{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:NDK4A55CQGLRTCEFJG5QVQLWPQ","short_pith_number":"pith:NDK4A55C","canonical_record":{"source":{"id":"1503.04769","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-03-16T19:01:37Z","cross_cats_sorted":[],"title_canon_sha256":"7dec358e9bdd1f14c5d99048c526ac9d6f94bf70de9167b06e1bbdf5ce3052cf","abstract_canon_sha256":"1f79df2397cec7befe14f2fb8ba9ff3fd5698c347fcfb989dec675e9ac7bf940"},"schema_version":"1.0"},"canonical_sha256":"68d5c077a2819719888549bb0ac1767c1e076b41740712c5e4762d3e1ee3f923","source":{"kind":"arxiv","id":"1503.04769","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.04769","created_at":"2026-05-18T00:34:45Z"},{"alias_kind":"arxiv_version","alias_value":"1503.04769v1","created_at":"2026-05-18T00:34:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.04769","created_at":"2026-05-18T00:34:45Z"},{"alias_kind":"pith_short_12","alias_value":"NDK4A55CQGLR","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NDK4A55CQGLRTCEF","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NDK4A55C","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:NDK4A55CQGLRTCEFJG5QVQLWPQ","target":"record","payload":{"canonical_record":{"source":{"id":"1503.04769","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-03-16T19:01:37Z","cross_cats_sorted":[],"title_canon_sha256":"7dec358e9bdd1f14c5d99048c526ac9d6f94bf70de9167b06e1bbdf5ce3052cf","abstract_canon_sha256":"1f79df2397cec7befe14f2fb8ba9ff3fd5698c347fcfb989dec675e9ac7bf940"},"schema_version":"1.0"},"canonical_sha256":"68d5c077a2819719888549bb0ac1767c1e076b41740712c5e4762d3e1ee3f923","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:45.148499Z","signature_b64":"e7eVPRAtwGtGCBJjFo5FSvYnZUdO9qbL9ZMuqFipJlVYxTQ7OGwKVLtO+rEQjo8bsJB0Ux74fmai2ul7VyVpCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68d5c077a2819719888549bb0ac1767c1e076b41740712c5e4762d3e1ee3f923","last_reissued_at":"2026-05-18T00:34:45.147703Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:45.147703Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.04769","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":"2026-05-18T00:34:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cb4ZM5R/zm/SM7HSp4OvjF7HDbm4nSyjVQMPhC59qCZaiLvOhmgkZzRKFglWusGMYRm8sKAm3lRcsHK11OxKDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T21:35:06.591039Z"},"content_sha256":"8aeb0ab34efce334fe586ecaf30a80bb19c62646da6c6b5fa2bffeae56c3cf26","schema_version":"1.0","event_id":"sha256:8aeb0ab34efce334fe586ecaf30a80bb19c62646da6c6b5fa2bffeae56c3cf26"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:NDK4A55CQGLRTCEFJG5QVQLWPQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Resistive Networks of Constant Power Devices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Florian Dorfler, Francesco Bullo, John W. Simpson-Porco","submitted_at":"2015-03-16T19:01:37Z","abstract_excerpt":"This brief examines the behavior of DC circuits comprised of resistively interconnected constant power devices, as may arise in DC microgrids containing micro-sources and constant power loads. We derive a sufficient condition for all operating points of the circuit to lie in a desirable set, where the average nodal voltage level is high and nodal voltages are tightly clustered near one another. Our condition has the elegant physical interpretation that the ratio of resistive losses to total injected power should be small compared to a measure of network heterogeneity, as quantified by a ratio "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04769","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":"2026-05-18T00:34:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JMSCgdBGp0v/q6Zlx3UIM8UVxPCBH8SOijqBXlgcFf+PXGP6Q0S79jdIWPOiais+wotfpbu/g4V39NLZ7WbmCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T21:35:06.591401Z"},"content_sha256":"f1ceb64b39731b39b19914daf608f59798f3a6b7aae9e3e6e04e260d4705fe93","schema_version":"1.0","event_id":"sha256:f1ceb64b39731b39b19914daf608f59798f3a6b7aae9e3e6e04e260d4705fe93"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NDK4A55CQGLRTCEFJG5QVQLWPQ/bundle.json","state_url":"https://pith.science