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This paper studies the packing chromatic number of infinite distance graphs $G(\\mathbb{Z},D)$, i.e. graphs with the set $\\mathbb{Z}$ of integers as vertex set, with two distinct vertices $i,j\\in \\mathbb{Z}$ being adjacent if and only if $|i-j|\\in D$. We present lower and upper bounds for $\\chi_{\\rho}(G(\\mathbb{Z},D))$, showing that for finite $D$, the packing ch"},"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":"1011.0971","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-11-03T19:01:11Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"eba2b592f8367ca320df989cb3939029ae756390dc5e1daad9606ee4d99bec58","abstract_canon_sha256":"1043b308df26b5fd4d2e97029764743ab4e07f21cb10ca0bbca12432f0b2086a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:33.025940Z","signature_b64":"BNSQYswCsbOpo/u73DVf/sCwVKKXnJyiGldIP7bLO0m4h2M3LQFjIAxAtMFBUogDQ8hvKgPswrH6J6JpExy1BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eee8ec6c1c48a04f124f3da97aa71b42f66a1e6632ae62e8a5d798b2d8da79cd","last_reissued_at":"2026-05-18T02:58:33.025223Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:33.025223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Packing Colorings of Distance Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Olivier Togni (Le2i)","submitted_at":"2010-11-03T19:01:11Z","abstract_excerpt":"The {\\em packing chromatic number} $\\chi_{\\rho}(G)$ of a graph $G$ is the least integer $k$ for which there exists a mapping $f$ from $V(G)$ to $\\{1,2,\\ldots ,k\\}$ such that any two vertices of color $i$ are at distance at least $i+1$. 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