{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:2F6QXXYZUOU4K5VWA2SAWO6KOY","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":"1de4c05867b3d0c63c02d27fcffe1ffa03c711830337a8f67da1a358b99288f9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-07-10T05:47:47Z","title_canon_sha256":"39c511e604d62d3b11e7201c7bc7c83a2ee84f21e7cf1508d0a8eba36d876435"},"schema_version":"1.0","source":{"id":"2607.09110","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.09110","created_at":"2026-07-13T01:18:42Z"},{"alias_kind":"arxiv_version","alias_value":"2607.09110v1","created_at":"2026-07-13T01:18:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.09110","created_at":"2026-07-13T01:18:42Z"},{"alias_kind":"pith_short_12","alias_value":"2F6QXXYZUOU4","created_at":"2026-07-13T01:18:42Z"},{"alias_kind":"pith_short_16","alias_value":"2F6QXXYZUOU4K5VW","created_at":"2026-07-13T01:18:42Z"},{"alias_kind":"pith_short_8","alias_value":"2F6QXXYZ","created_at":"2026-07-13T01:18:42Z"}],"graph_snapshots":[{"event_id":"sha256:34bfc8f80421fb6e39db43e169d731b64ec602ef1b441d55d1803fea1b05b109","target":"graph","created_at":"2026-07-13T01:18:42Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.09110/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recalling that the so-called Elliott-Halberstam conjecture twisted by the M\\\"obius function $\\mu(n)$ claims that \\[ \\sum_{q\\leq N^{\\theta}}\\max_{y\\leq N}\\max_{(a,q)=1}\\left|\\sum_{\\underset{{\\scriptstyle n\\equiv a\\,\\mod\\,q}}{n\\leq y}}\\Lambda(n)\\mu\\left(N-n\\right)-\\frac{1}{\\varphi\\left(q\\right)}\\sum_{n\\leq y}\\Lambda(n)\\mu\\left(N-n\\right)\\right|\\ll\\frac{N}{\\log\\left(N\\right)^{A}} \\] for every $A>0$, where $0<\\theta<1$ is fixed, and also recalling that the validity of this conjecture, in combination with the validity of the classical Elliott-Halberstam for suitable $\\theta$, proves the binary Gold","authors_text":"Marco Cantarini","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-07-10T05:47:47Z","title":"Averages of diagonal Elliott-Halberstam problem twisted by M\\\"obius function with Sobolev and H\\\"older-Zygmund weights"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.09110","kind":"arxiv","version":1},"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":"sha256:52d4149920f573f86ee45ed2c378580654c21062ebf05fc3b52c729041880dee","target":"record","created_at":"2026-07-13T01:18:42Z","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":"1de4c05867b3d0c63c02d27fcffe1ffa03c711830337a8f67da1a358b99288f9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-07-10T05:47:47Z","title_canon_sha256":"39c511e604d62d3b11e7201c7bc7c83a2ee84f21e7cf1508d0a8eba36d876435"},"schema_version":"1.0","source":{"id":"2607.09110","kind":"arxiv","version":1}},"canonical_sha256":"d17d0bdf19a3a9c576b606a40b3bca7621f83aeb754be7e57e575d499aa01d47","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d17d0bdf19a3a9c576b606a40b3bca7621f83aeb754be7e57e575d499aa01d47","first_computed_at":"2026-07-13T01:18:42.899109Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-13T01:18:42.899109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hTig5qDjgizgMCEo7gdT+PIKpzM4SsFyVEPfj5tzO13eyJl6HhTQPk6+g/WTefGtpxocyNxy8UoVGdjEz+KFDg==","signature_status":"signed_v1","signed_at":"2026-07-13T01:18:42.900901Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.09110","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:52d4149920f573f86ee45ed2c378580654c21062ebf05fc3b52c729041880dee","sha256:34bfc8f80421fb6e39db43e169d731b64ec602ef1b441d55d1803fea1b05b109"],"state_sha256":"7b8030044b2c51e26e9fe3b073aad72ef2365158098e6ef959afb13df9bf9170"}