{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZFPF5F6IEWB2HRROBSUX2IBQLZ","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":"f32e2ee4a125906ba0d9e9f6a1d65824d92806a8d3b584fcc028cf472db70cc5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-18T19:37:50Z","title_canon_sha256":"32f572f3e3ba48b03f480768dd10826190397c3d6db0868ec7d3bd469fd0afc8"},"schema_version":"1.0","source":{"id":"1701.05214","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.05214","created_at":"2026-05-18T00:52:30Z"},{"alias_kind":"arxiv_version","alias_value":"1701.05214v1","created_at":"2026-05-18T00:52:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.05214","created_at":"2026-05-18T00:52:30Z"},{"alias_kind":"pith_short_12","alias_value":"ZFPF5F6IEWB2","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZFPF5F6IEWB2HRRO","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZFPF5F6I","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:5bdd2d424864229a8fcf5f9da699d7b796aae0c86303f78ead4470bbbe5532e0","target":"graph","created_at":"2026-05-18T00:52:30Z","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":"In 2007, Dmytrenko, Lazebnik and Williford posed two related conjectures about polynomials over finite fields. Conjecture~1 is a claim about the uniqueness of certain monomial graphs. Conjecture~2, which implies Conjecture~1, deals with certain permutation polynomials of finite fields. Two natural strengthenings of Conjecture~2, referred to as Conjectures~A and B in the present paper, were also insinuated. In a recent development, Conjecture~2 and hence Conjecture~1 have been confirmed. The present paper gives a proof of Conjecture~A.","authors_text":"Xiang-dong Hou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-18T19:37:50Z","title":"On the DLW Conjectures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05214","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":"sha256:61ed0b2e1d7848ef279eeb407ac82d4c2c6cc81a62eed09bd08087018bc3520f","target":"record","created_at":"2026-05-18T00:52:30Z","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":"f32e2ee4a125906ba0d9e9f6a1d65824d92806a8d3b584fcc028cf472db70cc5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-18T19:37:50Z","title_canon_sha256":"32f572f3e3ba48b03f480768dd10826190397c3d6db0868ec7d3bd469fd0afc8"},"schema_version":"1.0","source":{"id":"1701.05214","kind":"arxiv","version":1}},"canonical_sha256":"c95e5e97c82583a3c62e0ca97d20305e4eb743d626bac2d3de1bef8bb7aeda3a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c95e5e97c82583a3c62e0ca97d20305e4eb743d626bac2d3de1bef8bb7aeda3a","first_computed_at":"2026-05-18T00:52:30.513190Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:30.513190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YrsEuS6ULcZPz/djPDKrN0n+KbQ7ljb/BdaNkkSCoaO2g27/Edi0kw5ZXDNLtmFNPdpyS+nv+opBolJyMHsRBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:30.513752Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.05214","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61ed0b2e1d7848ef279eeb407ac82d4c2c6cc81a62eed09bd08087018bc3520f","sha256:5bdd2d424864229a8fcf5f9da699d7b796aae0c86303f78ead4470bbbe5532e0"],"state_sha256":"870db5678ead89857103d289c6cee97bc287028c406e0277e63c250af1fbe6a9"}