{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:PR2WVD2U3NTYXYCWTWDIZ5BFTM","short_pith_number":"pith:PR2WVD2U","canonical_record":{"source":{"id":"1609.03435","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-12T15:08:11Z","cross_cats_sorted":["math.CV","math.NT"],"title_canon_sha256":"d5a5798b17eb9b23e28e94014c6421c2adb1f88665c3a87c98b85e7a5e0b4641","abstract_canon_sha256":"6d047d7fb3289d3c5dff541374b2fa4b1025adf821136ea2585a2f0fd535be73"},"schema_version":"1.0"},"canonical_sha256":"7c756a8f54db678be0569d868cf4259b09a9ac23bcf7ec858e567ee22f6a0e94","source":{"kind":"arxiv","id":"1609.03435","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.03435","created_at":"2026-05-18T00:53:02Z"},{"alias_kind":"arxiv_version","alias_value":"1609.03435v2","created_at":"2026-05-18T00:53:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03435","created_at":"2026-05-18T00:53:02Z"},{"alias_kind":"pith_short_12","alias_value":"PR2WVD2U3NTY","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PR2WVD2U3NTYXYCW","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PR2WVD2U","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:PR2WVD2U3NTYXYCWTWDIZ5BFTM","target":"record","payload":{"canonical_record":{"source":{"id":"1609.03435","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-12T15:08:11Z","cross_cats_sorted":["math.CV","math.NT"],"title_canon_sha256":"d5a5798b17eb9b23e28e94014c6421c2adb1f88665c3a87c98b85e7a5e0b4641","abstract_canon_sha256":"6d047d7fb3289d3c5dff541374b2fa4b1025adf821136ea2585a2f0fd535be73"},"schema_version":"1.0"},"canonical_sha256":"7c756a8f54db678be0569d868cf4259b09a9ac23bcf7ec858e567ee22f6a0e94","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:02.300170Z","signature_b64":"obSiDZ/UT21OBiElDyl/qqkuPyGahcAXfDtmTjBcWXCj5kXuz5L79RVVWoc5fLinlLzSY7ibhVTtzpZTVrbLDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c756a8f54db678be0569d868cf4259b09a9ac23bcf7ec858e567ee22f6a0e94","last_reissued_at":"2026-05-18T00:53:02.299556Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:02.299556Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.03435","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:53:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rVIzUg6FTxwHryEUFMIkAK98X7ITPneH+XUMcRxjzAggHj9PEdcklT7x8BZEwX8bVf0dsnbpcZ5p1cnOtGrOCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:35:37.531663Z"},"content_sha256":"7b29e94587782cfb61b5140dbaf9c5ae67310b08f9259fe5ad8b7c4efad39962","schema_version":"1.0","event_id":"sha256:7b29e94587782cfb61b5140dbaf9c5ae67310b08f9259fe5ad8b7c4efad39962"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:PR2WVD2U3NTYXYCWTWDIZ5BFTM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Erd\\\"{o}s flat polynomials problem, Chowla conjecture and Riemann Hypothesis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.NT"],"primary_cat":"math.CO","authors_text":"el Houcein el Abdalaoui","submitted_at":"2016-09-12T15:08:11Z","abstract_excerpt":"There are no square $L^2$-flat sequences of polynomials of the type\n  $$\\frac{1}{\\sqrt q}( \\epsilon_0 + \\epsilon_1z + \\epsilon_2z^2 + \\cdots + \\epsilon_{q-2}z^{q-2} +\\epsilon_q z^{q-1}),$$ where for each $j,~~ 0 \\leq j\\leq q-1,~\\epsilon_j = \\pm 1$. It follows that Erd\\\"{o}s's conjectures on Littlewood polynomials hold. Consequently, Turyn-Golay's conjecture is true, that is, there are only finitely many Barker sequences. We further get that the spectrum of dynamical systems arising from continuous Morse sequences is singular. This settles an old question due to M. Keane. Applying our reasoning"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03435","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T00:53:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8RbRvP1BSrchukuJoaNm7oUjanMgUsEgqi67cgfSj1MNgLRdiFYgBR+64Z3GQUFpmr2IGQa4GmtEeEhBVlb5CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:35:37.532010Z"},"content_sha256":"57cff9a5e45991d1412757ebff1db70c254a3dd3cd175689294010443c3a4a39","schema_version":"1.0","event_id":"sha256:57cff9a5e45991d1412757ebff1db70c254a3dd3cd175689294010443c3a4a39"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PR2WVD2U3NTYXYCWTWDIZ5BFTM/bundle.json","state_url":"https://pith.science/pith/PR2WVD2U3NTYXYCWTWDIZ5BFTM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PR2WVD2U3NTYXYCWTWDIZ5BFTM/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":"2026-06-02T04:35:37Z","links":{"resolver":"https://pith.science/pith/PR2WVD2U3NTYXYCWTWDIZ5BFTM","bundle":"https://pith.science/pith/PR2WVD2U3NTYXYCWTWDIZ5BFTM/bundle.json","state":"https://pith.science/pith/PR2WVD2U3NTYXYCWTWDIZ5BFTM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PR2WVD2U3NTYXYCWTWDIZ5BFTM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PR2WVD2U3NTYXYCWTWDIZ5BFTM","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":"6d047d7fb3289d3c5dff541374b2fa4b1025adf821136ea2585a2f0fd535be73","cross_cats_sorted":["math.CV","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-12T15:08:11Z","title_canon_sha256":"d5a5798b17eb9b23e28e94014c6421c2adb1f88665c3a87c98b85e7a5e0b4641"},"schema_version":"1.0","source":{"id":"1609.03435","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.03435","created_at":"2026-05-18T00:53:02Z"},{"alias_kind":"arxiv_version","alias_value":"1609.03435v2","created_at":"2026-05-18T00:53:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03435","created_at":"2026-05-18T00:53:02Z"},{"alias_kind":"pith_short_12","alias_value":"PR2WVD2U3NTY","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PR2WVD2U3NTYXYCW","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PR2WVD2U","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:57cff9a5e45991d1412757ebff1db70c254a3dd3cd175689294010443c3a4a39","target":"graph","created_at":"2026-05-18T00:53:02Z","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":"There are no square $L^2$-flat sequences of polynomials of the type\n  $$\\frac{1}{\\sqrt q}( \\epsilon_0 + \\epsilon_1z + \\epsilon_2z^2 + \\cdots + \\epsilon_{q-2}z^{q-2} +\\epsilon_q z^{q-1}),$$ where for each $j,~~ 0 \\leq j\\leq q-1,~\\epsilon_j = \\pm 1$. It follows that Erd\\\"{o}s's conjectures on Littlewood polynomials hold. Consequently, Turyn-Golay's conjecture is true, that is, there are only finitely many Barker sequences. We further get that the spectrum of dynamical systems arising from continuous Morse sequences is singular. This settles an old question due to M. Keane. Applying our reasoning","authors_text":"el Houcein el Abdalaoui","cross_cats":["math.CV","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-12T15:08:11Z","title":"On the Erd\\\"{o}s flat polynomials problem, Chowla conjecture and Riemann Hypothesis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03435","kind":"arxiv","version":2},"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":"sha256:7b29e94587782cfb61b5140dbaf9c5ae67310b08f9259fe5ad8b7c4efad39962","target":"record","created_at":"2026-05-18T00:53:02Z","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":"6d047d7fb3289d3c5dff541374b2fa4b1025adf821136ea2585a2f0fd535be73","cross_cats_sorted":["math.CV","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-12T15:08:11Z","title_canon_sha256":"d5a5798b17eb9b23e28e94014c6421c2adb1f88665c3a87c98b85e7a5e0b4641"},"schema_version":"1.0","source":{"id":"1609.03435","kind":"arxiv","version":2}},"canonical_sha256":"7c756a8f54db678be0569d868cf4259b09a9ac23bcf7ec858e567ee22f6a0e94","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c756a8f54db678be0569d868cf4259b09a9ac23bcf7ec858e567ee22f6a0e94","first_computed_at":"2026-05-18T00:53:02.299556Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:02.299556Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"obSiDZ/UT21OBiElDyl/qqkuPyGahcAXfDtmTjBcWXCj5kXuz5L79RVVWoc5fLinlLzSY7ibhVTtzpZTVrbLDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:02.300170Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.03435","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7b29e94587782cfb61b5140dbaf9c5ae67310b08f9259fe5ad8b7c4efad39962","sha256:57cff9a5e45991d1412757ebff1db70c254a3dd3cd175689294010443c3a4a39"],"state_sha256":"41813c46ad4a1bb5e89a9c7e711753490e3792ca6d724088baf614460cd53e1c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1jDKs8BCRuF70PArxfbTnuB0L6w/urPfgCkQE+Mkh0yWvL3Y1G81x5fYOpzXkcFPZyc7x/tcXyAph1DaJVb2Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T04:35:37.534482Z","bundle_sha256":"221edb71d3ca982f45c6d989e533e4d0476a935351d6d1d086423fbeb5b1e491"}}