{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:A37UXGZF4NKAGHYTGILA3GKGHR","short_pith_number":"pith:A37UXGZF","canonical_record":{"source":{"id":"1411.2864","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2014-11-11T16:06:24Z","cross_cats_sorted":[],"title_canon_sha256":"665654c8407ee78f975dc1abf0c1c21a49d96c756b33894ba284d6b1f28aea9c","abstract_canon_sha256":"8fdf4224bb955ac0f769c21d63090cc02c5ebbfdcf001d25e92b2fdfd5d1ba49"},"schema_version":"1.0"},"canonical_sha256":"06ff4b9b25e354031f1332160d99463c759f7b0bf084e46917cff2cb65a13cb7","source":{"kind":"arxiv","id":"1411.2864","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2864","created_at":"2026-05-18T02:28:47Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2864v2","created_at":"2026-05-18T02:28:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2864","created_at":"2026-05-18T02:28:47Z"},{"alias_kind":"pith_short_12","alias_value":"A37UXGZF4NKA","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"A37UXGZF4NKAGHYT","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"A37UXGZF","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:A37UXGZF4NKAGHYTGILA3GKGHR","target":"record","payload":{"canonical_record":{"source":{"id":"1411.2864","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2014-11-11T16:06:24Z","cross_cats_sorted":[],"title_canon_sha256":"665654c8407ee78f975dc1abf0c1c21a49d96c756b33894ba284d6b1f28aea9c","abstract_canon_sha256":"8fdf4224bb955ac0f769c21d63090cc02c5ebbfdcf001d25e92b2fdfd5d1ba49"},"schema_version":"1.0"},"canonical_sha256":"06ff4b9b25e354031f1332160d99463c759f7b0bf084e46917cff2cb65a13cb7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:47.453335Z","signature_b64":"jXXI48WrGAUQkOP4tkHSrwiN5DuQP0+bfwXuxwOFTrI4bNAJiLmYPkmx/ErZyrkm+/9Mc/hvXW3mltiWcypXBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06ff4b9b25e354031f1332160d99463c759f7b0bf084e46917cff2cb65a13cb7","last_reissued_at":"2026-05-18T02:28:47.452959Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:47.452959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.2864","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":"2026-05-18T02:28:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K0e1vhv86bmYYWQ759ql6ZVqyyAQ/nXNT05QIjK1Z0PVoi8OASZYcjXkp6htsIr8+bTS+1SGNqAUCTmB0RrHDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T12:25:02.662342Z"},"content_sha256":"c27afb6616e9a135add05b0d204936b159f0920ce17be759c9b0bb9d2063274e","schema_version":"1.0","event_id":"sha256:c27afb6616e9a135add05b0d204936b159f0920ce17be759c9b0bb9d2063274e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:A37UXGZF4NKAGHYTGILA3GKGHR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Modeling Populations of Thermostatic Loads with Switching Rate Actuation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SY","authors_text":"Aalborg University), Control, John Leth (Automation, Luminita Cristiana Totu (Automation, Rafael Wisniewski (Automation","submitted_at":"2014-11-11T16:06:24Z","abstract_excerpt":"We model thermostatic devices using a stochastic hybrid description, and introduce an external actuation mechanism that creates random switch events in the discrete dynamics. We then conjecture the form of the Fokker-Planck equation and successfully verify it numerically using Monte Carlo simulations. The actuation mechanism and subsequent modeling result are relevant for power system operation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2864","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":"2026-05-18T02:28:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gd2lkB96ved9xOVfWprocgfaHvSNy4j34HYZGTehgAt27oi37gHWSjgZ1qwayDKkoFwn6soSxKSyGZxyD6Y9Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T12:25:02.662703Z"},"content_sha256":"8b9821a605c3d1749b44f2a524506f3cddd98c7a98e264799f87f420df6e2516","schema_version":"1.0","event_id":"sha256:8b9821a605c3d1749b44f2a524506f3cddd98c7a98e264799f87f420df6e2516"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A37UXGZF4NKAGHYTGILA3GKGHR/bundle.json","state_url":"https://pith.science/pith/A37UXGZF4NKAGHYTGILA3GKGHR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A37UXGZF4NKAGHYTGILA3GKGHR/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":"2026-06-02T12:25:02Z","links":{"resolver":"https://pith.science/pith/A37UXGZF4NKAGHYTGILA3GKGHR","bundle":"https://pith.science/pith/A37UXGZF4NKAGHYTGILA3GKGHR/bundle.json","state":"https://pith.science/pith/A37UXGZF4NKAGHYTGILA3GKGHR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A37UXGZF4NKAGHYTGILA3GKGHR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:A37UXGZF4NKAGHYTGILA3GKGHR","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":"8fdf4224bb955ac0f769c21d63090cc02c5ebbfdcf001d25e92b2fdfd5d1ba49","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2014-11-11T16:06:24Z","title_canon_sha256":"665654c8407ee78f975dc1abf0c1c21a49d96c756b33894ba284d6b1f28aea9c"},"schema_version":"1.0","source":{"id":"1411.2864","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2864","created_at":"2026-05-18T02:28:47Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2864v2","created_at":"2026-05-18T02:28:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2864","created_at":"2026-05-18T02:28:47Z"},{"alias_kind":"pith_short_12","alias_value":"A37UXGZF4NKA","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"A37UXGZF4NKAGHYT","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"A37UXGZF","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:8b9821a605c3d1749b44f2a524506f3cddd98c7a98e264799f87f420df6e2516","target":"graph","created_at":"2026-05-18T02:28:47Z","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 model thermostatic devices using a stochastic hybrid description, and introduce an external actuation mechanism that creates random switch events in the discrete dynamics. We then conjecture the form of the Fokker-Planck equation and successfully verify it numerically using Monte Carlo simulations. The actuation mechanism and subsequent modeling result are relevant for power system operation.","authors_text":"Aalborg University), Control, John Leth (Automation, Luminita Cristiana Totu (Automation, Rafael Wisniewski (Automation","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2014-11-11T16:06:24Z","title":"Modeling Populations of Thermostatic Loads with Switching Rate Actuation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2864","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:c27afb6616e9a135add05b0d204936b159f0920ce17be759c9b0bb9d2063274e","target":"record","created_at":"2026-05-18T02:28:47Z","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":"8fdf4224bb955ac0f769c21d63090cc02c5ebbfdcf001d25e92b2fdfd5d1ba49","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2014-11-11T16:06:24Z","title_canon_sha256":"665654c8407ee78f975dc1abf0c1c21a49d96c756b33894ba284d6b1f28aea9c"},"schema_version":"1.0","source":{"id":"1411.2864","kind":"arxiv","version":2}},"canonical_sha256":"06ff4b9b25e354031f1332160d99463c759f7b0bf084e46917cff2cb65a13cb7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"06ff4b9b25e354031f1332160d99463c759f7b0bf084e46917cff2cb65a13cb7","first_computed_at":"2026-05-18T02:28:47.452959Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:47.452959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jXXI48WrGAUQkOP4tkHSrwiN5DuQP0+bfwXuxwOFTrI4bNAJiLmYPkmx/ErZyrkm+/9Mc/hvXW3mltiWcypXBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:47.453335Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.2864","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c27afb6616e9a135add05b0d204936b159f0920ce17be759c9b0bb9d2063274e","sha256:8b9821a605c3d1749b44f2a524506f3cddd98c7a98e264799f87f420df6e2516"],"state_sha256":"8c3fc3ef68bb505330586f82e0975debc47416d1985178c556bf67491ff2001b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z7ppEoo4qAPRNqE9HX5gjGb0bcSyS+i0Vm5+VuGXvZTMrWooFsWPue25aJ3NTXJCOAK7n04Ce5EMexvMI0jLCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T12:25:02.664650Z","bundle_sha256":"15138bf09c252b1bac9944c8f5cb928c472f7ce115228a7b3b89e8bdba4ef44e"}}