{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:MWXJTNGAXSO6CKPLPKN5BXPW5B","short_pith_number":"pith:MWXJTNGA","canonical_record":{"source":{"id":"1402.6261","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-25T18:04:17Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"2aacc54c7a56268609df7b3d4f81cb69e1fdf253318221fe74c1795b07c82b12","abstract_canon_sha256":"e819e9958055da73ecda8976754f52043e1275a96544bd1b992596363d064ee7"},"schema_version":"1.0"},"canonical_sha256":"65ae99b4c0bc9de129eb7a9bd0ddf6e869a8d919904902010f459935bf67e0ec","source":{"kind":"arxiv","id":"1402.6261","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.6261","created_at":"2026-05-18T00:06:44Z"},{"alias_kind":"arxiv_version","alias_value":"1402.6261v4","created_at":"2026-05-18T00:06:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.6261","created_at":"2026-05-18T00:06:44Z"},{"alias_kind":"pith_short_12","alias_value":"MWXJTNGAXSO6","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MWXJTNGAXSO6CKPL","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MWXJTNGA","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:MWXJTNGAXSO6CKPLPKN5BXPW5B","target":"record","payload":{"canonical_record":{"source":{"id":"1402.6261","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-25T18:04:17Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"2aacc54c7a56268609df7b3d4f81cb69e1fdf253318221fe74c1795b07c82b12","abstract_canon_sha256":"e819e9958055da73ecda8976754f52043e1275a96544bd1b992596363d064ee7"},"schema_version":"1.0"},"canonical_sha256":"65ae99b4c0bc9de129eb7a9bd0ddf6e869a8d919904902010f459935bf67e0ec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:44.826811Z","signature_b64":"dAdU0FdgzGFEYKxGw4Oo3AXtX7lVfG4KADQRXa3h3D+QV+FkkNTFY20MDE4FpfmcPWqC1YGqYqJfWQkdBc0ZAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65ae99b4c0bc9de129eb7a9bd0ddf6e869a8d919904902010f459935bf67e0ec","last_reissued_at":"2026-05-18T00:06:44.826345Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:44.826345Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.6261","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":"2026-05-18T00:06:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WXO3keQDft+ASCgE9zoDyVMJDB0qKR7Qxi/rAlwoaPtP0RtWdUap1Ajmg8wTsJav35TTeTqf5yVKOHlp0tZOBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T15:54:18.286550Z"},"content_sha256":"8eb33ecf28c24f6eeb383edc604b5a2e25ff3826f9c18cbead27ed508963411c","schema_version":"1.0","event_id":"sha256:8eb33ecf28c24f6eeb383edc604b5a2e25ff3826f9c18cbead27ed508963411c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:MWXJTNGAXSO6CKPLPKN5BXPW5B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Electroid varieties and a compactification of the space of electrical networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CO","authors_text":"Thomas Lam","submitted_at":"2014-02-25T18:04:17Z","abstract_excerpt":"We construct a compactification of the space of circular planar electrical networks studied by Curtis-Ingerman-Morrow and De Verdiere-Gitler-Vertigan, using cactus networks. We embed this compactification as a linear slice of the totally nonnegative Grassmannian, and relate Kenyon and Wilson's grove measurements to Postnikov's boundary measurements. Intersections of the slice with the positroid stratification leads to a class of electroid varieties, indexed by matchings. The partial order on matchings arising from electrical networks is shown to be dual to a subposet of affine Bruhat order. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6261","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":"2026-05-18T00:06:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hZqRnSP8MqFmJuzq/oSzfdHpJh8D9vXMOUh82O6nBbmMxkXFXDzmFRuteTKQnIM3GfqMyoJagTfueaPTCd4XCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T15:54:18.286907Z"},"content_sha256":"d1ae3547b5bc735fc4aa0e40096ab10c29d5414490d072f4aabe71f2417723c7","schema_version":"1.0","event_id":"sha256:d1ae3547b5bc735fc4aa0e40096ab10c29d5414490d072f4aabe71f2417723c7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MWXJTNGAXSO6CKPLPKN5BXPW5B/bundle.json","state_url":"https