{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:74Z3NV6E23PJF76JECDGFZZUQQ","short_pith_number":"pith:74Z3NV6E","canonical_record":{"source":{"id":"2102.11708","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2021-02-23T14:22:22Z","cross_cats_sorted":["cond-mat.stat-mech","cs.SI","physics.soc-ph"],"title_canon_sha256":"c14cbb7a46fb74d96292e94c60a06659ab8cfff47939a71d42324e22379a240f","abstract_canon_sha256":"4617f5c0d4a0e5855cd4d98313e20916bb74ecba02a5c1a5e9c998d48c2f09cf"},"schema_version":"1.0"},"canonical_sha256":"ff33b6d7c4d6de92ffc9208662e73484391ee5e58e59b9d22988a646f352a316","source":{"kind":"arxiv","id":"2102.11708","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.11708","created_at":"2026-07-05T02:17:53Z"},{"alias_kind":"arxiv_version","alias_value":"2102.11708v1","created_at":"2026-07-05T02:17:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.11708","created_at":"2026-07-05T02:17:53Z"},{"alias_kind":"pith_short_12","alias_value":"74Z3NV6E23PJ","created_at":"2026-07-05T02:17:53Z"},{"alias_kind":"pith_short_16","alias_value":"74Z3NV6E23PJF76J","created_at":"2026-07-05T02:17:53Z"},{"alias_kind":"pith_short_8","alias_value":"74Z3NV6E","created_at":"2026-07-05T02:17:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:74Z3NV6E23PJF76JECDGFZZUQQ","target":"record","payload":{"canonical_record":{"source":{"id":"2102.11708","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2021-02-23T14:22:22Z","cross_cats_sorted":["cond-mat.stat-mech","cs.SI","physics.soc-ph"],"title_canon_sha256":"c14cbb7a46fb74d96292e94c60a06659ab8cfff47939a71d42324e22379a240f","abstract_canon_sha256":"4617f5c0d4a0e5855cd4d98313e20916bb74ecba02a5c1a5e9c998d48c2f09cf"},"schema_version":"1.0"},"canonical_sha256":"ff33b6d7c4d6de92ffc9208662e73484391ee5e58e59b9d22988a646f352a316","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:17:53.618738Z","signature_b64":"nDNRWoncXhIBWF0xzjZ85zD31QTGVakRbk4rWtRdF7eGE5+w1vM3YgeS1/ykaoxxclZ8/GAFoYSupyzVwmYlAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff33b6d7c4d6de92ffc9208662e73484391ee5e58e59b9d22988a646f352a316","last_reissued_at":"2026-07-05T02:17:53.618242Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:17:53.618242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2102.11708","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":"2026-07-05T02:17:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hlLmZDNL9VJFg8f+EWsSyAYXm5/hX6a2qINqJj7ZcPEyc2zOXCAnc2Rp3mj5IETNWkvNBlFHNXDr3Oizftx2CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T17:40:31.345879Z"},"content_sha256":"4f37c1e93d564bf901bee68b836037b71c071967ee6f444d6a9f50aa7c9d5576","schema_version":"1.0","event_id":"sha256:4f37c1e93d564bf901bee68b836037b71c071967ee6f444d6a9f50aa7c9d5576"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:74Z3NV6E23PJF76JECDGFZZUQQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exact epidemic models from a tensor product formulation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cs.SI","physics.soc-ph"],"primary_cat":"q-bio.PE","authors_text":"Wout Merbis","submitted_at":"2021-02-23T14:22:22Z","abstract_excerpt":"A general framework for obtaining exact transition rate matrices for stochastic systems on networks is presented and applied to many well-known compartmental models of epidemiology. The state of the population is described as a vector in the tensor product space of $N$ individual probability vector spaces, whose dimension equals the number of compartments of the epidemiological model $n_c$. The transition rate matrix for the $n_c^N$-dimensional Markov chain is obtained by taking suitable linear combinations of tensor products of $n_c$-dimensional matrices. The resulting transition rate matrix "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.11708","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2102.11708/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T02:17:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yft3JEONy4rd/vOnZvSt+qx8HM5FPTugO0kNO2sui/mty4sdZFmkCaS5PzxAnVhOHQDieLlRQimPa1OQneQdAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T17:40:31.350516Z"},"content_sha256":"1c29db447ff8a6874b9ed6808c03d0fc7ddc6561cdeecd1463272e280ad7609a","schema_version":"1.0","event_id":"sha256:1c29db447ff8a6874b9ed6808c03d0fc7ddc6561cdeecd1463272e280ad7609a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/74Z3NV6E23PJF76JECDGFZZUQQ/bundle.json","state_url":"https://pith.science