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It is shown that for every integer $s\\geq 1$, we have the equality ${\\rm reg}(I(G)^{(s)})=2s+\\ind-match(G)-1$, where $I(G)^{(s)}$ denotes the $s$-th symbolic power of $I(G)$."},"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":"1907.02743","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-07-05T09:38:21Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"c92f9ff73d41fb24f303a4a3d401d3bc96ecddee7dcd63480127d907fa75d9fc","abstract_canon_sha256":"fb6d9a1977b4f32a3a84a0d6c86e34a6ab09f3b5084d5cd36a9e8100c1ecb641"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:23.319685Z","signature_b64":"Rkwyr86Eg3KBAlL9bF0lPPTBCM4+v8HXMsoz7BbUWPBBSA05t8ChTQfSDI7sTrRxIQdqw+ujTi27DsQbQbruDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1e5f274940f19f5bb3230a9d89484206c5dddb0381a74c2c786529dc246ec6e","last_reissued_at":"2026-05-17T23:41:23.318847Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:23.318847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Regularity of symbolic powers of edge ideals of Cameron-Walker graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"S. 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