{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:7TKEJQW74WAWCYLEZFJ2YOJWJU","short_pith_number":"pith:7TKEJQW7","canonical_record":{"source":{"id":"1410.7683","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-28T16:09:22Z","cross_cats_sorted":[],"title_canon_sha256":"55c4b598a676e63cabca4cbf7dc2dfb5251e1d42fcfffb7596257bb09d7aee70","abstract_canon_sha256":"ed7b306eb385be8e3d2511eca467c651b104e185b3b007cb2cdadc29e85db4f1"},"schema_version":"1.0"},"canonical_sha256":"fcd444c2dfe581616164c953ac39364d162e987c25a9a772f03a6a78a57bb85b","source":{"kind":"arxiv","id":"1410.7683","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.7683","created_at":"2026-05-18T01:15:53Z"},{"alias_kind":"arxiv_version","alias_value":"1410.7683v2","created_at":"2026-05-18T01:15:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7683","created_at":"2026-05-18T01:15:53Z"},{"alias_kind":"pith_short_12","alias_value":"7TKEJQW74WAW","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7TKEJQW74WAWCYLE","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7TKEJQW7","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:7TKEJQW74WAWCYLEZFJ2YOJWJU","target":"record","payload":{"canonical_record":{"source":{"id":"1410.7683","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-28T16:09:22Z","cross_cats_sorted":[],"title_canon_sha256":"55c4b598a676e63cabca4cbf7dc2dfb5251e1d42fcfffb7596257bb09d7aee70","abstract_canon_sha256":"ed7b306eb385be8e3d2511eca467c651b104e185b3b007cb2cdadc29e85db4f1"},"schema_version":"1.0"},"canonical_sha256":"fcd444c2dfe581616164c953ac39364d162e987c25a9a772f03a6a78a57bb85b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:53.273369Z","signature_b64":"/Ao4rigfc1Zq5i9ItzAZolInz9UBPGd0rrm3GrZ6BdKqmSoiw3Bzx97bh5oUJUQQYopZ6Di3U+1UoU0Zrnh6BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fcd444c2dfe581616164c953ac39364d162e987c25a9a772f03a6a78a57bb85b","last_reissued_at":"2026-05-18T01:15:53.272896Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:53.272896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.7683","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":"2026-05-18T01:15:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"85IEifxwMDOrdXFNx3pNX5fbZopCkwxdondMvhBv0MG8kEACFaJtTzj/NxLsJS4HPFJANNBGrvBiRHS9mzPeDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T01:59:06.570872Z"},"content_sha256":"2153f8318f8c939511727f65981c61bd2a14dc561b0d2615b78e804a43ceafde","schema_version":"1.0","event_id":"sha256:2153f8318f8c939511727f65981c61bd2a14dc561b0d2615b78e804a43ceafde"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:7TKEJQW74WAWCYLEZFJ2YOJWJU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dual Filtered Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Pavlo Pylyavskyy, Rebecca Patrias","submitted_at":"2014-10-28T16:09:22Z","abstract_excerpt":"We define a K-theoretic analogue of Fomin's dual graded graphs, which we call dual filtered graphs. The key formula in the definition is DU-UD= D + I. Our major examples are K-theoretic analogues of Young's lattice, of shifted Young's lattice, and of the Young-Fibonacci lattice. We suggest notions of tableaux, insertion algorithms, and growth rules whenever such objects are not already present in the literature. We also provide a large number of other examples. Most of our examples arise via two constructions, which we call the Pieri construction and the Mobius construction. The Pieri construc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7683","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":"2026-05-18T01:15:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tMBAl83sExngQAWpwMO/dtdSTk1xWC+E8aLw3sg+St3Kv9x8wc1uS75cJw4zTuDmpnRfUhszToro9OXtmwONDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T01:59:06.571463Z"},"content_sha256":"8bd8093990980fff36f408a1d48d6f8c8ee64086aefba204ee926673ca3c436e","schema_version":"1.0","event_id":"sha256:8bd8093990980fff36f408a1d48d6f8c8ee64086aefba204ee926673ca3c436e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7TKEJQW74WAWCYLEZFJ2YOJWJU/bundle.json","state_url":"https://pith.science