{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NU25KFVKNBFE3YFCREZJJSQ56V","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0f8f1f9e694f5b0b58d12c3f13b1d3601d0500c4b03e7dc213c656e2ec30a5bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2017-07-03T07:13:08Z","title_canon_sha256":"500e470e407c1e07a3c1cd03c7b382224eaf7b9de99f8485f49dd35b205b84a8"},"schema_version":"1.0","source":{"id":"1707.01754","kind":"arxiv","version":8}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.01754","created_at":"2026-05-18T00:36:21Z"},{"alias_kind":"arxiv_version","alias_value":"1707.01754v8","created_at":"2026-05-18T00:36:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.01754","created_at":"2026-05-18T00:36:21Z"},{"alias_kind":"pith_short_12","alias_value":"NU25KFVKNBFE","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NU25KFVKNBFE3YFC","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NU25KFVK","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:512ab29384a7b28d458afe8f77018290ce608be6ae106e2597ca5d2ee557b545","target":"graph","created_at":"2026-05-18T00:36:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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. For instance, the spectrum of semi-limits $ \\lambda(z) \\subset \\mathbb{R}$ and the core function $C","authors_text":"Yochay Jerby","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2017-07-03T07:13:08Z","title":"An experimental study of the monotonicity property of the Riemann zeta function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01754","kind":"arxiv","version":8},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d76cf9dacec6aa18452391430a0aea4c1e1991ebdea7ac8e1daa55d5708ef4fd","target":"record","created_at":"2026-05-18T00:36:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0f8f1f9e694f5b0b58d12c3f13b1d3601d0500c4b03e7dc213c656e2ec30a5bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2017-07-03T07:13:08Z","title_canon_sha256":"500e470e407c1e07a3c1cd03c7b382224eaf7b9de99f8485f49dd35b205b84a8"},"schema_version":"1.0","source":{"id":"1707.01754","kind":"arxiv","version":8}},"canonical_sha256":"6d35d516aa684a4de0a2893294ca1df57ba50ed622c86eeac4b421588ce18452","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d35d516aa684a4de0a2893294ca1df57ba50ed622c86eeac4b421588ce18452","first_computed_at":"2026-05-18T00:36:21.939096Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:21.939096Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Km++x6sSL/Zbgu7F9f8Vd6IScIpdJykdBwkHox9y0VSCFbbT0bNlXDvoVSFPC8yMTslQ0mUcs4dGeITjpxqODA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:21.939696Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.01754","source_kind":"arxiv","source_version":8}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d76cf9dacec6aa18452391430a0aea4c1e1991ebdea7ac8e1daa55d5708ef4fd","sha256:512ab29384a7b28d458afe8f77018290ce608be6ae106e2597ca5d2ee557b545"],"state_sha256":"6a95582f3fa13b840a1249b47b6fbd413ce5c5e720ff4a1f724af8b8fd432588"}