{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:7WDPXHZABXC6A5CYI5RSKGEVK5","short_pith_number":"pith:7WDPXHZA","canonical_record":{"source":{"id":"1710.09636","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2017-10-26T10:49:43Z","cross_cats_sorted":[],"title_canon_sha256":"08d09637328f1e2f8f67cda5954735bd1f1e162f4e100058d80a1d48ec1e11b1","abstract_canon_sha256":"f5331f19f5c5675c6910cebe43e26e8e8c05b25eca1a8065bcc7258d29f0a583"},"schema_version":"1.0"},"canonical_sha256":"fd86fb9f200dc5e074584763251895575ffde92a47fee53fc0a5866ed260423f","source":{"kind":"arxiv","id":"1710.09636","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.09636","created_at":"2026-05-18T00:24:48Z"},{"alias_kind":"arxiv_version","alias_value":"1710.09636v2","created_at":"2026-05-18T00:24:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.09636","created_at":"2026-05-18T00:24:48Z"},{"alias_kind":"pith_short_12","alias_value":"7WDPXHZABXC6","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7WDPXHZABXC6A5CY","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7WDPXHZA","created_at":"2026-05-18T12:31:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:7WDPXHZABXC6A5CYI5RSKGEVK5","target":"record","payload":{"canonical_record":{"source":{"id":"1710.09636","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2017-10-26T10:49:43Z","cross_cats_sorted":[],"title_canon_sha256":"08d09637328f1e2f8f67cda5954735bd1f1e162f4e100058d80a1d48ec1e11b1","abstract_canon_sha256":"f5331f19f5c5675c6910cebe43e26e8e8c05b25eca1a8065bcc7258d29f0a583"},"schema_version":"1.0"},"canonical_sha256":"fd86fb9f200dc5e074584763251895575ffde92a47fee53fc0a5866ed260423f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:48.736215Z","signature_b64":"eTpX8q5ajywdBNbLH++TM25/DfmVsIlmn52EukoBY5yiGIbRBL/JjkWiqMMu2PNUIbzSU32yobgZ6CCZYBe4Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd86fb9f200dc5e074584763251895575ffde92a47fee53fc0a5866ed260423f","last_reissued_at":"2026-05-18T00:24:48.735341Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:48.735341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.09636","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":"2026-05-18T00:24:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IiLH68sbFJXJpgo6O7s4cByplnL4G8ioHfao7f4lepjvd+5L1R50miCb2yvIQxOYfyMC2wPXtWkkYV07E641Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T06:55:45.467764Z"},"content_sha256":"472f3fadc5c8c4c0b988c8cc4c0ec89a0adc90ab04f6fe5a569bd6c26ed8c9d9","schema_version":"1.0","event_id":"sha256:472f3fadc5c8c4c0b988c8cc4c0ec89a0adc90ab04f6fe5a569bd6c26ed8c9d9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:7WDPXHZABXC6A5CYI5RSKGEVK5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The interconnection of quadratic droop voltage controllers is a Lotka-Volterra system: implications for stability analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SY","authors_text":"Henrik Sandberg, Karl H. Johansson, Matin Jafarian","submitted_at":"2017-10-26T10:49:43Z","abstract_excerpt":"This paper studies the stability of voltage dynamics for a power network in which nodal voltages are controlled by means of quadratic droop controllers with nonlinear AC reactive power as inputs. We show that the voltage dynamics is a Lotka-Volterra system, which is a class of nonlinear positive systems. We study the stability of the closed-loop system by proving a uniform ultimate boundedness result and investigating conditions under which the network is cooperative. We then restrict to study the stability of voltage dynamics under a decoupling assumption (i.e., zero relative angles). We anal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.09636","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":"2026-05-18T00:24:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pk8wizJadiIij2uc1jOHIWgDgYMx1e2Rjc4A0YaRUz+9MfaPmSq61EGSe3kEo3t0GOP6RtgWHsTxWZ4u9AMxAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T06:55:45.468147Z"},"content_sha256":"a1ea3a5391aceb3dbfb031ac185f942779b6ce61c9ebb7cde66f7daffb5b3c89","schema_version":"1.0","event_id":"sha256:a1ea3a5391aceb3dbfb031ac185f942779b6ce61c9ebb7cde66f7daffb5b3c89"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7WDPXHZABXC6A5CYI5RSKGEVK5/bundle.json","state_url":