{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:AHMHKGY6F2W5QEJVM43GRTFOAI","short_pith_number":"pith:AHMHKGY6","canonical_record":{"source":{"id":"1805.10239","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-25T16:33:53Z","cross_cats_sorted":[],"title_canon_sha256":"cb73ca09388ea4cb80ddd035299cde681cd8d4cfb0ebc274c4a4442709495b44","abstract_canon_sha256":"d3fbf27016dd6d21e2eb02141ab41b1442166a336470fef9d0ac282e65560e72"},"schema_version":"1.0"},"canonical_sha256":"01d8751b1e2eadd81135673668ccae02241c754464ddea2aea409cb227f81a89","source":{"kind":"arxiv","id":"1805.10239","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.10239","created_at":"2026-05-18T00:14:57Z"},{"alias_kind":"arxiv_version","alias_value":"1805.10239v1","created_at":"2026-05-18T00:14:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.10239","created_at":"2026-05-18T00:14:57Z"},{"alias_kind":"pith_short_12","alias_value":"AHMHKGY6F2W5","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AHMHKGY6F2W5QEJV","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AHMHKGY6","created_at":"2026-05-18T12:32:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:AHMHKGY6F2W5QEJVM43GRTFOAI","target":"record","payload":{"canonical_record":{"source":{"id":"1805.10239","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-25T16:33:53Z","cross_cats_sorted":[],"title_canon_sha256":"cb73ca09388ea4cb80ddd035299cde681cd8d4cfb0ebc274c4a4442709495b44","abstract_canon_sha256":"d3fbf27016dd6d21e2eb02141ab41b1442166a336470fef9d0ac282e65560e72"},"schema_version":"1.0"},"canonical_sha256":"01d8751b1e2eadd81135673668ccae02241c754464ddea2aea409cb227f81a89","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:57.892196Z","signature_b64":"ecz8brl2DVnL/mpWXKgM3h+dX6prpEadQ2/N+nANaHmY4NoU7j5DlU8glTR3AQfINEsJGw0GiCbjEHuez760Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01d8751b1e2eadd81135673668ccae02241c754464ddea2aea409cb227f81a89","last_reissued_at":"2026-05-18T00:14:57.891476Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:57.891476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.10239","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":"2026-05-18T00:14:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YzEA1nXXj9e7qEO1f5IPhjTp31dvIxYpIS+Q/Mtum9wcBRuZi/ZQafCYyVzu1WdhIQNMzNU6AzPdqNjzZ2lnCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T16:40:02.523828Z"},"content_sha256":"8aac288d34db1b3c95592b85a7239b3795a4f8305153e581744b969442d8de7b","schema_version":"1.0","event_id":"sha256:8aac288d34db1b3c95592b85a7239b3795a4f8305153e581744b969442d8de7b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:AHMHKGY6F2W5QEJVM43GRTFOAI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A principle for converting Lindstr\\\"om-type lemmas to Stembridge-type theorems, with applications to walks, groves, and alternating flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Owen Biesel","submitted_at":"2018-05-25T16:33:53Z","abstract_excerpt":"We prove that Fomin's generalization of Lindstr\\\"om's lemma for paths on acyclic directed graphs to walks on general directed graphs also generalizes a theorem of Stembridge in the same way. Moreover, we show that whenever a family of operations satisfies a Lindstr\\\"om-type determinant relation, a related family of operations satisfies a Stembridge-type Pfaffian relation. We give example applications to Kenyon and Wilson's work on groves and to Talaska's work on alternating flows."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10239","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":"2026-05-18T00:14:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"up/WNTGCepYJTijaPQzd23wH6QzAFAJqK41tI3UmyRxGVVI9kNYui6hwDCnyxHZvoDV5KtPSHRT8u/7xEIvQBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T16:40:02.524555Z"},"content_sha256":"7f44b1dd9154969e57b4914884c4f01e5fac7086da5f61eea87ba25a30fa3494","schema_version":"1.0","event_id":"sha256:7f44b1dd9154969e57b4914884c4f01e5fac7086da5f61eea87ba25a30fa3494"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AHMHKGY6F2W5QEJVM43GRTFOAI/bundle.json","state_url":"https