id":"1604.08947","kind":"arxiv","version":2}},"canonical_sha256":"949350a5bc123b7ab8ce7cd606e452d0600840c0e22b56d91d4bc7037d344b67","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"949350a5bc123b7ab8ce7cd606e452d0600840c0e22b56d91d4bc7037d344b67","first_computed_at":"2026-05-18T00:35:18.670425Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:18.670425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+vviLB6ikqS0hIqSO9l03i91SLSeB9NJWdLwHDi+vU5acfRTHIu8322TieRJ+Y2Ujim8QlVr5tCg44Rs9TQdBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:18.670821Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.08947","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f264c29d7f15f2fa3a39548c7be11e135c57daaf04f2b1c5b32700396d84023","sha256:b12fa63562f0cbfcd01c47899d06a53ef7bdce6503521c97e03f077009abc927"],"state_sha256":"f0781ab02ea976ce6ce07d5eee5400809466e6bb26587e8862f0a2e31c883f5b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ghF547l+rQQzZiTg0WIzd97PAvZCdHOBSH+rVJ8HhJ7ygju5zwsvPv3OHETjcBtMVraFTbBrR/OZVAaX3dwlCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T18:47:30.506444Z","bundle_sha256":"4f134ce154140d92027cb4a36644f29916a73d69e11f80a1afaa44c18d5447af"}}