{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:ZTRKLHYKEBHGYWK3BZQMPYCZYY","short_pith_number":"pith:ZTRKLHYK","canonical_record":{"source":{"id":"2607.13762","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-15T12:22:23Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"af582919be2528511f322c8b1ee8037242dc2b2d169a2ac3023d9d4226aed06e","abstract_canon_sha256":"d5f928d3ba63fbecbd3054e9804c3d89a3d9b892cab28b00c8f475195ad18f6a"},"schema_version":"1.0"},"canonical_sha256":"cce2a59f0a204e6c595b0e60c7e059c634e2e0183e9efd43505578abe274d3ca","source":{"kind":"arxiv","id":"2607.13762","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.13762","created_at":"2026-07-16T01:23:05Z"},{"alias_kind":"arxiv_version","alias_value":"2607.13762v1","created_at":"2026-07-16T01:23:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.13762","created_at":"2026-07-16T01:23:05Z"},{"alias_kind":"pith_short_12","alias_value":"ZTRKLHYKEBHG","created_at":"2026-07-16T01:23:05Z"},{"alias_kind":"pith_short_16","alias_value":"ZTRKLHYKEBHGYWK3","created_at":"2026-07-16T01:23:05Z"},{"alias_kind":"pith_short_8","alias_value":"ZTRKLHYK","created_at":"2026-07-16T01:23:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:ZTRKLHYKEBHGYWK3BZQMPYCZYY","target":"record","payload":{"canonical_record":{"source":{"id":"2607.13762","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-15T12:22:23Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"af582919be2528511f322c8b1ee8037242dc2b2d169a2ac3023d9d4226aed06e","abstract_canon_sha256":"d5f928d3ba63fbecbd3054e9804c3d89a3d9b892cab28b00c8f475195ad18f6a"},"schema_version":"1.0"},"canonical_sha256":"cce2a59f0a204e6c595b0e60c7e059c634e2e0183e9efd43505578abe274d3ca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-16T01:23:05.048966Z","signature_b64":"+EPKfbXnbnKbKd/4Fsno4EBuZIhP3bNMlm5NIFipWl6OHHY0D2CTqGb2H0N9/9ZH7YfVlgiaQJeWWX+2OydKAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cce2a59f0a204e6c595b0e60c7e059c634e2e0183e9efd43505578abe274d3ca","last_reissued_at":"2026-07-16T01:23:05.047412Z","signature_status":"signed_v1","first_computed_at":"2026-07-16T01:23:05.047412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.13762","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":"2026-07-16T01:23:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cBS1Ntkcw8EZdJPd31FwPC3TKZXjXwFsLqXMV9+b/V8de2EjveRI4KZciEKltZlx/uk7QU9swgRsUlEhRtxIDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T04:27:32.245022Z"},"content_sha256":"9c96bcf72525a3e4061058516fd59cfe822deb871ddc19838a5cd7eeadfbf5c0","schema_version":"1.0","event_id":"sha256:9c96bcf72525a3e4061058516fd59cfe822deb871ddc19838a5cd7eeadfbf5c0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:ZTRKLHYKEBHGYWK3BZQMPYCZYY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"No finite level of the NPA hierarchy is exact for the doubly-tilted CHSH functional near the critical tilt","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"quant-ph","authors_text":"Anton Pakhunov","submitted_at":"2026-07-15T12:22:23Z","abstract_excerpt":"Gigena, Panwar, Scala, Araujo, Farkas and Chaturvedi [npj Quantum Inf. 11, 82 (2025)] determined the quantum maximum of the doubly-tilted CHSH functionals, observed that the Navascues-Pironio-Acin level needed for exactness grows without evident bound toward the critical tilt, and asked whether any finite level suffices. We answer this in the negative. For the symmetric critical family $B_s=(1-s/2)(\\langle A_0\\rangle+\\langle B_0\\rangle)+\\mathrm{CHSH}$ we prove: for every NPA level $k\\ge 2$ there are an explicit rational $g_k>0$ and an $s^*_k>0$ with $c_k(s)\\ge 4-s+g_k s^2$ on $(0,s^*_k]$; sinc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.13762","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/2607.13762/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":"2026-07-16T01:23:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"54RpUE9B9uSEZVImRVtO3iNYyPQ9dTa9BrT0zrpxtfZQo9BPX6KjHJlRVyaLznaUrmLxK1QiClVDPrmx4vltCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T04:27:32.245543Z"},"content_sha256":"16504805b28be13c9baa3fbfecf57b25378bbb36c2b792be78f44288b9d7e6ca","schema_version":"1.0","event_id":"sha256:16504805b28be13c9baa3fbfecf57b25378bbb36c2b792be78f44288b9d7e6ca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZTRKLHYKEBHGYWK3BZQMPYCZYY/bundle.json","state