{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:RXEYAYFWH7FPNJH7HI736XDHTH","short_pith_number":"pith:RXEYAYFW","schema_version":"1.0","canonical_sha256":"8dc98060b63fcaf6a4ff3a3fbf5c6799f5ccec10f3bbf8ce4f432bb2a872cf92","source":{"kind":"arxiv","id":"1805.01693","version":1},"attestation_state":"computed","paper":{"title":"Solving a Conjecture on Identification in Hamming Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Tero Laihonen, Tuomo Lehtil\\\"a, Ville Junnila","submitted_at":"2018-05-04T10:02:06Z","abstract_excerpt":"Identifying codes in graphs have been widely studied since their introduction by Karpovsky, Chakrabarty and Levitin in 1998. In particular, there are a lot of results regarding the binary hypercubes, that is, the Hamming graphs $K_2^n$. In 2008, Gravier et al. started investigating identification in $K_q^2$. Goddard and Wash, in 2013, studied identifying codes in the general Hamming graphs $K_q^n$. They stated, for instance, that $\\gamma^{ID}(K_q^n)\\leq q^{n-1}$ for any $q$ and $n\\geq3$. Moreover, they conjectured that $\\gamma^{ID}(K_q^3)=q^2$. In this article, we show that $\\gamma^{ID}(K_q^3)"},"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":"1805.01693","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-04T10:02:06Z","cross_cats_sorted":[],"title_canon_sha256":"117f5150b32f36fc4107ef36c17d27f1cc56dd757b4b278d61a0bafb843882a9","abstract_canon_sha256":"8f06fd27791f108a9439fa199b96375df9741e740b877a42ea706b58f94caf38"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:47.039676Z","signature_b64":"mxgbsmGbo79m7rKhQQJ3Amntk0bDKRfVPuqr2qrITWjveOMfARE3oL1VDKs4qy6ZlzOLPYK5pnqDT76J4BcCCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8dc98060b63fcaf6a4ff3a3fbf5c6799f5ccec10f3bbf8ce4f432bb2a872cf92","last_reissued_at":"2026-05-18T00:16:47.038932Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:47.038932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Solving a Conjecture on Identification in Hamming Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Tero Laihonen, Tuomo Lehtil\\\"a, Ville Junnila","submitted_at":"2018-05-04T10:02:06Z","abstract_excerpt":"Identifying codes in graphs have been widely studied since their introduction by Karpovsky, Chakrabarty and Levitin in 1998. In particular, there are a lot of results regarding the binary hypercubes, that is, the Hamming graphs $K_2^n$. In 2008, Gravier et al. started investigating identification in $K_q^2$. Goddard and Wash, in 2013, studied identifying codes in the general Hamming graphs $K_q^n$. They stated, for instance, that $\\gamma^{ID}(K_q^n)\\leq q^{n-1}$ for any $q$ and $n\\geq3$. Moreover, they conjectured that $\\gamma^{ID}(K_q^3)=q^2$. In this article, we show that $\\gamma^{ID}(K_q^3)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.01693","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1805.01693","created_at":"2026-05-18T00:16:47.039053+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.01693v1","created_at":"2026-05-18T00:16:47.039053+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.01693","created_at":"2026-05-18T00:16:47.039053+00:00"},{"alias_kind":"pith_short_12","alias_value":"RXEYAYFWH7FP","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_16","alias_value":"RXEYAYFWH7FPNJH7","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_8","alias_value":"RXEYAYFW","created_at":"2026-05-18T12:32:50.500415+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RXEYAYFWH7FPNJH7HI736XDHTH","json":"https://pith.science/pith/RXEYAYFWH7FPNJH7HI736XDHTH.json","graph_json":"https://pith.science/api/pith-number/RXEYAYFWH7FPNJH7HI736XDHTH/graph.json","events_json":"https://pith.science/api/pith-number/RXEYAYFWH7FPNJH7HI736XDHTH/events.json","paper":"https://pith.science/paper/RXEYAYFW"},"agent_actions":{"view_html":"https://pith.science/pith/RXEYAYFWH7FPNJH7HI736XDHTH","download_json":"https://pith.science/pith/RXEYAYFWH7FPNJH7HI736XDHTH.json","view_paper":"https://pith.science/paper/RXEYAYFW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.01693&json=true","fetch_graph":"https://pith.science/api/pith-number/RXEYAYFWH7FPNJH7HI736XDHTH/graph.json","fetch_events":"https://pith.science/api/pith-number/RXEYAYFWH7FPNJH7HI736XDHTH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RXEYAYFWH7FPNJH7HI736XDHTH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RXEYAYFWH7FPNJH7HI736XDHTH/action/storage_attestation","attest_author":"https://pith.science/pith/RXEYAYFWH7FPNJH7HI736XDHTH/action/author_attestation","sign_citation":"https://pith.science/pith/RXEYAYFWH7FPNJH7HI736XDHTH/action/citation_signature","submit_replication":"https://pith.science/pith/RXEYAYFWH7FPNJH7HI736XDHTH/action/replication_record"}},"created_at":"2026-05-18T00:16:47.039053+00:00","updated_at":"2026-05-18T00:16:47.039053+00:00"}