{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:VVPGV25QANHUNJVPDSKKIEVDQ5","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":"0942507b9c16de82433704e723df6f4393127ee67b74c84bbfbaa82cd4e42c08","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-04-18T00:51:15Z","title_canon_sha256":"c7815320a5e648878653aca2575d7f3e56728726ca16d8707788f3927a69a2ae"},"schema_version":"1.0","source":{"id":"1304.4998","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.4998","created_at":"2026-05-18T02:58:57Z"},{"alias_kind":"arxiv_version","alias_value":"1304.4998v2","created_at":"2026-05-18T02:58:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4998","created_at":"2026-05-18T02:58:57Z"},{"alias_kind":"pith_short_12","alias_value":"VVPGV25QANHU","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VVPGV25QANHUNJVP","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VVPGV25Q","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:a9197d5debcfaf1ca3de6d14e51ce6fe40df55150195dbb2ea3ab3aeb169ac8b","target":"graph","created_at":"2026-05-18T02:58:57Z","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":"Orbits of the Weyl reflection groups attached to the simple Lie groups $A_2, C_2, G_2$ and Coxeter group $H_2$ are considered. For each of the groups products of any two orbits are decomposed into the union of the orbits. Results are presented in a single formula for each of the groups. Orbits are considered as functions of two variables and limits for such functions are mentioned.","authors_text":"Agnieszka Tereszkiewicz","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-04-18T00:51:15Z","title":"Complete Decompositions of Coxeter groups orbit products of $A_2, C_2, G_2$ and $H_2$ and some limits for them"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4998","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":"sha256:36005b0bd2161eda8928760bc33519b68aee675eeffe046f46df6395193fc835","target":"record","created_at":"2026-05-18T02:58:57Z","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":"0942507b9c16de82433704e723df6f4393127ee67b74c84bbfbaa82cd4e42c08","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-04-18T00:51:15Z","title_canon_sha256":"c7815320a5e648878653aca2575d7f3e56728726ca16d8707788f3927a69a2ae"},"schema_version":"1.0","source":{"id":"1304.4998","kind":"arxiv","version":2}},"canonical_sha256":"ad5e6aebb0034f46a6af1c94a412a387663ee25d71df76a8f09a99369f83dd04","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad5e6aebb0034f46a6af1c94a412a387663ee25d71df76a8f09a99369f83dd04","first_computed_at":"2026-05-18T02:58:57.263261Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:57.263261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sxHzfPIBD+NrXSMAoQsejJyVjbGTCEX/HxHNGOq5mGZsOQYAEqp47OC3rsxKffGAXVLNix9f2T20ofeYWkDDDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:57.263898Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.4998","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36005b0bd2161eda8928760bc33519b68aee675eeffe046f46df6395193fc835","sha256:a9197d5debcfaf1ca3de6d14e51ce6fe40df55150195dbb2ea3ab3aeb169ac8b"],"state_sha256":"2d9bd546bdceddaa4e3f576c6fd1383c5d90400c2fd66178f5e1e7270653492c"}