{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:2ZRLE5ZPKGBYMXAUVXLZHVGGIZ","short_pith_number":"pith:2ZRLE5ZP","canonical_record":{"source":{"id":"2607.14028","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-15T16:57:33Z","cross_cats_sorted":[],"title_canon_sha256":"838779ebf6d43673c51c549916fde682ffd82b2cabedaf04a3deb5b890225587","abstract_canon_sha256":"9deb26a1515353553bb7eb3e2238e52e712c2b6d3796cfe89752aa941e5c74ab"},"schema_version":"1.0"},"canonical_sha256":"d662b2772f5183865c14add793d4c646676c5f99e7a9b80702615b0e697da373","source":{"kind":"arxiv","id":"2607.14028","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.14028","created_at":"2026-07-16T01:23:20Z"},{"alias_kind":"arxiv_version","alias_value":"2607.14028v1","created_at":"2026-07-16T01:23:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.14028","created_at":"2026-07-16T01:23:20Z"},{"alias_kind":"pith_short_12","alias_value":"2ZRLE5ZPKGBY","created_at":"2026-07-16T01:23:20Z"},{"alias_kind":"pith_short_16","alias_value":"2ZRLE5ZPKGBYMXAU","created_at":"2026-07-16T01:23:20Z"},{"alias_kind":"pith_short_8","alias_value":"2ZRLE5ZP","created_at":"2026-07-16T01:23:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:2ZRLE5ZPKGBYMXAUVXLZHVGGIZ","target":"record","payload":{"canonical_record":{"source":{"id":"2607.14028","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-15T16:57:33Z","cross_cats_sorted":[],"title_canon_sha256":"838779ebf6d43673c51c549916fde682ffd82b2cabedaf04a3deb5b890225587","abstract_canon_sha256":"9deb26a1515353553bb7eb3e2238e52e712c2b6d3796cfe89752aa941e5c74ab"},"schema_version":"1.0"},"canonical_sha256":"d662b2772f5183865c14add793d4c646676c5f99e7a9b80702615b0e697da373","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-16T01:23:20.456522Z","signature_b64":"kgQG5Gb2SuLZUf5+RSazgdur1iU/A78WOhs8h0Bd1DwGKgx49sx2RIFZ91p/xxJJpXJv4UCOvCwR/6/VLV8yBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d662b2772f5183865c14add793d4c646676c5f99e7a9b80702615b0e697da373","last_reissued_at":"2026-07-16T01:23:20.455625Z","signature_status":"signed_v1","first_computed_at":"2026-07-16T01:23:20.455625Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.14028","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":"2026-07-16T01:23:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l4ZKvqeOXjywYnA5crY50/iRtR2spSMb6LpWUhS4rnkH34Z1lgY0lh9bXTHSCyJyAPlFDkBqigDEN9oEDvzYDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T02:27:53.621556Z"},"content_sha256":"edb205e7089415071aee1a59ba0b2497d6acfadf8bf15b68dc3649ec72a4d27a","schema_version":"1.0","event_id":"sha256:edb205e7089415071aee1a59ba0b2497d6acfadf8bf15b68dc3649ec72a4d27a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:2ZRLE5ZPKGBYMXAUVXLZHVGGIZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cyclic Sieving for Staircase Plane Partitions via Crystals and Electrical Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jesse Kim, Sam Hopkins, Stephan Pfannerer","submitted_at":"2026-07-15T16:57:33Z","abstract_excerpt":"We prove a cyclic sieving result for the action of promotion on the staircase plane partitions of height two. Our proof has two major algebraic inputs: an interpretation of this promotion action in terms of tensor powers of the spin crystal that was recently studied by Pappe--Pfannerer--Schilling--Simone, and the bush basis of the degree two part of the coordinate ring of the space of electrical networks that was recently introduced by Gao--Lam--Xu. Moreover, we explain how the existence of an electrical canonical basis in all degrees would yield cyclic sieving for promotion of staircase plane"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.14028","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.14028/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-16T01:23:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0WizmOmf6+GrvGIaTS8wceFDGpnAdvhDEoEYoJuv8W0zQOz7fUl1Pv6zXMJlsqvNQeCreRkYCwzQqGax112/AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T02:27:53.622458Z"},"content_sha256":"d97715ebd27cda6d2a499ee78ebeb641597ee3e22124a384e9010a08f08e8366","schema_version":"1.0","event_id":"sha256:d97715ebd27cda6d2a499ee78ebeb641597ee3e22124a384e9010a08f08e8366"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2ZRLE5ZPKGBYMXAUVXLZHVGGIZ/bundle.json","state_url":"https://