{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:AVQZJL3B4KTQ3BT4VLTIDMJWES","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b5f56e1706949e4fe153e8ddac48ddd0471bcc91dc17d0bd0e848261fb0a715f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-11-01T16:12:33Z","title_canon_sha256":"0d6adf0ce5f1522071d4e25b2224ab2a3fad47ce62eac28a3db140ca4b569a74"},"schema_version":"1.0","source":{"id":"1411.0132","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.0132","created_at":"2026-05-18T02:38:52Z"},{"alias_kind":"arxiv_version","alias_value":"1411.0132v1","created_at":"2026-05-18T02:38:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0132","created_at":"2026-05-18T02:38:52Z"},{"alias_kind":"pith_short_12","alias_value":"AVQZJL3B4KTQ","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AVQZJL3B4KTQ3BT4","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AVQZJL3B","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:d7c5b439dc492de13d4d2525b9dc3452c15796d263723b77b9bed9532a966d85","target":"graph","created_at":"2026-05-18T02:38:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $G$ be a graph of order $n$. For every $v\\in V(G)$, let $E_G(v)$ denote the set of all edges incident with $v$. 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) ","authors_text":"K. Ehsani, M. Dalirrooyfard, R. Sherkati, S. Akbari","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-11-01T16:12:33Z","title":"A Note on Signed k-Submatching in Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0132","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3ecf2da03de0cd63f8994eca19b8af41149146ef017fc3dd1a7533246eedb7ec","target":"record","created_at":"2026-05-18T02:38:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"b5f56e1706949e4fe153e8ddac48ddd0471bcc91dc17d0bd0e848261fb0a715f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-11-01T16:12:33Z","title_canon_sha256":"0d6adf0ce5f1522071d4e25b2224ab2a3fad47ce62eac28a3db140ca4b569a74"},"schema_version":"1.0","source":{"id":"1411.0132","kind":"arxiv","version":1}},"canonical_sha256":"056194af61e2a70d867caae681b136249ce6140aca3c7bdea12f05398be5317d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"056194af61e2a70d867caae681b136249ce6140aca3c7bdea12f05398be5317d","first_computed_at":"2026-05-18T02:38:52.473475Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:52.473475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/TQoSc6E5cS1nnW9cGFD1jPd+sMW57+6X71Y+IdYX8v8w2+vBDZVbWpIUxU01fCJNPsW0LKtNom6zl182vqeCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:52.473848Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.0132","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ecf2da03de0cd63f8994eca19b8af41149146ef017fc3dd1a7533246eedb7ec","sha256:d7c5b439dc492de13d4d2525b9dc3452c15796d263723b77b9bed9532a966d85"],"state_sha256":"b8d732f9354a1f36b000c9f8ac928d7a8ad826fc37dafd5f06b055a33ff5a64d"}