{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:CVWM7CDDO2KTSTU7PYJAKF5RWI","short_pith_number":"pith:CVWM7CDD","canonical_record":{"source":{"id":"1510.04645","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-10-15T17:51:06Z","cross_cats_sorted":["cs.CE"],"title_canon_sha256":"3bfe4aa2c89a7ff1754abfc3a24f53991b0396dbea3b02d3455c91aec0ee79b2","abstract_canon_sha256":"1797a201503ae29fc4b8aad1abc057436f775f8566cbee7d59880eaad41cb417"},"schema_version":"1.0"},"canonical_sha256":"156ccf88637695394e9f7e120517b1b21061c442dd604e510dce31016b84dd51","source":{"kind":"arxiv","id":"1510.04645","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.04645","created_at":"2026-05-18T01:10:33Z"},{"alias_kind":"arxiv_version","alias_value":"1510.04645v4","created_at":"2026-05-18T01:10:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04645","created_at":"2026-05-18T01:10:33Z"},{"alias_kind":"pith_short_12","alias_value":"CVWM7CDDO2KT","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CVWM7CDDO2KTSTU7","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CVWM7CDD","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:CVWM7CDDO2KTSTU7PYJAKF5RWI","target":"record","payload":{"canonical_record":{"source":{"id":"1510.04645","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-10-15T17:51:06Z","cross_cats_sorted":["cs.CE"],"title_canon_sha256":"3bfe4aa2c89a7ff1754abfc3a24f53991b0396dbea3b02d3455c91aec0ee79b2","abstract_canon_sha256":"1797a201503ae29fc4b8aad1abc057436f775f8566cbee7d59880eaad41cb417"},"schema_version":"1.0"},"canonical_sha256":"156ccf88637695394e9f7e120517b1b21061c442dd604e510dce31016b84dd51","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:33.123915Z","signature_b64":"gJq4m3zrzjIXYG46XxehWCHN/mGxasv18gTsIM3Fgyyxy3Vy0uLj6W/ERIECK979Cv2T3QGBAGEDfcX7HaNeAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"156ccf88637695394e9f7e120517b1b21061c442dd604e510dce31016b84dd51","last_reissued_at":"2026-05-18T01:10:33.123367Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:33.123367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.04645","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:10:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V6ceII5BmoEad30jqRlZ7ztyUD3G7dDZk7zBJibaoSysQ6R2AwbLgxlclT2Y14RqyXgR7RMW9D8a5ezF7QTYDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T01:12:00.222806Z"},"content_sha256":"4102911ccef1b93ec452dc2370a6dccb6336d053bdb1d51a5757490c9405fc30","schema_version":"1.0","event_id":"sha256:4102911ccef1b93ec452dc2370a6dccb6336d053bdb1d51a5757490c9405fc30"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:CVWM7CDDO2KTSTU7PYJAKF5RWI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Dual Method for Computing Power Transfer Distribution Factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CE"],"primary_cat":"cs.SY","authors_text":"Dirk Witthaut, Henrik Ronellenfitsch, Marc Timme","submitted_at":"2015-10-15T17:51:06Z","abstract_excerpt":"Power Transfer Distribution Factors (PTDFs) play a crucial role in power grid security analysis, planning, and redispatch. Fast calculation of the PTDFs is therefore of great importance. In this paper, we present a non-approximative dual method of computing PTDFs. It uses power flows along topological cycles of the network but still relies on simple matrix algebra. At the core, our method changes the size of the matrix that needs to be inverted to calculate the PTDFs from $N\\times N$, where $N$ is the number of buses, to $(L-N+1)\\times (L-N+1)$, where $L$ is the number of lines and $L-N+1$ is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04645","kind":"arxiv","version":4},"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":"2026-05-18T01:10:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L5Zdd2hfuBoFosEb23ozI1dmSMEvCwahwawpKbjjQrPNDswy2itkKLfNsbE4w2YFwCP5ExlZ65zWcXSjEi5HAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T01:12:00.223522Z"},"content_sha256":"635ce017b6d02fdfc6739abac9bc8b0e59979c0bce51d33f1e4b15061d655da5","schema_version":"1.0","event_id":"sha256:635ce017b6d02fdfc6739abac9bc8b0e59979c0bce51d33f1e4b15061d655da5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CVWM7CDDO2KTSTU7PYJAKF5RWI/bundle.json","state_url":"https://pith.science/pith/CVWM7CDDO2KTSTU7PYJAKF5RWI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CVWM7CDDO2KTSTU7PYJAKF5RWI/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":"2026-05-30T01:12:00Z","links":{"resolver":"https://pith.science/pith/CVWM7CDDO2KTSTU7PYJAKF5RWI","bundle":"https://pith.science/pith/CVWM7CDDO2KTSTU7PYJAKF5RWI/bundle.json","state":"https://pith.science/pith/CVWM7CDDO2KTSTU7PYJAKF5RWI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CVWM7CDDO2KTSTU7PYJAKF5RWI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CVWM7CDDO2KTSTU7PYJAKF5RWI","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":"1797a201503ae29fc4b8aad1abc057436f775f8566cbee7d59880eaad41cb417","cross_cats_sorted":["cs.CE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-10-15T17:51:06Z","title_canon_sha256":"3bfe4aa2c89a7ff1754abfc3a24f53991b0396dbea3b02d3455c91aec0ee79b2"},"schema_version":"1.0","source":{"id":"1510.04645","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.04645","created_at":"2026-05-18T01:10:33Z"},{"alias_kind":"arxiv_version","alias_value":"1510.04645v4","created_at":"2026-05-18T01:10:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04645","created_at":"2026-05-18T01:10:33Z"},{"alias_kind":"pith_short_12","alias_value":"CVWM7CDDO2KT","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CVWM7CDDO2KTSTU7","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CVWM7CDD","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:635ce017b6d02fdfc6739abac9bc8b0e59979c0bce51d33f1e4b15061d655da5","target":"graph","created_at":"2026-05-18T01:10:33Z","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":"Power Transfer Distribution Factors (PTDFs) play a crucial role in power grid security analysis, planning, and redispatch. Fast calculation of the PTDFs is therefore of great importance. In this paper, we present a non-approximative dual method of computing PTDFs. It uses power flows along topological cycles of the network but still relies on simple matrix algebra. At the core, our method changes the size of the matrix that needs to be inverted to calculate the PTDFs from $N\\times N$, where $N$ is the number of buses, to $(L-N+1)\\times (L-N+1)$, where $L$ is the number of lines and $L-N+1$ is ","authors_text":"Dirk Witthaut, Henrik Ronellenfitsch, Marc Timme","cross_cats":["cs.CE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-10-15T17:51:06Z","title":"A Dual Method for Computing Power Transfer Distribution Factors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04645","kind":"arxiv","version":4},"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":"sha256:4102911ccef1b93ec452dc2370a6dccb6336d053bdb1d51a5757490c9405fc30","target":"record","created_at":"2026-05-18T01:10:33Z","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":"1797a201503ae29fc4b8aad1abc057436f775f8566cbee7d59880eaad41cb417","cross_cats_sorted":["cs.CE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-10-15T17:51:06Z","title_canon_sha256":"3bfe4aa2c89a7ff1754abfc3a24f53991b0396dbea3b02d3455c91aec0ee79b2"},"schema_version":"1.0","source":{"id":"1510.04645","kind":"arxiv","version":4}},"canonical_sha256":"156ccf88637695394e9f7e120517b1b21061c442dd604e510dce31016b84dd51","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"156ccf88637695394e9f7e120517b1b21061c442dd604e510dce31016b84dd51","first_computed_at":"2026-05-18T01:10:33.123367Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:33.123367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gJq4m3zrzjIXYG46XxehWCHN/mGxasv18gTsIM3Fgyyxy3Vy0uLj6W/ERIECK979Cv2T3QGBAGEDfcX7HaNeAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:33.123915Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.04645","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4102911ccef1b93ec452dc2370a6dccb6336d053bdb1d51a5757490c9405fc30","sha256:635ce017b6d02fdfc6739abac9bc8b0e59979c0bce51d33f1e4b15061d655da5"],"state_sha256":"3c0ff4bf698863fcfa33127fbadfd3d40f5120a171e7d74434ed04ff819ea9cc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YwAJnL2Abf4IgyeDdzdc1ZfLheaP/etDRByZeeG+oM5RvaCCpa5iLR15O5oWz7ZxZT+XmnUXPBKdD6uSY8KtDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T01:12:00.227229Z","bundle_sha256":"c67a482cea1c19148a28a275df7d7449f765c17eec9ae32a2658d268a0a9f204"}}