{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:TGGAYFMLNUCQN2ZHEGBCSZIDLT","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":"e9dcd28d4d83dfaad7496a9f71fe70735f5fe430b7ded0cdfe9135c528b8164f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-23T08:12:09Z","title_canon_sha256":"3490e9649ef172ecd875e31f84de85b641331a4333a076e40ed52e39644add34"},"schema_version":"1.0","source":{"id":"1212.5771","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.5771","created_at":"2026-05-18T03:37:51Z"},{"alias_kind":"arxiv_version","alias_value":"1212.5771v1","created_at":"2026-05-18T03:37:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.5771","created_at":"2026-05-18T03:37:51Z"},{"alias_kind":"pith_short_12","alias_value":"TGGAYFMLNUCQ","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TGGAYFMLNUCQN2ZH","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TGGAYFML","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:a1070e5f8cff2f22fdd8a7c472691e9ed72ffc1ad8cd5ca13c4a254903f38c53","target":"graph","created_at":"2026-05-18T03:37:51Z","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":"Regular $A_n$-crystals are certain edge-colored directed graphs which are related to representations of the quantized universal enveloping algebra $U_q(\\mathfrak{sl}_{n+1})$. For such a crystal $K$ with colors $1,2,...,n$, we consider its maximal connected subcrystals with colors $1,...,n-1$ and with colors $2,...,n$ and characterize the interlacing structure for all pairs of these subcrystals. This is used to give a recursive description of the combinatorial structure of $K$ and develop an efficient procedure of assembling $K$.","authors_text":"Alexander V. Karzanov, Gleb A. Koshevoy, Vladimir I. Danilov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-23T08:12:09Z","title":"Assembling crystals of type A"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5771","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":"sha256:3925ea7f4559f2cfdeb3de916ae3a75dcb73df0586841101a3c0752c2c89aea6","target":"record","created_at":"2026-05-18T03:37:51Z","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":"e9dcd28d4d83dfaad7496a9f71fe70735f5fe430b7ded0cdfe9135c528b8164f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-23T08:12:09Z","title_canon_sha256":"3490e9649ef172ecd875e31f84de85b641331a4333a076e40ed52e39644add34"},"schema_version":"1.0","source":{"id":"1212.5771","kind":"arxiv","version":1}},"canonical_sha256":"998c0c158b6d0506eb2721822965035cc1bd1ae408b26956a39104235ef0224e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"998c0c158b6d0506eb2721822965035cc1bd1ae408b26956a39104235ef0224e","first_computed_at":"2026-05-18T03:37:51.416896Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:51.416896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ANlvpOGCl+a1Vx0L6/gayxW3qTtPW557CoLqsM3ibxDVmy04ZgD1Eg7wbG8NZ/PKSa7oTS4k0pS+0lJFmtnqBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:51.417459Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.5771","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3925ea7f4559f2cfdeb3de916ae3a75dcb73df0586841101a3c0752c2c89aea6","sha256:a1070e5f8cff2f22fdd8a7c472691e9ed72ffc1ad8cd5ca13c4a254903f38c53"],"state_sha256":"55a883ff19a3d2b8788f5e3a214b4f9cb50410062eb3bd1e496f0649cfbe2ee8"}