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A signed $k$-submatching of $G$ is a function $f:E(G)\\longrightarrow \\{-1,1\\}$, satisfying $f(E_G(v))\\leq 1$ for at least $k$ vertices, where $f(S)=\\sum_{e\\in S}f(e)$, for each $ S\\subseteq E(G)$. The maximum of the value of $f(E(G))$, taken over all signed $k$-submatching $f$ of $G$, is called the signed $k$-submatching number and is denoted by $\\beta ^k_S(G)$. In this paper, we prove that for every graph $G$ of order $n$ and for any positive integer $k \\leq n$, $\\beta ^k_S (G) "},"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":"1411.0132","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-11-01T16:12:33Z","cross_cats_sorted":[],"title_canon_sha256":"0d6adf0ce5f1522071d4e25b2224ab2a3fad47ce62eac28a3db140ca4b569a74","abstract_canon_sha256":"b5f56e1706949e4fe153e8ddac48ddd0471bcc91dc17d0bd0e848261fb0a715f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:52.473848Z","signature_b64":"/TQoSc6E5cS1nnW9cGFD1jPd+sMW57+6X71Y+IdYX8v8w2+vBDZVbWpIUxU01fCJNPsW0LKtNom6zl182vqeCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"056194af61e2a70d867caae681b136249ce6140aca3c7bdea12f05398be5317d","last_reissued_at":"2026-05-18T02:38:52.473475Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:52.473475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Note on Signed k-Submatching in Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"K. 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