{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:TD2WXQVKOY46CPIPFTL767TYE7","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":"36d194b44272d7adc4183ad4928e8577ff3584b05f80419cc7978e0034daecf2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-03-28T20:37:26Z","title_canon_sha256":"03d887a06b2e6a57bead4cd94e79e0d2752d7e6b3d5cf0c95308a7a99fb5ad89"},"schema_version":"1.0","source":{"id":"2203.15079","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.15079","created_at":"2026-07-05T06:48:44Z"},{"alias_kind":"arxiv_version","alias_value":"2203.15079v3","created_at":"2026-07-05T06:48:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.15079","created_at":"2026-07-05T06:48:44Z"},{"alias_kind":"pith_short_12","alias_value":"TD2WXQVKOY46","created_at":"2026-07-05T06:48:44Z"},{"alias_kind":"pith_short_16","alias_value":"TD2WXQVKOY46CPIP","created_at":"2026-07-05T06:48:44Z"},{"alias_kind":"pith_short_8","alias_value":"TD2WXQVK","created_at":"2026-07-05T06:48:44Z"}],"graph_snapshots":[{"event_id":"sha256:10531c506c6e7f1d6dadf41f742c9ee6a6c6b33a667819e23c34fd4ffe658183","target":"graph","created_at":"2026-07-05T06:48:44Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2203.15079/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We make precise and prove a conjecture of Klivans about actions of the sandpile group on spanning trees. More specifically, the conjecture states that there exists a unique ``suitably nice'' sandpile torsor structure on plane graphs which is induced by rotor-routing.\n  First, we rigorously define a sandpile torsor algorithm (on plane graphs) to be a map which associates each plane graph (i.e., planar graph with an appropriate ribbon structure) with a free transitive action of its sandpile group on its spanning trees. Then, we define a notion of consistency, which requires a torsor algorithm to","authors_text":"Alex McDonough, Ankan Ganguly","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-03-28T20:37:26Z","title":"Rotor-Routing Induces the Only Consistent Sandpile Torsor Structure on Plane Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.15079","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":"sha256:61e69eb95789443edac65c4a23da05fc8e229d76a5c34b530a369aa40e3e9d6c","target":"record","created_at":"2026-07-05T06:48:44Z","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":"36d194b44272d7adc4183ad4928e8577ff3584b05f80419cc7978e0034daecf2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-03-28T20:37:26Z","title_canon_sha256":"03d887a06b2e6a57bead4cd94e79e0d2752d7e6b3d5cf0c95308a7a99fb5ad89"},"schema_version":"1.0","source":{"id":"2203.15079","kind":"arxiv","version":3}},"canonical_sha256":"98f56bc2aa7639e13d0f2cd7ff7e7827d986d8e08aad44e9dd4e58e97ef77e82","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98f56bc2aa7639e13d0f2cd7ff7e7827d986d8e08aad44e9dd4e58e97ef77e82","first_computed_at":"2026-07-05T06:48:44.660555Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:48:44.660555Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RlC5yZ/AsFRA8ekDOrfAOhx3Xt/iQutXGiG2jcuaIaxXxlAgx0/DT1IbE01GruIxFRG4KRqG8PmYsAaFqUQ7DA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:48:44.661063Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.15079","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61e69eb95789443edac65c4a23da05fc8e229d76a5c34b530a369aa40e3e9d6c","sha256:10531c506c6e7f1d6dadf41f742c9ee6a6c6b33a667819e23c34fd4ffe658183"],"state_sha256":"092258f5bdda50de0eb679c39e8c15d7e04d4085fb976093fc624662ea08b4a1"}