{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:HZMQPUJSK5XAUPWWEBASK4AV5E","short_pith_number":"pith:HZMQPUJS","canonical_record":{"source":{"id":"math/0604333","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.RT","submitted_at":"2006-04-14T10:09:33Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"a470802f31a40ebb0f4e347e94c0af8fbb058a36f199d6af7f80e894673f9a3c","abstract_canon_sha256":"fa64e55db87cce963fba604baa162feb9c427ebcf879a7479bea817c28669fb0"},"schema_version":"1.0"},"canonical_sha256":"3e5907d132576e0a3ed62041257015e93fcdc62decffd95267453b49540700c9","source":{"kind":"arxiv","id":"math/0604333","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0604333","created_at":"2026-05-18T04:35:57Z"},{"alias_kind":"arxiv_version","alias_value":"math/0604333v1","created_at":"2026-05-18T04:35:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0604333","created_at":"2026-05-18T04:35:57Z"},{"alias_kind":"pith_short_12","alias_value":"HZMQPUJSK5XA","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"HZMQPUJSK5XAUPWW","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"HZMQPUJS","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:HZMQPUJSK5XAUPWWEBASK4AV5E","target":"record","payload":{"canonical_record":{"source":{"id":"math/0604333","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.RT","submitted_at":"2006-04-14T10:09:33Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"a470802f31a40ebb0f4e347e94c0af8fbb058a36f199d6af7f80e894673f9a3c","abstract_canon_sha256":"fa64e55db87cce963fba604baa162feb9c427ebcf879a7479bea817c28669fb0"},"schema_version":"1.0"},"canonical_sha256":"3e5907d132576e0a3ed62041257015e93fcdc62decffd95267453b49540700c9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:35:57.833330Z","signature_b64":"kMApWT/hI/jgvNXaT/TmXhjfQrNM/nCshfHzCLgkv0fmxJOIOhkt5g12RjERvoU1Oz6+TaW0rNb/Nw/GXvhGCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e5907d132576e0a3ed62041257015e93fcdc62decffd95267453b49540700c9","last_reissued_at":"2026-05-18T04:35:57.832470Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:35:57.832470Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0604333","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:35:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ulGCC7udw+VfTIP5ubL/4KXSmZdbcJCCzBteOlk4Cf2ki/3l1StN8PxThoX5UwdOa6cewKzlMPrZzEUFnpRGBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T14:13:20.794190Z"},"content_sha256":"861826a76b92841b762965b5470d78bc70c6b6a90e85dc4f477539f70c6eda12","schema_version":"1.0","event_id":"sha256:861826a76b92841b762965b5470d78bc70c6b6a90e85dc4f477539f70c6eda12"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:HZMQPUJSK5XAUPWWEBASK4AV5E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Combinatorics of $A_2$-crystals","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"A.V. Karzanov, G.A. Koshevoy, V.I. Danilov","submitted_at":"2006-04-14T10:09:33Z","abstract_excerpt":"We show that a connected regular $A_2$-crystal (the crystal graph of an irreducible representation of $sl_3$) can be produced from two half-grids by replicating them and glying together in a certain way. Also some extensions and related aspects are discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0604333","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:35:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SModgziGWov0Tx76oQ1x7nvSmk1IyNqYEVyM4MKpyubOurWvSVYi4PkwhzV6cEFEc1LVgiqtY8INsSLI5T/kAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T14:13:20.794554Z"},"content_sha256":"6d4dd6aee364920f0571d1f4493e5ba809a6675881670ddb4c8d73c784b051f3","schema_version":"1.0","event_id":"sha256:6d4dd6aee364920f0571d1f4493e5ba809a6675881670ddb4c8d73c784b051f3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HZMQPUJSK5XAUPWWEBASK4AV5E/bundle.json","state_url":"https://pith.science/pith/HZMQPUJSK5XAUPWWEBASK4AV5E