_url":"https://pith.science/pith/ZTRKLHYKEBHGYWK3BZQMPYCZYY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZTRKLHYKEBHGYWK3BZQMPYCZYY/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":"2026-08-04T04:27:32Z","links":{"resolver":"https://pith.science/pith/ZTRKLHYKEBHGYWK3BZQMPYCZYY","bundle":"https://pith.science/pith/ZTRKLHYKEBHGYWK3BZQMPYCZYY/bundle.json","state":"https://pith.science/pith/ZTRKLHYKEBHGYWK3BZQMPYCZYY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZTRKLHYKEBHGYWK3BZQMPYCZYY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ZTRKLHYKEBHGYWK3BZQMPYCZYY","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":"d5f928d3ba63fbecbd3054e9804c3d89a3d9b892cab28b00c8f475195ad18f6a","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-15T12:22:23Z","title_canon_sha256":"af582919be2528511f322c8b1ee8037242dc2b2d169a2ac3023d9d4226aed06e"},"schema_version":"1.0","source":{"id":"2607.13762","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.13762","created_at":"2026-07-16T01:23:05Z"},{"alias_kind":"arxiv_version","alias_value":"2607.13762v1","created_at":"2026-07-16T01:23:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.13762","created_at":"2026-07-16T01:23:05Z"},{"alias_kind":"pith_short_12","alias_value":"ZTRKLHYKEBHG","created_at":"2026-07-16T01:23:05Z"},{"alias_kind":"pith_short_16","alias_value":"ZTRKLHYKEBHGYWK3","created_at":"2026-07-16T01:23:05Z"},{"alias_kind":"pith_short_8","alias_value":"ZTRKLHYK","created_at":"2026-07-16T01:23:05Z"}],"graph_snapshots":[{"event_id":"sha256:16504805b28be13c9baa3fbfecf57b25378bbb36c2b792be78f44288b9d7e6ca","target":"graph","created_at":"2026-07-16T01:23:05Z","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/2607.13762/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Gigena, Panwar, Scala, Araujo, Farkas and Chaturvedi [npj Quantum Inf. 11, 82 (2025)] determined the quantum maximum of the doubly-tilted CHSH functionals, observed that the Navascues-Pironio-Acin level needed for exactness grows without evident bound toward the critical tilt, and asked whether any finite level suffices. We answer this in the negative. For the symmetric critical family $B_s=(1-s/2)(\\langle A_0\\rangle+\\langle B_0\\rangle)+\\mathrm{CHSH}$ we prove: for every NPA level $k\\ge 2$ there are an explicit rational $g_k>0$ and an $s^*_k>0$ with $c_k(s)\\ge 4-s+g_k s^2$ on $(0,s^*_k]$; sinc","authors_text":"Anton Pakhunov","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-15T12:22:23Z","title":"No finite level of the NPA hierarchy is exact for the doubly-tilted CHSH functional near the critical tilt"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.13762","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":"sha256:9c96bcf72525a3e4061058516fd59cfe822deb871ddc19838a5cd7eeadfbf5c0","target":"record","created_at":"2026-07-16T01:23:05Z","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":"d5f928d3ba63fbecbd3054e9804c3d89a3d9b892cab28b00c8f475195ad18f6a","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-15T12:22:23Z","title_canon_sha256":"af582919be2528511f322c8b1ee8037242dc2b2d169a2ac3023d9d4226aed06e"},"schema_version":"1.0","source":{"id":"2607.13762","kind":"arxiv","version":1}},"canonical_sha256":"cce2a59f0a204e6c595b0e60c7e059c634e2e0183e9efd43505578abe274d3ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cce2a59f0a204e6c595b0e60c7e059c634e2e0183e9efd43505578abe274d3ca","first_computed_at":"2026-07-16T01:23:05.047412Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-16T01:23:05.047412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+EPKfbXnbnKbKd/4Fsno4EBuZIhP3bNMlm5NIFipWl6OHHY0D2CTqGb2H0N9/9ZH7YfVlgiaQJeWWX+2OydKAQ==","signature_status":"signed_v1","signed_at":"2026-07-16T01:23:05.048966Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.13762","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c96bcf72525a3e4061058516fd59cfe822deb871ddc19838a5cd7eeadfbf5c0","sha256:16504805b28be13c9baa3fbfecf57b25378bbb36c2b792be78f44288b9d7e6ca"],"state_sha256":"c47046e44c85d1ede23f2647b4bb1c9fe8ba0cc26a288182d0e992754782e727"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/BVSfNNDRWzx7dUh7PxXN62gB783Nkggy7WbKjSiRf2NZLsBjjWT8+sxDtUnyvnicrhsyHZ75w+VpP7t0iadCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T04:27:32.250759Z","bundle_sha256":"b977a3ca055a360157ba20e38d690ca49556f3309df46c3a75f1da8aa691e04e"}}