"https://pith.science/pith/7WDPXHZABXC6A5CYI5RSKGEVK5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7WDPXHZABXC6A5CYI5RSKGEVK5/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":"2026-06-03T06:55:45Z","links":{"resolver":"https://pith.science/pith/7WDPXHZABXC6A5CYI5RSKGEVK5","bundle":"https://pith.science/pith/7WDPXHZABXC6A5CYI5RSKGEVK5/bundle.json","state":"https://pith.science/pith/7WDPXHZABXC6A5CYI5RSKGEVK5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7WDPXHZABXC6A5CYI5RSKGEVK5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7WDPXHZABXC6A5CYI5RSKGEVK5","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":"f5331f19f5c5675c6910cebe43e26e8e8c05b25eca1a8065bcc7258d29f0a583","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2017-10-26T10:49:43Z","title_canon_sha256":"08d09637328f1e2f8f67cda5954735bd1f1e162f4e100058d80a1d48ec1e11b1"},"schema_version":"1.0","source":{"id":"1710.09636","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.09636","created_at":"2026-05-18T00:24:48Z"},{"alias_kind":"arxiv_version","alias_value":"1710.09636v2","created_at":"2026-05-18T00:24:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.09636","created_at":"2026-05-18T00:24:48Z"},{"alias_kind":"pith_short_12","alias_value":"7WDPXHZABXC6","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7WDPXHZABXC6A5CY","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7WDPXHZA","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:a1ea3a5391aceb3dbfb031ac185f942779b6ce61c9ebb7cde66f7daffb5b3c89","target":"graph","created_at":"2026-05-18T00:24:48Z","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":"This paper studies the stability of voltage dynamics for a power network in which nodal voltages are controlled by means of quadratic droop controllers with nonlinear AC reactive power as inputs. We show that the voltage dynamics is a Lotka-Volterra system, which is a class of nonlinear positive systems. We study the stability of the closed-loop system by proving a uniform ultimate boundedness result and investigating conditions under which the network is cooperative. We then restrict to study the stability of voltage dynamics under a decoupling assumption (i.e., zero relative angles). We anal","authors_text":"Henrik Sandberg, Karl H. Johansson, Matin Jafarian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2017-10-26T10:49:43Z","title":"The interconnection of quadratic droop voltage controllers is a Lotka-Volterra system: implications for stability analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.09636","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":"sha256:472f3fadc5c8c4c0b988c8cc4c0ec89a0adc90ab04f6fe5a569bd6c26ed8c9d9","target":"record","created_at":"2026-05-18T00:24:48Z","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":"f5331f19f5c5675c6910cebe43e26e8e8c05b25eca1a8065bcc7258d29f0a583","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2017-10-26T10:49:43Z","title_canon_sha256":"08d09637328f1e2f8f67cda5954735bd1f1e162f4e100058d80a1d48ec1e11b1"},"schema_version":"1.0","source":{"id":"1710.09636","kind":"arxiv","version":2}},"canonical_sha256":"fd86fb9f200dc5e074584763251895575ffde92a47fee53fc0a5866ed260423f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd86fb9f200dc5e074584763251895575ffde92a47fee53fc0a5866ed260423f","first_computed_at":"2026-05-18T00:24:48.735341Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:48.735341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eTpX8q5ajywdBNbLH++TM25/DfmVsIlmn52EukoBY5yiGIbRBL/JjkWiqMMu2PNUIbzSU32yobgZ6CCZYBe4Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:48.736215Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.09636","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:472f3fadc5c8c4c0b988c8cc4c0ec89a0adc90ab04f6fe5a569bd6c26ed8c9d9","sha256:a1ea3a5391aceb3dbfb031ac185f942779b6ce61c9ebb7cde66f7daffb5b3c89"],"state_sha256":"ffa88257caba946038e11f5d07e98191786aea5b64211a8170d6737cfc118925"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/JL7sGqoysPHu1DJaEWYQiFCff+8NMYdv9r4MaOGCi2u04PYz3jErFo9AEYiDNP/uJ1n9QuZfr1TPI6shQezCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T06:55:45.470073Z","bundle_sha256":"08a056b72631e9cd3c4aa1470bd303d151fe1f7f0bf3b1b1c74404d83a580bdf"}}