{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:ZCGORYOOCXN7XMPTX3X7PGD25A","short_pith_number":"pith:ZCGORYOO","canonical_record":{"source":{"id":"1906.09813","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-06-24T09:39:00Z","cross_cats_sorted":[],"title_canon_sha256":"514a4c1d198241adf1d7b68661e3c79d037cfaf5658ecfe05154083af8f22422","abstract_canon_sha256":"f309bde10f7790177f5b3c2b4fa6643151ccb6dbdb15861ed979f68c26702af6"},"schema_version":"1.0"},"canonical_sha256":"c88ce8e1ce15dbfbb1f3beeff7987ae81293d13f3e1041d74aa740f2495e0507","source":{"kind":"arxiv","id":"1906.09813","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.09813","created_at":"2026-05-17T23:42:36Z"},{"alias_kind":"arxiv_version","alias_value":"1906.09813v1","created_at":"2026-05-17T23:42:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.09813","created_at":"2026-05-17T23:42:36Z"},{"alias_kind":"pith_short_12","alias_value":"ZCGORYOOCXN7","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"ZCGORYOOCXN7XMPT","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"ZCGORYOO","created_at":"2026-05-18T12:33:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:ZCGORYOOCXN7XMPTX3X7PGD25A","target":"record","payload":{"canonical_record":{"source":{"id":"1906.09813","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-06-24T09:39:00Z","cross_cats_sorted":[],"title_canon_sha256":"514a4c1d198241adf1d7b68661e3c79d037cfaf5658ecfe05154083af8f22422","abstract_canon_sha256":"f309bde10f7790177f5b3c2b4fa6643151ccb6dbdb15861ed979f68c26702af6"},"schema_version":"1.0"},"canonical_sha256":"c88ce8e1ce15dbfbb1f3beeff7987ae81293d13f3e1041d74aa740f2495e0507","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:36.597269Z","signature_b64":"PFi5lBFKsXnQ9xD3FIBx3hnHb6V//qnYbludoQjXJxlzo24qvKzT9GKsRBRELl7XGXEVyQ6hEmE5XuOKXK7eAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c88ce8e1ce15dbfbb1f3beeff7987ae81293d13f3e1041d74aa740f2495e0507","last_reissued_at":"2026-05-17T23:42:36.596532Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:36.596532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.09813","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:42:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/4/IHdLPB47AlkA9Z1qHj7bOLsmVPLDVIBY5VpwwttwlhoA5SMDCI7pnw+6RGstmCaQJmZMChhjP8kEJ/wvyCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T13:08:10.948915Z"},"content_sha256":"70bcde20c5a77bf7cd9d0c9e5ec03e8859b2e71485851f932af26f506fb71d9e","schema_version":"1.0","event_id":"sha256:70bcde20c5a77bf7cd9d0c9e5ec03e8859b2e71485851f932af26f506fb71d9e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:ZCGORYOOCXN7XMPTX3X7PGD25A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Simulation of Conditioned Diffusions on the Flat Torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anton Mallasto, Mathias H{\\o}jgaard Jensen, Stefan Sommer","submitted_at":"2019-06-24T09:39:00Z","abstract_excerpt":"Diffusion processes are fundamental in modelling stochastic dynamics in natural sciences. Recently, simulating such processes on complicated geometries has found applications for example in biology, where toroidal data arises naturally when studying the backbone of protein sequences, creating a demand for efficient sampling methods. In this paper, we propose a method for simulating diffusions on the flat torus, conditioned on hitting a terminal point after a fixed time, by considering a diffusion process in R 2 which we project onto the torus. We contribute a convergence result for this diffus"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.09813","kind":"arxiv","version":1},"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":"2026-05-17T23:42:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4Go2eSCemBbIb23G1euth/1k4p8a75PSzCAiEkAgzyXbUKt3WEHW14+08tyZwFC90U+kld2uV4ckA1MLn4UeAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T13:08:10.949265Z"},"content_sha256":"cd9ae42d8c336b702f0ffa5f0ce8e69160c438afa377b4ae1890a346be2d5162","schema_version":"1.0","event_id":"sha256:cd9ae42d8c336b702f0ffa5f0ce8e69160c438afa377b4ae1890a346be2d5162"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZCGORYOOCXN7XMPTX3X7PGD25A/bundle.json","state_url":"https://pith