{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:V62TEHEL557UA2IDOA5AZWVR56","short_pith_number":"pith:V62TEHEL","schema_version":"1.0","canonical_sha256":"afb5321c8bef7f406903703a0cdab1efb2bac7deb62c86d1ffc732e1560a49ab","source":{"kind":"arxiv","id":"1703.02787","version":1},"attestation_state":"computed","paper":{"title":"Distant irregularity strength of graphs with bounded minimum degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jakub Przyby{\\l}o","submitted_at":"2017-03-08T11:05:35Z","abstract_excerpt":"Consider a graph $G=(V,E)$ without isolated edges and with maximum degree $\\Delta$. Given a colouring $c:E\\to\\{1,2,\\ldots,k\\}$, the weighted degree of a vertex $v\\in V$ is the sum of its incident colours, i.e., $\\sum_{e\\ni v}c(e)$. For any integer $r\\geq 2$, the least $k$ admitting the existence of such $c$ attributing distinct weighted degrees to any two different vertices at distance at most $r$ in $G$ is called the $r$-distant irregularity strength of $G$ and denoted by $s_r(G)$. This graph invariant provides a natural link between the well known 1--2--3 Conjecture and irregularity strength"},"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":"1703.02787","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-08T11:05:35Z","cross_cats_sorted":[],"title_canon_sha256":"faa5f8361836adc2ecf4ee56065351df0841c6545e643273e501e1a6dbaf6558","abstract_canon_sha256":"6ad6f1ed84796dcb2f20df05418618c7a2a363638e3953a212737d9b4ca1f413"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:35.233774Z","signature_b64":"4ExjC7QtGvPhbkc+6aTn/XRBHUAKW6MD6157oghEXCNH+/A+g87JQmS5TfwM23oAd+gll9qfT/WvaWhByWZABw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"afb5321c8bef7f406903703a0cdab1efb2bac7deb62c86d1ffc732e1560a49ab","last_reissued_at":"2026-05-18T00:21:35.233030Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:35.233030Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Distant irregularity strength of graphs with bounded minimum degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jakub Przyby{\\l}o","submitted_at":"2017-03-08T11:05:35Z","abstract_excerpt":"Consider a graph $G=(V,E)$ without isolated edges and with maximum degree $\\Delta$. Given a colouring $c:E\\to\\{1,2,\\ldots,k\\}$, the weighted degree of a vertex $v\\in V$ is the sum of its incident colours, i.e., $\\sum_{e\\ni v}c(e)$. For any integer $r\\geq 2$, the least $k$ admitting the existence of such $c$ attributing distinct weighted degrees to any two different vertices at distance at most $r$ in $G$ is called the $r$-distant irregularity strength of $G$ and denoted by $s_r(G)$. This graph invariant provides a natural link between the well known 1--2--3 Conjecture and irregularity strength"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.02787","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":"1703.02787","created_at":"2026-05-18T00:21:35.233156+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.02787v1","created_at":"2026-05-18T00:21:35.233156+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.02787","created_at":"2026-05-18T00:21:35.233156+00:00"},{"alias_kind":"pith_short_12","alias_value":"V62TEHEL557U","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_16","alias_value":"V62TEHEL557UA2ID","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_8","alias_value":"V62TEHEL","created_at":"2026-05-18T12:31:49.984773+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/V62TEHEL557UA2IDOA5AZWVR56","json":"https://pith.science/pith/V62TEHEL557UA2IDOA5AZWVR56.json","graph_json":"https://pith.science/api/pith-number/V62TEHEL557UA2IDOA5AZWVR56/graph.json","events_json":"https://pith.science/api/pith-number/V62TEHEL557UA2IDOA5AZWVR56/events.json","paper":"https://pith.science/paper/V62TEHEL"},"agent_actions":{"view_html":"https://pith.science/pith/V62TEHEL557UA2IDOA5AZWVR56","download_json":"https://pith.science/pith/V62TEHEL557UA2IDOA5AZWVR56.json","view_paper":"https://pith.science/paper/V62TEHEL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.02787&json=true","fetch_graph":"https://pith.science/api/pith-number/V62TEHEL557UA2IDOA5AZWVR56/graph.json","fetch_events":"https://pith.science/api/pith-number/V62TEHEL557UA2IDOA5AZWVR56/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V62TEHEL557UA2IDOA5AZWVR56/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V62TEHEL557UA2IDOA5AZWVR56/action/storage_attestation","attest_author":"https://pith.science/pith/V62TEHEL557UA2IDOA5AZWVR56/action/author_attestation","sign_citation":"https://pith.science/pith/V62TEHEL557UA2IDOA5AZWVR56/action/citation_signature","submit_replication":"https://pith.science/pith/V62TEHEL557UA2IDOA5AZWVR56/action/replication_record"}},"created_at":"2026-05-18T00:21:35.233156+00:00","updated_at":"2026-05-18T00:21:35.233156+00:00"}