{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:2F6QXXYZUOU4K5VWA2SAWO6KOY","short_pith_number":"pith:2F6QXXYZ","canonical_record":{"source":{"id":"2607.09110","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-07-10T05:47:47Z","cross_cats_sorted":[],"title_canon_sha256":"39c511e604d62d3b11e7201c7bc7c83a2ee84f21e7cf1508d0a8eba36d876435","abstract_canon_sha256":"1de4c05867b3d0c63c02d27fcffe1ffa03c711830337a8f67da1a358b99288f9"},"schema_version":"1.0"},"canonical_sha256":"d17d0bdf19a3a9c576b606a40b3bca7621f83aeb754be7e57e575d499aa01d47","source":{"kind":"arxiv","id":"2607.09110","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:2F6QXXYZUOU4K5VWA2SAWO6KOY","target":"record","payload":{"canonical_record":{"source":{"id":"2607.09110","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-07-10T05:47:47Z","cross_cats_sorted":[],"title_canon_sha256":"39c511e604d62d3b11e7201c7bc7c83a2ee84f21e7cf1508d0a8eba36d876435","abstract_canon_sha256":"1de4c05867b3d0c63c02d27fcffe1ffa03c711830337a8f67da1a358b99288f9"},"schema_version":"1.0"},"canonical_sha256":"d17d0bdf19a3a9c576b606a40b3bca7621f83aeb754be7e57e575d499aa01d47","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-13T01:18:42.900901Z","signature_b64":"hTig5qDjgizgMCEo7gdT+PIKpzM4SsFyVEPfj5tzO13eyJl6HhTQPk6+g/WTefGtpxocyNxy8UoVGdjEz+KFDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d17d0bdf19a3a9c576b606a40b3bca7621f83aeb754be7e57e575d499aa01d47","last_reissued_at":"2026-07-13T01:18:42.899109Z","signature_status":"signed_v1","first_computed_at":"2026-07-13T01:18:42.899109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.09110","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-13T01:18:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XrfuIg0d+bxch06kiwl4SL8QvWFOhS85XEasrF5aVkA3wBPyJcBL01r/8Yn7bOh35cSopg6DuP88hicIA9MOAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T22:16:03.693669Z"},"content_sha256":"52d4149920f573f86ee45ed2c378580654c21062ebf05fc3b52c729041880dee","schema_version":"1.0","event_id":"sha256:52d4149920f573f86ee45ed2c378580654c21062ebf05fc3b52c729041880dee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:2F6QXXYZUOU4K5VWA2SAWO6KOY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Averages of diagonal Elliott-Halberstam problem twisted by M\\\"obius function with Sobolev and H\\\"older-Zygmund weights","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Marco Cantarini","submitted_at":"2026-07-10T05:47:47Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.09110","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.09110/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-13T01:18:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e981QHN+CgZHagQgpH5jBESPsTS/bEGwVxSjw9OXF6n4VFs7R85PbpfGg0V4Ys39Mjjvh+kTAsle1/yElI4+CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T22:16:03.694352Z"},"content_sha256":"34bfc8f80421fb6e39db43e169d731b64ec602ef1b441d55d1803fea1b05b109","schema_version":"1.0","event_id":"sha256:34bfc8f80421fb6e39db43e169d731b64ec602ef1b441d55d1803fea1b05b109"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2F6QXXYZUOU4K5VWA2SAWO6KOY/bundle.json","state_url":"https://pith.science/pith/2F6QXXYZUOU4K5VWA2SAWO6KOY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2F6QXXYZUOU4K5VWA2SAWO6KOY/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-11T22:16:03Z","links":{"resolver":"https://pith.science/pith/2F6QXXYZUOU4K5VWA2SAWO6KOY","bundle":"https://pith.science/pith/2F6QXXYZUOU4K5VWA2SAWO6KOY/bundle.json","state":"https://pith.science/pith/2F6QXXYZUOU4K5VWA2SAWO6KOY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2F6QXXYZUOU4K5VWA2SAWO6KOY/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C5pHlHH5GxtUw5PVqERVE5UmkN+PzoSTN8bY6PVQCmnQk6x+iFTN8nu2FVOiJDZ0Ybp1UD1OKw2rP3Nez34YBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T22:16:03.700125Z","bundle_sha256":"71ae7aa66f89290481589d3c352262cf05d07204e0f36949de65ecf8b2bdfdcf"}}