{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:AWUQ2PV3C5HNMSWMEDUSEYC4I6","short_pith_number":"pith:AWUQ2PV3","canonical_record":{"source":{"id":"1608.04422","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-08-15T22:01:39Z","cross_cats_sorted":[],"title_canon_sha256":"54c039df88c1de764999678c8377080dbc6085673a3f70b7be5e003a94594f4c","abstract_canon_sha256":"ef4175cd39318c7e815d226f38b543bcb7b6dc649f215b46d91b87692cb0f730"},"schema_version":"1.0"},"canonical_sha256":"05a90d3ebb174ed64acc20e922605c479f29fe6415463e8757c8e965369a4b51","source":{"kind":"arxiv","id":"1608.04422","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.04422","created_at":"2026-05-18T00:47:26Z"},{"alias_kind":"arxiv_version","alias_value":"1608.04422v2","created_at":"2026-05-18T00:47:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.04422","created_at":"2026-05-18T00:47:26Z"},{"alias_kind":"pith_short_12","alias_value":"AWUQ2PV3C5HN","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AWUQ2PV3C5HNMSWM","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AWUQ2PV3","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:AWUQ2PV3C5HNMSWMEDUSEYC4I6","target":"record","payload":{"canonical_record":{"source":{"id":"1608.04422","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-08-15T22:01:39Z","cross_cats_sorted":[],"title_canon_sha256":"54c039df88c1de764999678c8377080dbc6085673a3f70b7be5e003a94594f4c","abstract_canon_sha256":"ef4175cd39318c7e815d226f38b543bcb7b6dc649f215b46d91b87692cb0f730"},"schema_version":"1.0"},"canonical_sha256":"05a90d3ebb174ed64acc20e922605c479f29fe6415463e8757c8e965369a4b51","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:26.898704Z","signature_b64":"MoVHAOl/nY58Q3vppZgqbbYHxT7nk2x1FTpHm7DTjYnMrfydjmKVfu9DeQyk2V9LOxy8BIuyTTgevtmGpVCLCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05a90d3ebb174ed64acc20e922605c479f29fe6415463e8757c8e965369a4b51","last_reissued_at":"2026-05-18T00:47:26.898149Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:26.898149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.04422","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":"2026-05-18T00:47:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0MMPR2t/Ji9cy6Gu6ipbb1LXGn+fif4vfjmZcy++/vUMR2P+TWaixUobWEYp0gaDoGLvME6t4D0Llp0tqPgoBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T08:27:37.516538Z"},"content_sha256":"57a8f7fbf984bb5c554a255f7cd3641a939faca85ccf351a5661821a3d926ba1","schema_version":"1.0","event_id":"sha256:57a8f7fbf984bb5c554a255f7cd3641a939faca85ccf351a5661821a3d926ba1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:AWUQ2PV3C5HNMSWMEDUSEYC4I6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Geometric Approach to Aggregate Flexibility Modeling of Thermostatically Controlled Loads","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"He Hao, Karan Kalsi, Lin Zhao, Wei Zhang","submitted_at":"2016-08-15T22:01:39Z","abstract_excerpt":"Coordinated aggregation of a large population of thermostatically controlled loads (TCLs) presents a great potential to provide various ancillary services to the grid. One of the key challenges of integrating TCLs into system level operation and control is developing a simple and portable model to accurately capture their aggregate flexibility. In this paper, we propose a geometric approach to model the aggregate flexibility of TCLs. We show that the set of admissible power profiles of an individual TCL is a polytope, and their aggregate flexibility is the Minkowski sum of the individual polyt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04422","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":"2026-05-18T00:47:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FF5saOiaJXtjCQOiQ/8zrgPr5eHXkFIfjM7gF+tAxqfOEoahfCiDSQXr3MxbYm1vamqQyH8mwHPmktowVUy7Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T08:27:37.516885Z"},"content_sha256":"2809f8641da396f34adc98dbdbbcf27eb59557b82ce8ccbb23de587f963ead2b","schema_version":"1.0","event_id":"sha256:2809f8641da396f34adc98dbdbbcf27eb59557b82ce8ccbb23de587f963ead2b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AWUQ2PV3C5HNMSWMEDUSEYC4I6/bundle.json","state_url":"https://pith.science