{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:HVD4XY3OSPHSS226TBOBYSD6IC","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":"bf71c6270a2f63fca52d86a5bd0dd14e432229aab37e85b4e011701c40a6a3b8","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2007-08-20T18:19:14Z","title_canon_sha256":"1cd55d0112f7b461d7330fb7f4b9ae7a4dfdab0da19a6cd593926f8432f89b38"},"schema_version":"1.0","source":{"id":"0708.2478","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0708.2478","created_at":"2026-07-04T15:50:18Z"},{"alias_kind":"arxiv_version","alias_value":"0708.2478v3","created_at":"2026-07-04T15:50:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0708.2478","created_at":"2026-07-04T15:50:18Z"},{"alias_kind":"pith_short_12","alias_value":"HVD4XY3OSPHS","created_at":"2026-07-04T15:50:18Z"},{"alias_kind":"pith_short_16","alias_value":"HVD4XY3OSPHSS226","created_at":"2026-07-04T15:50:18Z"},{"alias_kind":"pith_short_8","alias_value":"HVD4XY3O","created_at":"2026-07-04T15:50:18Z"}],"graph_snapshots":[{"event_id":"sha256:0126723c5a9d44a0792c868ba34b50d771cb9e0d5c8d890120f1c7f5393d3ffa","target":"graph","created_at":"2026-07-04T15:50:18Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0708.2478/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a recurrence which we term the multidimensional cube recurrence, generalizing the octahedron recurrence studied by Propp, Fomin and Zelevinsky, Speyer, and Fock and Goncharov and the three-dimensional cube recurrence studied by Fomin and Zelevinsky, and Carroll and Speyer. The states of this recurrence are indexed by tilings of a polygon with rhombi, and the variables in the recurrence are indexed by vertices of these tilings. We travel from one state of the recurrence to another by performing elementary flips. We show that the values of the recurrence are independent of the order","authors_text":"Andre Henriques, David E. Speyer","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2007-08-20T18:19:14Z","title":"The Multidimensional Cube Recurrence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0708.2478","kind":"arxiv","version":3},"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":"sha256:8ed63933cf08850fc810bb2cf898c2f54950789a546344037716e4af55723561","target":"record","created_at":"2026-07-04T15:50:18Z","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":"bf71c6270a2f63fca52d86a5bd0dd14e432229aab37e85b4e011701c40a6a3b8","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2007-08-20T18:19:14Z","title_canon_sha256":"1cd55d0112f7b461d7330fb7f4b9ae7a4dfdab0da19a6cd593926f8432f89b38"},"schema_version":"1.0","source":{"id":"0708.2478","kind":"arxiv","version":3}},"canonical_sha256":"3d47cbe36e93cf296b5e985c1c487e408c298ac250665117308a3a66520002e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d47cbe36e93cf296b5e985c1c487e408c298ac250665117308a3a66520002e0","first_computed_at":"2026-07-04T15:50:18.474200Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:50:18.474200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bJxo3IDmcOMA2UfkJUoHMDyUVyDgYPCSQahDpG4PSaLLwmjd67vclRd13q6FTi53TDvjxHpNqhluLUtq7AjDBQ==","signature_status":"signed_v1","signed_at":"2026-07-04T15:50:18.474615Z","signed_message":"canonical_sha256_bytes"},"source_id":"0708.2478","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ed63933cf08850fc810bb2cf898c2f54950789a546344037716e4af55723561","sha256:0126723c5a9d44a0792c868ba34b50d771cb9e0d5c8d890120f1c7f5393d3ffa"],"state_sha256":"3a2f005cde289b3925f34f761161ac5a994de9c5db273db19bba106fa44e276d"}