{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:4QIIEGWP3YCBUJZNYH2YAQO232","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":"1af2bc5fd720df7f04edba328bdf964dbc6507cfbb5da1fe5a11d6e619d0d47a","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-04-07T05:04:26Z","title_canon_sha256":"87661fe6c674a54fd109d41ed15b729ba4be95f5dbef9864fbbad3b6bd334ccf"},"schema_version":"1.0","source":{"id":"2104.02914","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.02914","created_at":"2026-07-05T06:02:44Z"},{"alias_kind":"arxiv_version","alias_value":"2104.02914v2","created_at":"2026-07-05T06:02:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.02914","created_at":"2026-07-05T06:02:44Z"},{"alias_kind":"pith_short_12","alias_value":"4QIIEGWP3YCB","created_at":"2026-07-05T06:02:44Z"},{"alias_kind":"pith_short_16","alias_value":"4QIIEGWP3YCBUJZN","created_at":"2026-07-05T06:02:44Z"},{"alias_kind":"pith_short_8","alias_value":"4QIIEGWP","created_at":"2026-07-05T06:02:44Z"}],"graph_snapshots":[{"event_id":"sha256:76baf1ebbd114ebafb6539c6f30b66d17c580588270f67a5d907f97e9009a9a9","target":"graph","created_at":"2026-07-05T06:02:44Z","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/2104.02914/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce an additive basis of the integral cohomology ring of the Peterson variety which reflects the geometry of certain subvarieties of the Peterson variety. We explain the positivity of the structure constants from a geometric viewpoint, and provide a manifestly positive combinatorial formula for them. We also prove that our basis coincides with the additive basis introduced by Harada-Tymoczko.","authors_text":"Haozhi Zeng, Hideya Kuwata, Hiraku Abe, Tatsuya Horiguchi","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-04-07T05:04:26Z","title":"Geometry of Peterson Schubert calculus in type A and left-right diagrams"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.02914","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:f326a585a30f3f2d1ebc77d8f440e7c4c5e5a2dd00270d8d3ca41db623ccba48","target":"record","created_at":"2026-07-05T06:02:44Z","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":"1af2bc5fd720df7f04edba328bdf964dbc6507cfbb5da1fe5a11d6e619d0d47a","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-04-07T05:04:26Z","title_canon_sha256":"87661fe6c674a54fd109d41ed15b729ba4be95f5dbef9864fbbad3b6bd334ccf"},"schema_version":"1.0","source":{"id":"2104.02914","kind":"arxiv","version":2}},"canonical_sha256":"e410821acfde041a272dc1f58041dade85c64da955f396db32bca073f9905aa4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e410821acfde041a272dc1f58041dade85c64da955f396db32bca073f9905aa4","first_computed_at":"2026-07-05T06:02:44.032597Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:02:44.032597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TQq+XRF8z/ggvVkEeeGZTL+tB+t/nNjhytqgmLm/0pi54oz2YjpGlh8fMhPZLX80saJZGrAH+y8w4Ya1JO29DA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:02:44.033007Z","signed_message":"canonical_sha256_bytes"},"source_id":"2104.02914","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f326a585a30f3f2d1ebc77d8f440e7c4c5e5a2dd00270d8d3ca41db623ccba48","sha256:76baf1ebbd114ebafb6539c6f30b66d17c580588270f67a5d907f97e9009a9a9"],"state_sha256":"8088e43a6da980880617566f2d62dea1dea042d5ecac08e068552c98572ee028"}