{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ZWH47COA3GD2QCM2V7OLQAAFWA","short_pith_number":"pith:ZWH47COA","canonical_record":{"source":{"id":"1805.07118","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2018-05-18T09:58:19Z","cross_cats_sorted":["cond-mat.stat-mech","q-bio.MN"],"title_canon_sha256":"761f67d693b46a807769645ecdcbacbdfddd658ed0eb514f37ca6955a9b02090","abstract_canon_sha256":"12f4a9fd79480546902df6ae2f01c0bfcbc7a7cb68f05586d78c4d0054d57456"},"schema_version":"1.0"},"canonical_sha256":"cd8fcf89c0d987a8099aafdcb80005b02b17a942158c1e32ba5a9d3f1f78921b","source":{"kind":"arxiv","id":"1805.07118","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.07118","created_at":"2026-05-18T00:12:13Z"},{"alias_kind":"arxiv_version","alias_value":"1805.07118v1","created_at":"2026-05-18T00:12:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.07118","created_at":"2026-05-18T00:12:13Z"},{"alias_kind":"pith_short_12","alias_value":"ZWH47COA3GD2","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZWH47COA3GD2QCM2","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZWH47COA","created_at":"2026-05-18T12:33:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ZWH47COA3GD2QCM2V7OLQAAFWA","target":"record","payload":{"canonical_record":{"source":{"id":"1805.07118","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2018-05-18T09:58:19Z","cross_cats_sorted":["cond-mat.stat-mech","q-bio.MN"],"title_canon_sha256":"761f67d693b46a807769645ecdcbacbdfddd658ed0eb514f37ca6955a9b02090","abstract_canon_sha256":"12f4a9fd79480546902df6ae2f01c0bfcbc7a7cb68f05586d78c4d0054d57456"},"schema_version":"1.0"},"canonical_sha256":"cd8fcf89c0d987a8099aafdcb80005b02b17a942158c1e32ba5a9d3f1f78921b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:13.527404Z","signature_b64":"5usYwXJ1KfHqLR6JWhgctcP1qbfQFuNkUx1C+mdAFzbieAUN5DxwmFfG2QzwJ73Z792aXsRYua//TWUIKxA2CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd8fcf89c0d987a8099aafdcb80005b02b17a942158c1e32ba5a9d3f1f78921b","last_reissued_at":"2026-05-18T00:12:13.525127Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:13.525127Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.07118","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":"2026-05-18T00:12:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+Umem/9gJMHkgl5+2liVPgM6HujOiN3q0T348ixkjfw9pFp5zriAbmFrBmubC61aXGZCTiO3mjZcdxMCwBc5Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T11:43:46.830964Z"},"content_sha256":"aaaf566a943c4367fa4a08fbe236f2d94761272e2922b846c5761e72a71c32d1","schema_version":"1.0","event_id":"sha256:aaaf566a943c4367fa4a08fbe236f2d94761272e2922b846c5761e72a71c32d1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ZWH47COA3GD2QCM2V7OLQAAFWA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Marginal process framework: A model reduction tool for Markov jump processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","q-bio.MN"],"primary_cat":"q-bio.QM","authors_text":"Heinz Koeppl, Leo Bronstein","submitted_at":"2018-05-18T09:58:19Z","abstract_excerpt":"Markov jump process models have many applications across science. Often, these models are defined on a state-space of product form and only one of the components of the process is of direct interest. In this paper, we extend the marginal process framework, which provides a marginal description of the component of interest, to the case of fully coupled processes. We use entropic matching to obtain a finite-dimensional approximation of the filtering equation, which governs the transition rates of the marginal process. The resulting equations can be seen as a combination of two projection operati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07118","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":"2026-05-18T00:12:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WPU14r5DrlSXMtnaqUta/tJXvtCsCALN0O8/Odh6/lNUoR1tjnJYKWOCt8CXisk/ka3S4vzrOij0QvW46QI0AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T11:43:46.831574Z"},"content_sha256":"eef11dfe15d570825421bb98172b1f2c0d6e12fb3d4a551ebc8195bbc220bd10","schema_version":"1.0","event_id":"sha256:eef11dfe15d570825421bb98172b1f2c0d6e12fb3d4a551ebc8195bbc220bd10"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZWH47COA3GD2QCM2V7OLQAAFWA/bundle.json","state_url":"https://pith.science