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Let $H(I, J)$ be the least positive $n$ such that there is an $(I,J,n)-DGR$. In this paper, we propose a series of conjectures on the constructions and structures of DGR. The main conjecture states that if $A$ is any set of positive integers such that $|A| = H(I, J)$, then there are $I$ disjoint Golomb rulers, each being a $J$-subset of $"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1405.4535","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-18T18:30:57Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"183de379ad1345506937d7875d6fe0f8e2fe58df32af8e3eee4cb8693081cc37","abstract_canon_sha256":"6480c6fc11d2d0f82c95156d9acf15ff282754798aec7e866ac2538feec771e8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:40.589808Z","signature_b64":"OoCTWK2EluOHO0uicnm9NCm2FvBrqEJOpR4RDV2qToYGKm+6kntj3ACJ7O0VxDFA1Z7wQqL9e7fHTL92aIYdBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a269a3dc1e47e42af036dcf1c913624e3f6f507535603cdbd4ce28e1ff51e74d","last_reissued_at":"2026-05-18T02:51:40.589273Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:40.589273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Disjoint Golomb Rulers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Changjun Fan, Meilian Liang, Xiu Baoxin","submitted_at":"2014-05-18T18:30:57Z","abstract_excerpt":"A set $\\{a_i\\:|\\: 1\\leq i \\leq k\\}$ of non-negative integers is a Golomb ruler if differences $a_i-a_j$, for any $i \\neq j$, are all distinct. 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