/pith/74Z3NV6E23PJF76JECDGFZZUQQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/74Z3NV6E23PJF76JECDGFZZUQQ/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":"2026-08-13T17:40:31Z","links":{"resolver":"https://pith.science/pith/74Z3NV6E23PJF76JECDGFZZUQQ","bundle":"https://pith.science/pith/74Z3NV6E23PJF76JECDGFZZUQQ/bundle.json","state":"https://pith.science/pith/74Z3NV6E23PJF76JECDGFZZUQQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/74Z3NV6E23PJF76JECDGFZZUQQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:74Z3NV6E23PJF76JECDGFZZUQQ","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":"4617f5c0d4a0e5855cd4d98313e20916bb74ecba02a5c1a5e9c998d48c2f09cf","cross_cats_sorted":["cond-mat.stat-mech","cs.SI","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2021-02-23T14:22:22Z","title_canon_sha256":"c14cbb7a46fb74d96292e94c60a06659ab8cfff47939a71d42324e22379a240f"},"schema_version":"1.0","source":{"id":"2102.11708","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.11708","created_at":"2026-07-05T02:17:53Z"},{"alias_kind":"arxiv_version","alias_value":"2102.11708v1","created_at":"2026-07-05T02:17:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.11708","created_at":"2026-07-05T02:17:53Z"},{"alias_kind":"pith_short_12","alias_value":"74Z3NV6E23PJ","created_at":"2026-07-05T02:17:53Z"},{"alias_kind":"pith_short_16","alias_value":"74Z3NV6E23PJF76J","created_at":"2026-07-05T02:17:53Z"},{"alias_kind":"pith_short_8","alias_value":"74Z3NV6E","created_at":"2026-07-05T02:17:53Z"}],"graph_snapshots":[{"event_id":"sha256:1c29db447ff8a6874b9ed6808c03d0fc7ddc6561cdeecd1463272e280ad7609a","target":"graph","created_at":"2026-07-05T02:17:53Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2102.11708/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A general framework for obtaining exact transition rate matrices for stochastic systems on networks is presented and applied to many well-known compartmental models of epidemiology. The state of the population is described as a vector in the tensor product space of $N$ individual probability vector spaces, whose dimension equals the number of compartments of the epidemiological model $n_c$. The transition rate matrix for the $n_c^N$-dimensional Markov chain is obtained by taking suitable linear combinations of tensor products of $n_c$-dimensional matrices. The resulting transition rate matrix ","authors_text":"Wout Merbis","cross_cats":["cond-mat.stat-mech","cs.SI","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2021-02-23T14:22:22Z","title":"Exact epidemic models from a tensor product formulation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.11708","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":"sha256:4f37c1e93d564bf901bee68b836037b71c071967ee6f444d6a9f50aa7c9d5576","target":"record","created_at":"2026-07-05T02:17:53Z","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":"4617f5c0d4a0e5855cd4d98313e20916bb74ecba02a5c1a5e9c998d48c2f09cf","cross_cats_sorted":["cond-mat.stat-mech","cs.SI","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2021-02-23T14:22:22Z","title_canon_sha256":"c14cbb7a46fb74d96292e94c60a06659ab8cfff47939a71d42324e22379a240f"},"schema_version":"1.0","source":{"id":"2102.11708","kind":"arxiv","version":1}},"canonical_sha256":"ff33b6d7c4d6de92ffc9208662e73484391ee5e58e59b9d22988a646f352a316","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff33b6d7c4d6de92ffc9208662e73484391ee5e58e59b9d22988a646f352a316","first_computed_at":"2026-07-05T02:17:53.618242Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:17:53.618242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nDNRWoncXhIBWF0xzjZ85zD31QTGVakRbk4rWtRdF7eGE5+w1vM3YgeS1/ykaoxxclZ8/GAFoYSupyzVwmYlAg==","signature_status":"signed_v1","signed_at":"2026-07-05T02:17:53.618738Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.11708","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f37c1e93d564bf901bee68b836037b71c071967ee6f444d6a9f50aa7c9d5576","sha256:1c29db447ff8a6874b9ed6808c03d0fc7ddc6561cdeecd1463272e280ad7609a"],"state_sha256":"664f6f465cad71a8c4e7a692369728f7997e42f0da3fbe28d1d2e58cd9c50e45"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y10yGIF86HYPpSkUWVPYXo7UGNK0h6WNuqV7dPgO8PKG2W9W/RIcVKUGg8z2oQmEP6Y7PDY9yZZniEKjGOSQCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T17:40:31.373164Z","bundle_sha256":"fde90e6796ac502611483f9967b71e4c91c4d231ce6c2388265768d8fee9938f"}}