/pith/7TKEJQW74WAWCYLEZFJ2YOJWJU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7TKEJQW74WAWCYLEZFJ2YOJWJU/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":"2026-06-05T01:59:06Z","links":{"resolver":"https://pith.science/pith/7TKEJQW74WAWCYLEZFJ2YOJWJU","bundle":"https://pith.science/pith/7TKEJQW74WAWCYLEZFJ2YOJWJU/bundle.json","state":"https://pith.science/pith/7TKEJQW74WAWCYLEZFJ2YOJWJU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7TKEJQW74WAWCYLEZFJ2YOJWJU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7TKEJQW74WAWCYLEZFJ2YOJWJU","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":"ed7b306eb385be8e3d2511eca467c651b104e185b3b007cb2cdadc29e85db4f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-28T16:09:22Z","title_canon_sha256":"55c4b598a676e63cabca4cbf7dc2dfb5251e1d42fcfffb7596257bb09d7aee70"},"schema_version":"1.0","source":{"id":"1410.7683","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.7683","created_at":"2026-05-18T01:15:53Z"},{"alias_kind":"arxiv_version","alias_value":"1410.7683v2","created_at":"2026-05-18T01:15:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7683","created_at":"2026-05-18T01:15:53Z"},{"alias_kind":"pith_short_12","alias_value":"7TKEJQW74WAW","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7TKEJQW74WAWCYLE","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7TKEJQW7","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:8bd8093990980fff36f408a1d48d6f8c8ee64086aefba204ee926673ca3c436e","target":"graph","created_at":"2026-05-18T01:15:53Z","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 define a K-theoretic analogue of Fomin's dual graded graphs, which we call dual filtered graphs. The key formula in the definition is DU-UD= D + I. Our major examples are K-theoretic analogues of Young's lattice, of shifted Young's lattice, and of the Young-Fibonacci lattice. We suggest notions of tableaux, insertion algorithms, and growth rules whenever such objects are not already present in the literature. We also provide a large number of other examples. Most of our examples arise via two constructions, which we call the Pieri construction and the Mobius construction. The Pieri construc","authors_text":"Pavlo Pylyavskyy, Rebecca Patrias","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-28T16:09:22Z","title":"Dual Filtered Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7683","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":"sha256:2153f8318f8c939511727f65981c61bd2a14dc561b0d2615b78e804a43ceafde","target":"record","created_at":"2026-05-18T01:15:53Z","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":"ed7b306eb385be8e3d2511eca467c651b104e185b3b007cb2cdadc29e85db4f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-28T16:09:22Z","title_canon_sha256":"55c4b598a676e63cabca4cbf7dc2dfb5251e1d42fcfffb7596257bb09d7aee70"},"schema_version":"1.0","source":{"id":"1410.7683","kind":"arxiv","version":2}},"canonical_sha256":"fcd444c2dfe581616164c953ac39364d162e987c25a9a772f03a6a78a57bb85b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fcd444c2dfe581616164c953ac39364d162e987c25a9a772f03a6a78a57bb85b","first_computed_at":"2026-05-18T01:15:53.272896Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:53.272896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/Ao4rigfc1Zq5i9ItzAZolInz9UBPGd0rrm3GrZ6BdKqmSoiw3Bzx97bh5oUJUQQYopZ6Di3U+1UoU0Zrnh6BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:53.273369Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.7683","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2153f8318f8c939511727f65981c61bd2a14dc561b0d2615b78e804a43ceafde","sha256:8bd8093990980fff36f408a1d48d6f8c8ee64086aefba204ee926673ca3c436e"],"state_sha256":"b3b86bb1be8a6befefe7a72e5ee4de44a56c8e686b50ebb0d3cfe0ecb8b6eb06"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"01urWEJlQ30ybVU8y27LzEpdSxq+1z6g6SPRtFUR7JnBGHMZ38gflPFSDyF9J1aFX2iK9OR2aK1388w8oqqfCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T01:59:06.574562Z","bundle_sha256":"1d3051fea6a5f627ffcefb34d6b5fb0967f4e17e716521f7d44e4f785cc25536"}}