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We derive self-consistency equations to obtain the birth points of the k-cores and their relative sizes for uncorrelated multiplex networks with an arbitrary degree di"},"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":"1405.1336","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2014-05-06T16:15:14Z","cross_cats_sorted":["math-ph","math.MP","physics.soc-ph"],"title_canon_sha256":"6f4ef4db9510b1a4179d490d57eb82956a726cb70889dc9238c266a5ca28e579","abstract_canon_sha256":"279f756bc3541dba6c63e45e0b7f517db8921b423ef924b8936ac89600ae7d4f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:56.034987Z","signature_b64":"YlOj5J5JHGPEchGxWqvm5TmNcbDpZ9uLuEzc7KO6ufWh56zbDYG4IbzaloR9+002ElDz1KuLkniXr5knnInVCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8862372d6fbc0a219f7879daaa2703d05953ac0f555a1b405a9f41a3c58846a2","last_reissued_at":"2026-05-18T02:40:56.034418Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:56.034418Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"k-Core percolation on multiplex networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","physics.soc-ph"],"primary_cat":"cond-mat.dis-nn","authors_text":"J. 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