/pith/NDK4A55CQGLRTCEFJG5QVQLWPQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NDK4A55CQGLRTCEFJG5QVQLWPQ/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":"2026-06-23T21:35:06Z","links":{"resolver":"https://pith.science/pith/NDK4A55CQGLRTCEFJG5QVQLWPQ","bundle":"https://pith.science/pith/NDK4A55CQGLRTCEFJG5QVQLWPQ/bundle.json","state":"https://pith.science/pith/NDK4A55CQGLRTCEFJG5QVQLWPQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NDK4A55CQGLRTCEFJG5QVQLWPQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NDK4A55CQGLRTCEFJG5QVQLWPQ","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":"1f79df2397cec7befe14f2fb8ba9ff3fd5698c347fcfb989dec675e9ac7bf940","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-03-16T19:01:37Z","title_canon_sha256":"7dec358e9bdd1f14c5d99048c526ac9d6f94bf70de9167b06e1bbdf5ce3052cf"},"schema_version":"1.0","source":{"id":"1503.04769","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.04769","created_at":"2026-05-18T00:34:45Z"},{"alias_kind":"arxiv_version","alias_value":"1503.04769v1","created_at":"2026-05-18T00:34:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.04769","created_at":"2026-05-18T00:34:45Z"},{"alias_kind":"pith_short_12","alias_value":"NDK4A55CQGLR","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NDK4A55CQGLRTCEF","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NDK4A55C","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:f1ceb64b39731b39b19914daf608f59798f3a6b7aae9e3e6e04e260d4705fe93","target":"graph","created_at":"2026-05-18T00:34:45Z","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 brief examines the behavior of DC circuits comprised of resistively interconnected constant power devices, as may arise in DC microgrids containing micro-sources and constant power loads. We derive a sufficient condition for all operating points of the circuit to lie in a desirable set, where the average nodal voltage level is high and nodal voltages are tightly clustered near one another. Our condition has the elegant physical interpretation that the ratio of resistive losses to total injected power should be small compared to a measure of network heterogeneity, as quantified by a ratio ","authors_text":"Florian Dorfler, Francesco Bullo, John W. Simpson-Porco","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-03-16T19:01:37Z","title":"On Resistive Networks of Constant Power Devices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04769","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":"sha256:8aeb0ab34efce334fe586ecaf30a80bb19c62646da6c6b5fa2bffeae56c3cf26","target":"record","created_at":"2026-05-18T00:34:45Z","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":"1f79df2397cec7befe14f2fb8ba9ff3fd5698c347fcfb989dec675e9ac7bf940","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-03-16T19:01:37Z","title_canon_sha256":"7dec358e9bdd1f14c5d99048c526ac9d6f94bf70de9167b06e1bbdf5ce3052cf"},"schema_version":"1.0","source":{"id":"1503.04769","kind":"arxiv","version":1}},"canonical_sha256":"68d5c077a2819719888549bb0ac1767c1e076b41740712c5e4762d3e1ee3f923","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68d5c077a2819719888549bb0ac1767c1e076b41740712c5e4762d3e1ee3f923","first_computed_at":"2026-05-18T00:34:45.147703Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:45.147703Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e7eVPRAtwGtGCBJjFo5FSvYnZUdO9qbL9ZMuqFipJlVYxTQ7OGwKVLtO+rEQjo8bsJB0Ux74fmai2ul7VyVpCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:45.148499Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.04769","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8aeb0ab34efce334fe586ecaf30a80bb19c62646da6c6b5fa2bffeae56c3cf26","sha256:f1ceb64b39731b39b19914daf608f59798f3a6b7aae9e3e6e04e260d4705fe93"],"state_sha256":"cb68a50f8cbddb886494225735c09a4dbe296636f63834cf77c05948b1cf8b35"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xkOLrI4iniqmMJeb13lz4TV4R/CL5w0nr2AdjLidlbazF9IOQHU42pL1pzEGjiycmf5620zxdO9q9CC56hkxDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T21:35:06.593376Z","bundle_sha256":"44bcde39d1adce74ab2cb0f6c69e9fb170a67ec617792eca2edfdb5cb11333fc"}}