://pith.science/pith/MWXJTNGAXSO6CKPLPKN5BXPW5B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MWXJTNGAXSO6CKPLPKN5BXPW5B/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":"2026-05-27T15:54:18Z","links":{"resolver":"https://pith.science/pith/MWXJTNGAXSO6CKPLPKN5BXPW5B","bundle":"https://pith.science/pith/MWXJTNGAXSO6CKPLPKN5BXPW5B/bundle.json","state":"https://pith.science/pith/MWXJTNGAXSO6CKPLPKN5BXPW5B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MWXJTNGAXSO6CKPLPKN5BXPW5B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:MWXJTNGAXSO6CKPLPKN5BXPW5B","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":"e819e9958055da73ecda8976754f52043e1275a96544bd1b992596363d064ee7","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-25T18:04:17Z","title_canon_sha256":"2aacc54c7a56268609df7b3d4f81cb69e1fdf253318221fe74c1795b07c82b12"},"schema_version":"1.0","source":{"id":"1402.6261","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.6261","created_at":"2026-05-18T00:06:44Z"},{"alias_kind":"arxiv_version","alias_value":"1402.6261v4","created_at":"2026-05-18T00:06:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.6261","created_at":"2026-05-18T00:06:44Z"},{"alias_kind":"pith_short_12","alias_value":"MWXJTNGAXSO6","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MWXJTNGAXSO6CKPL","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MWXJTNGA","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:d1ae3547b5bc735fc4aa0e40096ab10c29d5414490d072f4aabe71f2417723c7","target":"graph","created_at":"2026-05-18T00:06:44Z","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 construct a compactification of the space of circular planar electrical networks studied by Curtis-Ingerman-Morrow and De Verdiere-Gitler-Vertigan, using cactus networks. We embed this compactification as a linear slice of the totally nonnegative Grassmannian, and relate Kenyon and Wilson's grove measurements to Postnikov's boundary measurements. Intersections of the slice with the positroid stratification leads to a class of electroid varieties, indexed by matchings. The partial order on matchings arising from electrical networks is shown to be dual to a subposet of affine Bruhat order. Th","authors_text":"Thomas Lam","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-25T18:04:17Z","title":"Electroid varieties and a compactification of the space of electrical networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6261","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":"sha256:8eb33ecf28c24f6eeb383edc604b5a2e25ff3826f9c18cbead27ed508963411c","target":"record","created_at":"2026-05-18T00:06:44Z","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":"e819e9958055da73ecda8976754f52043e1275a96544bd1b992596363d064ee7","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-25T18:04:17Z","title_canon_sha256":"2aacc54c7a56268609df7b3d4f81cb69e1fdf253318221fe74c1795b07c82b12"},"schema_version":"1.0","source":{"id":"1402.6261","kind":"arxiv","version":4}},"canonical_sha256":"65ae99b4c0bc9de129eb7a9bd0ddf6e869a8d919904902010f459935bf67e0ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65ae99b4c0bc9de129eb7a9bd0ddf6e869a8d919904902010f459935bf67e0ec","first_computed_at":"2026-05-18T00:06:44.826345Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:44.826345Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dAdU0FdgzGFEYKxGw4Oo3AXtX7lVfG4KADQRXa3h3D+QV+FkkNTFY20MDE4FpfmcPWqC1YGqYqJfWQkdBc0ZAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:44.826811Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.6261","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8eb33ecf28c24f6eeb383edc604b5a2e25ff3826f9c18cbead27ed508963411c","sha256:d1ae3547b5bc735fc4aa0e40096ab10c29d5414490d072f4aabe71f2417723c7"],"state_sha256":"4a1842b027ab79711cc71fb643979e314c84689787d558a5ec79f3a7584ee05e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XYJ86736QeOobEpQUtIfPyh/Tfnys/Eid4J0M3eRI8RcXCPvCbTdIhZceArNcnrtfoghG2wNKORcXDE8kFjUCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T15:54:18.289442Z","bundle_sha256":"a303bf97a7bd6a73b769a5d786881aaaee750ca5fd0f4e510b7d03b38736b2b7"}}