{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:XSD76LFUE2OEBOKWTOMIMX6KL7","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":"c990b3bf291a3ec4886b556508f14d2d9d857719ae51d12ab99f0e1b8c87871e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-03T17:22:10Z","title_canon_sha256":"b75ff029bb328f84f41d46a1c44413384d8da77d92a356f5f4ad938c491c6882"},"schema_version":"1.0","source":{"id":"2606.05117","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.05117","created_at":"2026-06-04T01:10:06Z"},{"alias_kind":"arxiv_version","alias_value":"2606.05117v1","created_at":"2026-06-04T01:10:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.05117","created_at":"2026-06-04T01:10:06Z"},{"alias_kind":"pith_short_12","alias_value":"XSD76LFUE2OE","created_at":"2026-06-04T01:10:06Z"},{"alias_kind":"pith_short_16","alias_value":"XSD76LFUE2OEBOKW","created_at":"2026-06-04T01:10:06Z"},{"alias_kind":"pith_short_8","alias_value":"XSD76LFU","created_at":"2026-06-04T01:10:06Z"}],"graph_snapshots":[{"event_id":"sha256:dd37ee203037ddcd3d3d26137f1150db02619aba2bbdc16dde67c8936500fb38","target":"graph","created_at":"2026-06-04T01:10:06Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.05117/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper is motivated by a broad question about AI-assisted mathematics: can an AI system help discover and certify an explicit bijection between two infinite sequences of complicated combinatorial sets already known to be equinumerous? The challenge is to find a reversible structure explaining that equality uniformly across the sequence. We give an affirmative test case in the setting of a partition problem. Andrews and Dhar introduced two partition families $\\mathcal{C}_3(n)$ and $\\mathcal{D}_3(n)$, and for \"nonexceptional'' $n$, they asked for a bijective proof of their equality\n  \\[\n  |\\","authors_text":"Jujian Zhang, Ken Ono, Simon Mahns","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-03T17:22:10Z","title":"A problem of Andrews and Dhar on partitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.05117","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:a22532cec2173a5f1922e9ab997efa589737680e9290dc2a0eba2d3f0be3ab5e","target":"record","created_at":"2026-06-04T01:10:06Z","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":"c990b3bf291a3ec4886b556508f14d2d9d857719ae51d12ab99f0e1b8c87871e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-03T17:22:10Z","title_canon_sha256":"b75ff029bb328f84f41d46a1c44413384d8da77d92a356f5f4ad938c491c6882"},"schema_version":"1.0","source":{"id":"2606.05117","kind":"arxiv","version":1}},"canonical_sha256":"bc87ff2cb4269c40b9569b98865fca5fcd27c86cb8892343edf5d9797100e2d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc87ff2cb4269c40b9569b98865fca5fcd27c86cb8892343edf5d9797100e2d4","first_computed_at":"2026-06-04T01:10:06.944893Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T01:10:06.944893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LRUCMJxH/e/OQGfdV/g8SRpAvmJ5MWYEp6ERegWgIbDiztqaOOizcWtD7HUS/89Gvz2WXfM1Zpyx3JaFaXWGCw==","signature_status":"signed_v1","signed_at":"2026-06-04T01:10:06.945567Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.05117","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a22532cec2173a5f1922e9ab997efa589737680e9290dc2a0eba2d3f0be3ab5e","sha256:dd37ee203037ddcd3d3d26137f1150db02619aba2bbdc16dde67c8936500fb38"],"state_sha256":"8945ea0051f0a359903e8d3dad902c82eab1c203a02956579d0d55587c3cf60f"}