{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:OYLUDBKPRFQKN2YF4PJ67RZR4Q","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":"1b442416c8ce9a8ceea119bf470792f165fcf59eb9855a8ef54c55cdf2d77f87","cross_cats_sorted":["math.AC","math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-03-27T13:55:04Z","title_canon_sha256":"ef14301c7c79102d8567c2a188fbcff3db6c9013f29d6bebe04e1bd3f1038bca"},"schema_version":"1.0","source":{"id":"2403.18574","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.18574","created_at":"2026-07-05T08:03:50Z"},{"alias_kind":"arxiv_version","alias_value":"2403.18574v2","created_at":"2026-07-05T08:03:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.18574","created_at":"2026-07-05T08:03:50Z"},{"alias_kind":"pith_short_12","alias_value":"OYLUDBKPRFQK","created_at":"2026-07-05T08:03:50Z"},{"alias_kind":"pith_short_16","alias_value":"OYLUDBKPRFQKN2YF","created_at":"2026-07-05T08:03:50Z"},{"alias_kind":"pith_short_8","alias_value":"OYLUDBKP","created_at":"2026-07-05T08:03:50Z"}],"graph_snapshots":[{"event_id":"sha256:83530b8b54ebce58b0e5e85861575680d7ef11a4fa0892cd8e8e7fb9ad79b98d","target":"graph","created_at":"2026-07-05T08:03:50Z","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/2403.18574/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove the Box Conjecture for pairs of commuting nilpotent matrices, as formulated by Iarrobino et al [28]. This describes the Jordan type of the dense orbit in the nilpotent commutator of a given nilpotent matrix. Our main tool is the Burge correspondence between the set of all partitions and a set of binary words [15, 16]. For connection with the algebraic and geometric setup of matrices and orbits we employ some of Shayman's results on invariant subspaces of a nilpotent matrix [45, 46]. Our proof is valid over an arbitrary field.","authors_text":"J. Irving, M. Mastnak, T. Ko\\v{s}ir","cross_cats":["math.AC","math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-03-27T13:55:04Z","title":"A Proof of the Box Conjecture for Commuting Pairs of Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.18574","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":"sha256:625e8dc4107b687f2e7640a622030849200097e8b432454531739b76e33cedf9","target":"record","created_at":"2026-07-05T08:03:50Z","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":"1b442416c8ce9a8ceea119bf470792f165fcf59eb9855a8ef54c55cdf2d77f87","cross_cats_sorted":["math.AC","math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-03-27T13:55:04Z","title_canon_sha256":"ef14301c7c79102d8567c2a188fbcff3db6c9013f29d6bebe04e1bd3f1038bca"},"schema_version":"1.0","source":{"id":"2403.18574","kind":"arxiv","version":2}},"canonical_sha256":"761741854f8960a6eb05e3d3efc731e438a53ee18202352d1b38a257dffab7aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"761741854f8960a6eb05e3d3efc731e438a53ee18202352d1b38a257dffab7aa","first_computed_at":"2026-07-05T08:03:50.793034Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:03:50.793034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gZxUvMirUebGMxzgzUpMprWHTBVGvA5cIe3mKAXvBeiZSnOepe202WWLaTLkeB8t6cRkY6S9jwGJTK4dwEEwDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:03:50.793475Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.18574","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:625e8dc4107b687f2e7640a622030849200097e8b432454531739b76e33cedf9","sha256:83530b8b54ebce58b0e5e85861575680d7ef11a4fa0892cd8e8e7fb9ad79b98d"],"state_sha256":"89cb46c29326289b921979cfda42b701db5f676664d9dd3c4b48ee1a30c7eb26"}