{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3OVUD6FLKSHOXYCS2SGVENMYGP","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":"a885dcc0245aea6e06fea4d7f775dad5102256d756563a0b77a4276b8ba5926f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-06-23T03:32:08Z","title_canon_sha256":"982e3f33c5fdfa963e8ffced092d2be684543fa7f2f5d15c07980c8e8815e963"},"schema_version":"1.0","source":{"id":"1306.5371","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.5371","created_at":"2026-05-18T03:06:34Z"},{"alias_kind":"arxiv_version","alias_value":"1306.5371v2","created_at":"2026-05-18T03:06:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.5371","created_at":"2026-05-18T03:06:34Z"},{"alias_kind":"pith_short_12","alias_value":"3OVUD6FLKSHO","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3OVUD6FLKSHOXYCS","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3OVUD6FL","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:f81a30aec823349f7312c369ff130305b312bceb5770e1d9fcc13c5231d3d0f5","target":"graph","created_at":"2026-05-18T03:06:34Z","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 use an injection method to prove a new class of partition inequalities involving certain $q$-products with two to four finitization parameters. Our new theorems are a substantial generalization of work by Andrews and of previous work by Berkovich and Grizzell. We also briefly discuss how our products might relate to lecture hall partitions.","authors_text":"Alexander Berkovich, Keith Grizzell","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-06-23T03:32:08Z","title":"A partition inequality involving products of two $q$-Pochhammer symbols"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5371","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":"sha256:20c7c26c0dfff0b58369dd2b619122703a8b2691c30f4db13f8fe9b5be065d78","target":"record","created_at":"2026-05-18T03:06:34Z","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":"a885dcc0245aea6e06fea4d7f775dad5102256d756563a0b77a4276b8ba5926f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-06-23T03:32:08Z","title_canon_sha256":"982e3f33c5fdfa963e8ffced092d2be684543fa7f2f5d15c07980c8e8815e963"},"schema_version":"1.0","source":{"id":"1306.5371","kind":"arxiv","version":2}},"canonical_sha256":"dbab41f8ab548eebe052d48d52359833fd3f8d2f4976fa755706ab5fbcc6d7d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dbab41f8ab548eebe052d48d52359833fd3f8d2f4976fa755706ab5fbcc6d7d3","first_computed_at":"2026-05-18T03:06:34.363646Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:34.363646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aoBMIX+dI2vC0EAU937vu70p8S7W9/zr/ztizaksKDoAfAT1Orj30JkBi0U+KQyvJXyqkUE5GuTI4SKD8ZvCBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:34.364303Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.5371","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:20c7c26c0dfff0b58369dd2b619122703a8b2691c30f4db13f8fe9b5be065d78","sha256:f81a30aec823349f7312c369ff130305b312bceb5770e1d9fcc13c5231d3d0f5"],"state_sha256":"ca0b742b00c47e40ed492981eaa9189048bbb40bf27a6901c55462bceb140761"}