://pith.science/pith/AHMHKGY6F2W5QEJVM43GRTFOAI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AHMHKGY6F2W5QEJVM43GRTFOAI/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":"2026-06-08T16:40:02Z","links":{"resolver":"https://pith.science/pith/AHMHKGY6F2W5QEJVM43GRTFOAI","bundle":"https://pith.science/pith/AHMHKGY6F2W5QEJVM43GRTFOAI/bundle.json","state":"https://pith.science/pith/AHMHKGY6F2W5QEJVM43GRTFOAI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AHMHKGY6F2W5QEJVM43GRTFOAI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:AHMHKGY6F2W5QEJVM43GRTFOAI","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":"d3fbf27016dd6d21e2eb02141ab41b1442166a336470fef9d0ac282e65560e72","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-25T16:33:53Z","title_canon_sha256":"cb73ca09388ea4cb80ddd035299cde681cd8d4cfb0ebc274c4a4442709495b44"},"schema_version":"1.0","source":{"id":"1805.10239","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.10239","created_at":"2026-05-18T00:14:57Z"},{"alias_kind":"arxiv_version","alias_value":"1805.10239v1","created_at":"2026-05-18T00:14:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.10239","created_at":"2026-05-18T00:14:57Z"},{"alias_kind":"pith_short_12","alias_value":"AHMHKGY6F2W5","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AHMHKGY6F2W5QEJV","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AHMHKGY6","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:7f44b1dd9154969e57b4914884c4f01e5fac7086da5f61eea87ba25a30fa3494","target":"graph","created_at":"2026-05-18T00:14:57Z","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 prove that Fomin's generalization of Lindstr\\\"om's lemma for paths on acyclic directed graphs to walks on general directed graphs also generalizes a theorem of Stembridge in the same way. Moreover, we show that whenever a family of operations satisfies a Lindstr\\\"om-type determinant relation, a related family of operations satisfies a Stembridge-type Pfaffian relation. We give example applications to Kenyon and Wilson's work on groves and to Talaska's work on alternating flows.","authors_text":"Owen Biesel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-25T16:33:53Z","title":"A principle for converting Lindstr\\\"om-type lemmas to Stembridge-type theorems, with applications to walks, groves, and alternating flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10239","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":"sha256:8aac288d34db1b3c95592b85a7239b3795a4f8305153e581744b969442d8de7b","target":"record","created_at":"2026-05-18T00:14:57Z","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":"d3fbf27016dd6d21e2eb02141ab41b1442166a336470fef9d0ac282e65560e72","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-25T16:33:53Z","title_canon_sha256":"cb73ca09388ea4cb80ddd035299cde681cd8d4cfb0ebc274c4a4442709495b44"},"schema_version":"1.0","source":{"id":"1805.10239","kind":"arxiv","version":1}},"canonical_sha256":"01d8751b1e2eadd81135673668ccae02241c754464ddea2aea409cb227f81a89","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01d8751b1e2eadd81135673668ccae02241c754464ddea2aea409cb227f81a89","first_computed_at":"2026-05-18T00:14:57.891476Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:57.891476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ecz8brl2DVnL/mpWXKgM3h+dX6prpEadQ2/N+nANaHmY4NoU7j5DlU8glTR3AQfINEsJGw0GiCbjEHuez760Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:57.892196Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.10239","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8aac288d34db1b3c95592b85a7239b3795a4f8305153e581744b969442d8de7b","sha256:7f44b1dd9154969e57b4914884c4f01e5fac7086da5f61eea87ba25a30fa3494"],"state_sha256":"184cfcd534a9301974321df3388ce328cf40c1e18bd1c7c4156a6f14bf0ece86"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B/wvCsi+6V0vsTMKCs8tieX9mRdvN2G4N0f8RX2saFdelKNIeakVabHG4d1taAeFoV42WadhUfJn7+ew2g/xCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T16:40:02.528282Z","bundle_sha256":"24507269972cddb0764b49c67a3ffa144f290188d5c80bb14a5f076554e63df6"}}