.science/pith/ZCGORYOOCXN7XMPTX3X7PGD25A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZCGORYOOCXN7XMPTX3X7PGD25A/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":"2026-05-22T13:08:10Z","links":{"resolver":"https://pith.science/pith/ZCGORYOOCXN7XMPTX3X7PGD25A","bundle":"https://pith.science/pith/ZCGORYOOCXN7XMPTX3X7PGD25A/bundle.json","state":"https://pith.science/pith/ZCGORYOOCXN7XMPTX3X7PGD25A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZCGORYOOCXN7XMPTX3X7PGD25A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ZCGORYOOCXN7XMPTX3X7PGD25A","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":"f309bde10f7790177f5b3c2b4fa6643151ccb6dbdb15861ed979f68c26702af6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-06-24T09:39:00Z","title_canon_sha256":"514a4c1d198241adf1d7b68661e3c79d037cfaf5658ecfe05154083af8f22422"},"schema_version":"1.0","source":{"id":"1906.09813","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.09813","created_at":"2026-05-17T23:42:36Z"},{"alias_kind":"arxiv_version","alias_value":"1906.09813v1","created_at":"2026-05-17T23:42:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.09813","created_at":"2026-05-17T23:42:36Z"},{"alias_kind":"pith_short_12","alias_value":"ZCGORYOOCXN7","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"ZCGORYOOCXN7XMPT","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"ZCGORYOO","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:cd9ae42d8c336b702f0ffa5f0ce8e69160c438afa377b4ae1890a346be2d5162","target":"graph","created_at":"2026-05-17T23:42:36Z","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":"Diffusion processes are fundamental in modelling stochastic dynamics in natural sciences. Recently, simulating such processes on complicated geometries has found applications for example in biology, where toroidal data arises naturally when studying the backbone of protein sequences, creating a demand for efficient sampling methods. In this paper, we propose a method for simulating diffusions on the flat torus, conditioned on hitting a terminal point after a fixed time, by considering a diffusion process in R 2 which we project onto the torus. We contribute a convergence result for this diffus","authors_text":"Anton Mallasto, Mathias H{\\o}jgaard Jensen, Stefan Sommer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-06-24T09:39:00Z","title":"Simulation of Conditioned Diffusions on the Flat Torus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.09813","kind":"arxiv","version":1},"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":"sha256:70bcde20c5a77bf7cd9d0c9e5ec03e8859b2e71485851f932af26f506fb71d9e","target":"record","created_at":"2026-05-17T23:42:36Z","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":"f309bde10f7790177f5b3c2b4fa6643151ccb6dbdb15861ed979f68c26702af6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-06-24T09:39:00Z","title_canon_sha256":"514a4c1d198241adf1d7b68661e3c79d037cfaf5658ecfe05154083af8f22422"},"schema_version":"1.0","source":{"id":"1906.09813","kind":"arxiv","version":1}},"canonical_sha256":"c88ce8e1ce15dbfbb1f3beeff7987ae81293d13f3e1041d74aa740f2495e0507","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c88ce8e1ce15dbfbb1f3beeff7987ae81293d13f3e1041d74aa740f2495e0507","first_computed_at":"2026-05-17T23:42:36.596532Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:36.596532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PFi5lBFKsXnQ9xD3FIBx3hnHb6V//qnYbludoQjXJxlzo24qvKzT9GKsRBRELl7XGXEVyQ6hEmE5XuOKXK7eAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:36.597269Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.09813","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:70bcde20c5a77bf7cd9d0c9e5ec03e8859b2e71485851f932af26f506fb71d9e","sha256:cd9ae42d8c336b702f0ffa5f0ce8e69160c438afa377b4ae1890a346be2d5162"],"state_sha256":"ba15099a49fea9765bdf3e1661f62e2ed9d5a5d217ed40b3fe40d73cfe62fcfc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tILu4Fs+EAYC7zFA1V6LlYWc1AlVVC8/JDmCh9CLd3cKRmEVAvqdexC3bycCzTMzS/SvGJV8yZl93AGFdeC2AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T13:08:10.952024Z","bundle_sha256":"7be61700a89e9863d5fe57361939b16f054554c5a1077665de6e6604137541cc"}}