pith.science/pith/2ZRLE5ZPKGBYMXAUVXLZHVGGIZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2ZRLE5ZPKGBYMXAUVXLZHVGGIZ/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":"2026-08-18T02:27:53Z","links":{"resolver":"https://pith.science/pith/2ZRLE5ZPKGBYMXAUVXLZHVGGIZ","bundle":"https://pith.science/pith/2ZRLE5ZPKGBYMXAUVXLZHVGGIZ/bundle.json","state":"https://pith.science/pith/2ZRLE5ZPKGBYMXAUVXLZHVGGIZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2ZRLE5ZPKGBYMXAUVXLZHVGGIZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:2ZRLE5ZPKGBYMXAUVXLZHVGGIZ","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":"9deb26a1515353553bb7eb3e2238e52e712c2b6d3796cfe89752aa941e5c74ab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-15T16:57:33Z","title_canon_sha256":"838779ebf6d43673c51c549916fde682ffd82b2cabedaf04a3deb5b890225587"},"schema_version":"1.0","source":{"id":"2607.14028","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.14028","created_at":"2026-07-16T01:23:20Z"},{"alias_kind":"arxiv_version","alias_value":"2607.14028v1","created_at":"2026-07-16T01:23:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.14028","created_at":"2026-07-16T01:23:20Z"},{"alias_kind":"pith_short_12","alias_value":"2ZRLE5ZPKGBY","created_at":"2026-07-16T01:23:20Z"},{"alias_kind":"pith_short_16","alias_value":"2ZRLE5ZPKGBYMXAU","created_at":"2026-07-16T01:23:20Z"},{"alias_kind":"pith_short_8","alias_value":"2ZRLE5ZP","created_at":"2026-07-16T01:23:20Z"}],"graph_snapshots":[{"event_id":"sha256:d97715ebd27cda6d2a499ee78ebeb641597ee3e22124a384e9010a08f08e8366","target":"graph","created_at":"2026-07-16T01:23:20Z","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/2607.14028/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a cyclic sieving result for the action of promotion on the staircase plane partitions of height two. Our proof has two major algebraic inputs: an interpretation of this promotion action in terms of tensor powers of the spin crystal that was recently studied by Pappe--Pfannerer--Schilling--Simone, and the bush basis of the degree two part of the coordinate ring of the space of electrical networks that was recently introduced by Gao--Lam--Xu. Moreover, we explain how the existence of an electrical canonical basis in all degrees would yield cyclic sieving for promotion of staircase plane","authors_text":"Jesse Kim, Sam Hopkins, Stephan Pfannerer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-15T16:57:33Z","title":"Cyclic Sieving for Staircase Plane Partitions via Crystals and Electrical Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.14028","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:edb205e7089415071aee1a59ba0b2497d6acfadf8bf15b68dc3649ec72a4d27a","target":"record","created_at":"2026-07-16T01:23:20Z","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":"9deb26a1515353553bb7eb3e2238e52e712c2b6d3796cfe89752aa941e5c74ab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-15T16:57:33Z","title_canon_sha256":"838779ebf6d43673c51c549916fde682ffd82b2cabedaf04a3deb5b890225587"},"schema_version":"1.0","source":{"id":"2607.14028","kind":"arxiv","version":1}},"canonical_sha256":"d662b2772f5183865c14add793d4c646676c5f99e7a9b80702615b0e697da373","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d662b2772f5183865c14add793d4c646676c5f99e7a9b80702615b0e697da373","first_computed_at":"2026-07-16T01:23:20.455625Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-16T01:23:20.455625Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kgQG5Gb2SuLZUf5+RSazgdur1iU/A78WOhs8h0Bd1DwGKgx49sx2RIFZ91p/xxJJpXJv4UCOvCwR/6/VLV8yBQ==","signature_status":"signed_v1","signed_at":"2026-07-16T01:23:20.456522Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.14028","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:edb205e7089415071aee1a59ba0b2497d6acfadf8bf15b68dc3649ec72a4d27a","sha256:d97715ebd27cda6d2a499ee78ebeb641597ee3e22124a384e9010a08f08e8366"],"state_sha256":"3844d5168878f94606499bb60a405aec4373fdab5104fe20a310b07ba7a1dca6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qGaE7k2atpLrDInWElDuEc2eNZPQ1v/KQ3e/jb/4x+ipkQZ+MAk6aD2rnEyqx4O0E1HwWD/ehIttOKMUzi/gCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T02:27:53.628388Z","bundle_sha256":"e0655f1a3bd95fa8304d89432a6e0548f2ce2b3c2e43a9e0de40a5d69c0a34a0"}}