{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VC3FA2K5EKEBJZX3Q6GDS6P3GP","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":"2226902523060bf1f0e36bc5229bc038bd0bd633a05fe6c7589e65ab18ac7553","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-04-11T16:01:35Z","title_canon_sha256":"7223ca9b15394eba40a68151f3b92bbd34e754ee4123b4da638642e4bfa8aecd"},"schema_version":"1.0","source":{"id":"1204.2484","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.2484","created_at":"2026-05-18T03:19:23Z"},{"alias_kind":"arxiv_version","alias_value":"1204.2484v2","created_at":"2026-05-18T03:19:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2484","created_at":"2026-05-18T03:19:23Z"},{"alias_kind":"pith_short_12","alias_value":"VC3FA2K5EKEB","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VC3FA2K5EKEBJZX3","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VC3FA2K5","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:3402f9265406a46c2324b4702f009f863aa950f4493b52f4a41709bc221b0dfa","target":"graph","created_at":"2026-05-18T03:19:23Z","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":"Starting with Knutson and Tao's hive model (in J. Amer. Math. Soc., 1999) we characterize the Littlewood-Richardson coefficient $c_{\\lambda,\\mu}^\\nu$ of given partitions $\\lambda,\\mu,\\nu\\in N^n$ as the number of capacity achieving hive flows on the honeycomb graph. Based on this, we design a polynomial time algorithm for deciding $c_{\\lambda,\\mu}^\\nu >0$. This algorithm is easy to state and takes $O(n^3 \\log \\nu_1)$ arithmetic operations and comparisons. We further show that the capacity achieving hive flows can be seen as the vertices of a connected graph, which leads to new structural insigh","authors_text":"Christian Ikenmeyer, Peter B\\\"urgisser","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-04-11T16:01:35Z","title":"Deciding Positivity of Littlewood-Richardson Coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2484","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":"sha256:139558646a3f48b136489d86c49b9d1a0aab89ecd760504fa39bae8a9c5e98a6","target":"record","created_at":"2026-05-18T03:19:23Z","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":"2226902523060bf1f0e36bc5229bc038bd0bd633a05fe6c7589e65ab18ac7553","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-04-11T16:01:35Z","title_canon_sha256":"7223ca9b15394eba40a68151f3b92bbd34e754ee4123b4da638642e4bfa8aecd"},"schema_version":"1.0","source":{"id":"1204.2484","kind":"arxiv","version":2}},"canonical_sha256":"a8b650695d228814e6fb878c3979fb33e8121a192d74f5eb191d73a8eae4c7c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8b650695d228814e6fb878c3979fb33e8121a192d74f5eb191d73a8eae4c7c6","first_computed_at":"2026-05-18T03:19:23.400137Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:23.400137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FZG283nlRN9UDEMnW+J209JwRNVOFIWy9mjNZQlJvix901qCm0vYw3ySp1eZZzm1iC1l7Ii6v6uG/saofM6cAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:23.400699Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.2484","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:139558646a3f48b136489d86c49b9d1a0aab89ecd760504fa39bae8a9c5e98a6","sha256:3402f9265406a46c2324b4702f009f863aa950f4493b52f4a41709bc221b0dfa"],"state_sha256":"850a2c279a54ed71ececc02116cc8e9e780c268292433c7f3741b3bc4f8cc5d3"}