/pith/AWUQ2PV3C5HNMSWMEDUSEYC4I6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AWUQ2PV3C5HNMSWMEDUSEYC4I6/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":"2026-06-05T08:27:37Z","links":{"resolver":"https://pith.science/pith/AWUQ2PV3C5HNMSWMEDUSEYC4I6","bundle":"https://pith.science/pith/AWUQ2PV3C5HNMSWMEDUSEYC4I6/bundle.json","state":"https://pith.science/pith/AWUQ2PV3C5HNMSWMEDUSEYC4I6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AWUQ2PV3C5HNMSWMEDUSEYC4I6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:AWUQ2PV3C5HNMSWMEDUSEYC4I6","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":"ef4175cd39318c7e815d226f38b543bcb7b6dc649f215b46d91b87692cb0f730","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-08-15T22:01:39Z","title_canon_sha256":"54c039df88c1de764999678c8377080dbc6085673a3f70b7be5e003a94594f4c"},"schema_version":"1.0","source":{"id":"1608.04422","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.04422","created_at":"2026-05-18T00:47:26Z"},{"alias_kind":"arxiv_version","alias_value":"1608.04422v2","created_at":"2026-05-18T00:47:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.04422","created_at":"2026-05-18T00:47:26Z"},{"alias_kind":"pith_short_12","alias_value":"AWUQ2PV3C5HN","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AWUQ2PV3C5HNMSWM","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AWUQ2PV3","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:2809f8641da396f34adc98dbdbbcf27eb59557b82ce8ccbb23de587f963ead2b","target":"graph","created_at":"2026-05-18T00:47:26Z","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":"Coordinated aggregation of a large population of thermostatically controlled loads (TCLs) presents a great potential to provide various ancillary services to the grid. One of the key challenges of integrating TCLs into system level operation and control is developing a simple and portable model to accurately capture their aggregate flexibility. In this paper, we propose a geometric approach to model the aggregate flexibility of TCLs. We show that the set of admissible power profiles of an individual TCL is a polytope, and their aggregate flexibility is the Minkowski sum of the individual polyt","authors_text":"He Hao, Karan Kalsi, Lin Zhao, Wei Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-08-15T22:01:39Z","title":"A Geometric Approach to Aggregate Flexibility Modeling of Thermostatically Controlled Loads"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04422","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":"sha256:57a8f7fbf984bb5c554a255f7cd3641a939faca85ccf351a5661821a3d926ba1","target":"record","created_at":"2026-05-18T00:47:26Z","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":"ef4175cd39318c7e815d226f38b543bcb7b6dc649f215b46d91b87692cb0f730","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-08-15T22:01:39Z","title_canon_sha256":"54c039df88c1de764999678c8377080dbc6085673a3f70b7be5e003a94594f4c"},"schema_version":"1.0","source":{"id":"1608.04422","kind":"arxiv","version":2}},"canonical_sha256":"05a90d3ebb174ed64acc20e922605c479f29fe6415463e8757c8e965369a4b51","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05a90d3ebb174ed64acc20e922605c479f29fe6415463e8757c8e965369a4b51","first_computed_at":"2026-05-18T00:47:26.898149Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:26.898149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MoVHAOl/nY58Q3vppZgqbbYHxT7nk2x1FTpHm7DTjYnMrfydjmKVfu9DeQyk2V9LOxy8BIuyTTgevtmGpVCLCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:26.898704Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.04422","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57a8f7fbf984bb5c554a255f7cd3641a939faca85ccf351a5661821a3d926ba1","sha256:2809f8641da396f34adc98dbdbbcf27eb59557b82ce8ccbb23de587f963ead2b"],"state_sha256":"0bd98810209b6477dec475abb79cbea30d8bc37a97356e27df75bfcfa6b3ab89"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gpyq/4A6EYTvpc+4N1uZ8ohDuPjtOEBQZL3HfDKiZ1eWnkji/01pCPf5aT5A/fsGriNIsJbKJ39XiFn+3zjkDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T08:27:37.518882Z","bundle_sha256":"8b722591118ccd4f38372a7e8269e36b26a80ab3a908cd763c5a92ac80e53139"}}