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We introduce the partial order of degree spectra \\textit{on a cone} and begin the study of these objects. Using a result of Harizanov---that, assuming an effectiveness condition on $\\mathcal{A}$ and $R$, if $R$ is not intrinsically computable, then its degree spectrum cont"},"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":"1412.3842","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-12-11T22:12:57Z","cross_cats_sorted":[],"title_canon_sha256":"6456ed43c3ed388a78c308ae66c5111b2b5e692d50ffef1352e4e54810fc50fc","abstract_canon_sha256":"d7295e8f29c0c8a403b1f0c39683c28180e4694b86e5deb75c3672214be425ca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:29.509890Z","signature_b64":"MPKbZGssJPDQZGjf9UBByZSVZ+20UqSRQkHm7RyBZ9rddYxJ2mvVPl2nealPE2FO2Bdn/OgMfngnUpnWaEX0DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a64fdf0bdb0fcee657c942833eb2625e54643713bc275a289cdc515219289e90","last_reissued_at":"2026-05-18T02:31:29.509252Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:29.509252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Degree Spectra of Relations on a Cone","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Matthew Harrison-Trainor","submitted_at":"2014-12-11T22:12:57Z","abstract_excerpt":"Let $\\mathcal{A}$ be a mathematical structure with an additional relation $R$. 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