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In this paper, we show that $X \\in 2^\\omega$ is $s$-energy random if and only if $\\sum_{n\\in\\omega} 2^{sn - KM(X\\upharpoonright n)} < \\infty$, providing a characterization of energy randomness via a pr"},"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":"1509.00524","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-09-01T23:36:59Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"60ded75e2611c771bd9124e8cbfd3ddb80e89a2fd277181e0c525de65531caf1","abstract_canon_sha256":"5016c53d01a64f980a6c4ccbc034bd4c29dcea78a6517d2891720d7e0b45fd20"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:06.959409Z","signature_b64":"lSYJb4BXQTH3gCaCOFVYHt6Ibrx3kRKRjI5Ys8pHg2zpWRQt1q7efXoJ0MDTgUWGlK9B2wmr2buiFxXt5HzuAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fbac3e96b778b167444e04b64e9bffff95c60c1e7889948967ec32bb3a023b45","last_reissued_at":"2026-05-18T01:34:06.958897Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:06.958897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Energy randomness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"math.LO","authors_text":"Jason Rute, Joseph S. 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