{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6RBWUBTTLIIFQ5B4HT3BUD6M6V","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":"00c5b1086f0879d6ab5f0bb1e0a43b8f62cee772880fbbb1f5d2bfc409b7830b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-02-12T02:29:21Z","title_canon_sha256":"f12b34d81edc2f507ba8d7a323e48cf70c7d6af62415d9548eba767e6cc5ed02"},"schema_version":"1.0","source":{"id":"1202.2483","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2483","created_at":"2026-05-18T03:37:08Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2483v3","created_at":"2026-05-18T03:37:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2483","created_at":"2026-05-18T03:37:08Z"},{"alias_kind":"pith_short_12","alias_value":"6RBWUBTTLIIF","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6RBWUBTTLIIFQ5B4","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6RBWUBTT","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:69175b9df2bc308a23cd5aefd79d4eaeb4f67979dfe390746e63d68c0a554162","target":"graph","created_at":"2026-05-18T03:37:08Z","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":"We consider the set of alternating paths on a fixed fully packed loop of size n. This set is in bijection with the set of fully packed loops of size n. Furthermore, for a special choice of fully packed loop, we demonstrate that the set of alternating paths are nested osculating loops, which we call Dyck islands. Dyck islands can be constructed as a union of lattice Dyck paths, and we use this structure to give a simple graphical formula for the calculation of the inversion number of an alternating sign matrix.","authors_text":"Stephen Ng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-02-12T02:29:21Z","title":"Alternating paths of fully packed loops and inversion number"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2483","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":"sha256:864c360b9ef26096b895893579f4333623773b84325dfcc71f3a51b77a7ba45b","target":"record","created_at":"2026-05-18T03:37:08Z","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":"00c5b1086f0879d6ab5f0bb1e0a43b8f62cee772880fbbb1f5d2bfc409b7830b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-02-12T02:29:21Z","title_canon_sha256":"f12b34d81edc2f507ba8d7a323e48cf70c7d6af62415d9548eba767e6cc5ed02"},"schema_version":"1.0","source":{"id":"1202.2483","kind":"arxiv","version":3}},"canonical_sha256":"f4436a06735a1058743c3cf61a0fccf56016aff7f8180760dce392155fc0b575","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4436a06735a1058743c3cf61a0fccf56016aff7f8180760dce392155fc0b575","first_computed_at":"2026-05-18T03:37:08.838438Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:08.838438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ki3aLx7kApuD3z20YyWjyXs+e1r6EfXBzavYfq7pMD5sgvX7HWtom2GTJ/kRiKj/eVZOUdk22P5o+ogTRCntDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:08.839230Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.2483","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:864c360b9ef26096b895893579f4333623773b84325dfcc71f3a51b77a7ba45b","sha256:69175b9df2bc308a23cd5aefd79d4eaeb4f67979dfe390746e63d68c0a554162"],"state_sha256":"02d1a0d496e246acd94cec950908d3d22e7ece6275b27d4c537cf7713ed34f99"}