{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:EBWY2J3TCOQNW4YRWTHPSLYBFD","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":"7690d4e65329d5555e528e4a1e69bc46e52566c165c9fd6a8ad3aa9306833532","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-29T23:15:41Z","title_canon_sha256":"662df470043cc210c297a1bdeb5fab4f9301c4bdbae72f87284267b65819ec8c"},"schema_version":"1.0","source":{"id":"2606.00420","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.00420","created_at":"2026-06-02T01:03:54Z"},{"alias_kind":"arxiv_version","alias_value":"2606.00420v1","created_at":"2026-06-02T01:03:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.00420","created_at":"2026-06-02T01:03:54Z"},{"alias_kind":"pith_short_12","alias_value":"EBWY2J3TCOQN","created_at":"2026-06-02T01:03:54Z"},{"alias_kind":"pith_short_16","alias_value":"EBWY2J3TCOQNW4YR","created_at":"2026-06-02T01:03:54Z"},{"alias_kind":"pith_short_8","alias_value":"EBWY2J3T","created_at":"2026-06-02T01:03:54Z"}],"graph_snapshots":[{"event_id":"sha256:64b7457433f8cf6843cb6c485beff60e70cdbd1d40388f981743ce1cb8c7620f","target":"graph","created_at":"2026-06-02T01:03:54Z","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/2606.00420/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Ballantine, Beck, and Merca defined the elementary symmetric partition map pre$_j$ that sends a partition $\\lambda$ to a larger partition whose parts are the summands appearing in the evaluation of the $j$-th elementary symmetric polynomial on $\\lambda$. They conjectured that pre$_j$ is injective on the set of partitions of $n$ with length $\\ell \\geq j$. The $\\ell = j$ case was disproved by Devnani and Eyyunni; they instead conjectured the statement to be true for $\\ell > j$. In this article, we answer this refined conjecture in the negative by proving that pre$_j$ is not injective on partitio","authors_text":"Harper Niergarth, Vixail Hadelyn, Weiyou Li, Wenhui Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-29T23:15:41Z","title":"Counterexamples regarding elementary symmetric partitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.00420","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:e37785a2411f15295398fde74e87b1b2fa8ae073781b06f8f6d7338434eb5ea2","target":"record","created_at":"2026-06-02T01:03:54Z","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":"7690d4e65329d5555e528e4a1e69bc46e52566c165c9fd6a8ad3aa9306833532","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-29T23:15:41Z","title_canon_sha256":"662df470043cc210c297a1bdeb5fab4f9301c4bdbae72f87284267b65819ec8c"},"schema_version":"1.0","source":{"id":"2606.00420","kind":"arxiv","version":1}},"canonical_sha256":"206d8d277313a0db7311b4cef92f0128ee022d9921c28686bb4efe59b53986d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"206d8d277313a0db7311b4cef92f0128ee022d9921c28686bb4efe59b53986d8","first_computed_at":"2026-06-02T01:03:54.075733Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T01:03:54.075733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YMdVd9GLw6GYoIo0ykQzmEQQSW92zQOhXToOWHIho4EBLB7z49HMsM3PQLD6hCBMaokO/7mYemkGTUpplYnLBg==","signature_status":"signed_v1","signed_at":"2026-06-02T01:03:54.076131Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.00420","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e37785a2411f15295398fde74e87b1b2fa8ae073781b06f8f6d7338434eb5ea2","sha256:64b7457433f8cf6843cb6c485beff60e70cdbd1d40388f981743ce1cb8c7620f"],"state_sha256":"5afe34d453e63a284cd36d704a24ca9988bdf51a4c6bf4bf9d4e325555d5ee0f"}