/pith/ZWH47COA3GD2QCM2V7OLQAAFWA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZWH47COA3GD2QCM2V7OLQAAFWA/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":"2026-06-11T11:43:46Z","links":{"resolver":"https://pith.science/pith/ZWH47COA3GD2QCM2V7OLQAAFWA","bundle":"https://pith.science/pith/ZWH47COA3GD2QCM2V7OLQAAFWA/bundle.json","state":"https://pith.science/pith/ZWH47COA3GD2QCM2V7OLQAAFWA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZWH47COA3GD2QCM2V7OLQAAFWA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ZWH47COA3GD2QCM2V7OLQAAFWA","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":"12f4a9fd79480546902df6ae2f01c0bfcbc7a7cb68f05586d78c4d0054d57456","cross_cats_sorted":["cond-mat.stat-mech","q-bio.MN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2018-05-18T09:58:19Z","title_canon_sha256":"761f67d693b46a807769645ecdcbacbdfddd658ed0eb514f37ca6955a9b02090"},"schema_version":"1.0","source":{"id":"1805.07118","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.07118","created_at":"2026-05-18T00:12:13Z"},{"alias_kind":"arxiv_version","alias_value":"1805.07118v1","created_at":"2026-05-18T00:12:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.07118","created_at":"2026-05-18T00:12:13Z"},{"alias_kind":"pith_short_12","alias_value":"ZWH47COA3GD2","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZWH47COA3GD2QCM2","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZWH47COA","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:eef11dfe15d570825421bb98172b1f2c0d6e12fb3d4a551ebc8195bbc220bd10","target":"graph","created_at":"2026-05-18T00:12:13Z","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":"Markov jump process models have many applications across science. Often, these models are defined on a state-space of product form and only one of the components of the process is of direct interest. In this paper, we extend the marginal process framework, which provides a marginal description of the component of interest, to the case of fully coupled processes. We use entropic matching to obtain a finite-dimensional approximation of the filtering equation, which governs the transition rates of the marginal process. The resulting equations can be seen as a combination of two projection operati","authors_text":"Heinz Koeppl, Leo Bronstein","cross_cats":["cond-mat.stat-mech","q-bio.MN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2018-05-18T09:58:19Z","title":"Marginal process framework: A model reduction tool for Markov jump processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07118","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:aaaf566a943c4367fa4a08fbe236f2d94761272e2922b846c5761e72a71c32d1","target":"record","created_at":"2026-05-18T00:12:13Z","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":"12f4a9fd79480546902df6ae2f01c0bfcbc7a7cb68f05586d78c4d0054d57456","cross_cats_sorted":["cond-mat.stat-mech","q-bio.MN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2018-05-18T09:58:19Z","title_canon_sha256":"761f67d693b46a807769645ecdcbacbdfddd658ed0eb514f37ca6955a9b02090"},"schema_version":"1.0","source":{"id":"1805.07118","kind":"arxiv","version":1}},"canonical_sha256":"cd8fcf89c0d987a8099aafdcb80005b02b17a942158c1e32ba5a9d3f1f78921b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd8fcf89c0d987a8099aafdcb80005b02b17a942158c1e32ba5a9d3f1f78921b","first_computed_at":"2026-05-18T00:12:13.525127Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:13.525127Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5usYwXJ1KfHqLR6JWhgctcP1qbfQFuNkUx1C+mdAFzbieAUN5DxwmFfG2QzwJ73Z792aXsRYua//TWUIKxA2CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:13.527404Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.07118","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aaaf566a943c4367fa4a08fbe236f2d94761272e2922b846c5761e72a71c32d1","sha256:eef11dfe15d570825421bb98172b1f2c0d6e12fb3d4a551ebc8195bbc220bd10"],"state_sha256":"5fc016bb5d5ca2ae8d9e20671b329d8b916f5f903f73de566bfd0e3b3f577257"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WnVRzgpfHGn2c8nkNrQex4nnb/FropFIbqBQZ0cD72F4iqlWLhUN/kj/JoiwBOoCdmYHnD1UADNz9groETngBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T11:43:46.835127Z","bundle_sha256":"c0b5d8d0da2f2f09a4bf85572d7dd57cc527132b4a23aca40ccfae14a887241d"}}