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The $\\zeta$-monotonicity property can be written as follows: $$ | \\zeta (x_2 + y i ) | < | \\zeta \\left ( x_1 +y i \\right )| \\hspace{0.5cm} \\textrm {for any } \\hspace{0.25cm} x_1 < x_2 \\leq 0.5 \\textrm{ and } 6.29 <y. $$ In this work we present an experimental study of the monotonicity conjecture, in the course of which new properties of $\\zeta(z)$ are discovered. For instance, the spectrum of semi-limits $ \\lambda(z) \\subset \\mathbb{R}$ and the core function $C"},"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":"1707.01754","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2017-07-03T07:13:08Z","cross_cats_sorted":[],"title_canon_sha256":"500e470e407c1e07a3c1cd03c7b382224eaf7b9de99f8485f49dd35b205b84a8","abstract_canon_sha256":"0f8f1f9e694f5b0b58d12c3f13b1d3601d0500c4b03e7dc213c656e2ec30a5bf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:21.939696Z","signature_b64":"Km++x6sSL/Zbgu7F9f8Vd6IScIpdJykdBwkHox9y0VSCFbbT0bNlXDvoVSFPC8yMTslQ0mUcs4dGeITjpxqODA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d35d516aa684a4de0a2893294ca1df57ba50ed622c86eeac4b421588ce18452","last_reissued_at":"2026-05-18T00:36:21.939096Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:21.939096Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An experimental study of the monotonicity property of the Riemann zeta function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Yochay Jerby","submitted_at":"2017-07-03T07:13:08Z","abstract_excerpt":"In 1970, based on newly available empiric evidence, a remarkable monotonicity property for $| \\zeta(z) |$ was conjectured by R. Spira. The $\\zeta$-monotonicity property can be written as follows: $$ | \\zeta (x_2 + y i ) | < | \\zeta \\left ( x_1 +y i \\right )| \\hspace{0.5cm} \\textrm {for any } \\hspace{0.25cm} x_1 < x_2 \\leq 0.5 \\textrm{ and } 6.29 <y. $$ In this work we present an experimental study of the monotonicity conjecture, in the course of which new properties of $\\zeta(z)$ are discovered. 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