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HZMQPUJSK5XAUPWWEBASK4AV5E/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-02T14:13:20Z","links":{"resolver":"https://pith.science/pith/HZMQPUJSK5XAUPWWEBASK4AV5E","bundle":"https://pith.science/pith/HZMQPUJSK5XAUPWWEBASK4AV5E/bundle.json","state":"https://pith.science/pith/HZMQPUJSK5XAUPWWEBASK4AV5E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HZMQPUJSK5XAUPWWEBASK4AV5E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:HZMQPUJSK5XAUPWWEBASK4AV5E","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":"fa64e55db87cce963fba604baa162feb9c427ebcf879a7479bea817c28669fb0","cross_cats_sorted":["math.CO"],"license":"","primary_cat":"math.RT","submitted_at":"2006-04-14T10:09:33Z","title_canon_sha256":"a470802f31a40ebb0f4e347e94c0af8fbb058a36f199d6af7f80e894673f9a3c"},"schema_version":"1.0","source":{"id":"math/0604333","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0604333","created_at":"2026-05-18T04:35:57Z"},{"alias_kind":"arxiv_version","alias_value":"math/0604333v1","created_at":"2026-05-18T04:35:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0604333","created_at":"2026-05-18T04:35:57Z"},{"alias_kind":"pith_short_12","alias_value":"HZMQPUJSK5XA","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"HZMQPUJSK5XAUPWW","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"HZMQPUJS","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:6d4dd6aee364920f0571d1f4493e5ba809a6675881670ddb4c8d73c784b051f3","target":"graph","created_at":"2026-05-18T04:35:57Z","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 show that a connected regular $A_2$-crystal (the crystal graph of an irreducible representation of $sl_3$) can be produced from two half-grids by replicating them and glying together in a certain way. Also some extensions and related aspects are discussed.","authors_text":"A.V. Karzanov, G.A. Koshevoy, V.I. Danilov","cross_cats":["math.CO"],"headline":"","license":"","primary_cat":"math.RT","submitted_at":"2006-04-14T10:09:33Z","title":"Combinatorics of $A_2$-crystals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0604333","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":"sha256:861826a76b92841b762965b5470d78bc70c6b6a90e85dc4f477539f70c6eda12","target":"record","created_at":"2026-05-18T04:35:57Z","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":"fa64e55db87cce963fba604baa162feb9c427ebcf879a7479bea817c28669fb0","cross_cats_sorted":["math.CO"],"license":"","primary_cat":"math.RT","submitted_at":"2006-04-14T10:09:33Z","title_canon_sha256":"a470802f31a40ebb0f4e347e94c0af8fbb058a36f199d6af7f80e894673f9a3c"},"schema_version":"1.0","source":{"id":"math/0604333","kind":"arxiv","version":1}},"canonical_sha256":"3e5907d132576e0a3ed62041257015e93fcdc62decffd95267453b49540700c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e5907d132576e0a3ed62041257015e93fcdc62decffd95267453b49540700c9","first_computed_at":"2026-05-18T04:35:57.832470Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:35:57.832470Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kMApWT/hI/jgvNXaT/TmXhjfQrNM/nCshfHzCLgkv0fmxJOIOhkt5g12RjERvoU1Oz6+TaW0rNb/Nw/GXvhGCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:35:57.833330Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0604333","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:861826a76b92841b762965b5470d78bc70c6b6a90e85dc4f477539f70c6eda12","sha256:6d4dd6aee364920f0571d1f4493e5ba809a6675881670ddb4c8d73c784b051f3"],"state_sha256":"543a8ac5ff27e077a2b96fb602edfdfa5f886a919966d81ea48430d9ef83bc2d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nE/0/VHliefly0tVTPoUjzmUZST4sC4VmeE37f+LTtamhfzPt69YSLvXgzFuRb+pZroZvoPjoy/cuzOzo/8wAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T14:13:20.796449Z","bundle_sha256":"e72a6d528fa5c5e096d7adbfd87a350a77e918b9b7cf800a8deab94d5aeab80c"}}