{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6AWC6PJ4OIJK3M63WKW5SDGPOR","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":"cdb0b3d04690b7a166612f540c9a2491bf2719a80f449a90dcca52c9806e8f40","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-10T15:41:27Z","title_canon_sha256":"c918e7cb077c1e8d0eb98a9ee89d7b9e077e4dbdcecf43ab6144c22283422a53"},"schema_version":"1.0","source":{"id":"1501.02362","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.02362","created_at":"2026-05-18T02:29:38Z"},{"alias_kind":"arxiv_version","alias_value":"1501.02362v1","created_at":"2026-05-18T02:29:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.02362","created_at":"2026-05-18T02:29:38Z"},{"alias_kind":"pith_short_12","alias_value":"6AWC6PJ4OIJK","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6AWC6PJ4OIJK3M63","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6AWC6PJ4","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:fd7e4a2b8ffab5979a4dfa964af71857da03e7cbd30548a1c26749152f5e5955","target":"graph","created_at":"2026-05-18T02:29:38Z","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"},"paper":{"abstract_excerpt":"This article has the sole purpose of presenting a simple, self-contained and direct proof of the fact that the Pak-Stanley labeling is a bijection. The construction behind the proof is subsumed in a forthcoming paper [R. Duarte and A. Guedes de Oliveira, The braid and the Shi arrangements and the Pak-Stanley labeling, Eur. J. Combinatorics, in press.], but an actual self-contained proof is not explicitly included in that paper.","authors_text":"Ant\\'onio Guedes de Oliveira, Rui Duarte","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-10T15:41:27Z","title":"Note on the bijectivity of the Pak-Stanley labelling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02362","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":"sha256:1a99cb46f00e1ad543dd54b9dce241264b75aea695c351b9c612fe22b731100e","target":"record","created_at":"2026-05-18T02:29:38Z","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":"cdb0b3d04690b7a166612f540c9a2491bf2719a80f449a90dcca52c9806e8f40","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-10T15:41:27Z","title_canon_sha256":"c918e7cb077c1e8d0eb98a9ee89d7b9e077e4dbdcecf43ab6144c22283422a53"},"schema_version":"1.0","source":{"id":"1501.02362","kind":"arxiv","version":1}},"canonical_sha256":"f02c2f3d3c7212adb3dbb2add90ccf7443f94e198e1a3d02dbc1767081e8b363","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f02c2f3d3c7212adb3dbb2add90ccf7443f94e198e1a3d02dbc1767081e8b363","first_computed_at":"2026-05-18T02:29:38.155730Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:38.155730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M06gbAHEezyOMfsN6dsHzyX8LVWiN1q8OFDEE6KsJdKPofq7nBkZimM9iVT0JZozdqSK3pppT2mWuNinfNvWCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:38.156190Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.02362","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a99cb46f00e1ad543dd54b9dce241264b75aea695c351b9c612fe22b731100e","sha256:fd7e4a2b8ffab5979a4dfa964af71857da03e7cbd30548a1c26749152f5e5955"],"state_sha256":"f8eb52088259b8d821188aa8a15f51f8fa19c902d999f1ac0204a4febfdb3ba9"}