{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:OW7GS7RKFMISYPR2RN25DPWVQL","short_pith_number":"pith:OW7GS7RK","canonical_record":{"source":{"id":"1407.2510","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-05-15T20:43:48Z","cross_cats_sorted":[],"title_canon_sha256":"0353486c3c5cd94f758b02927b198246df4309842bb10d0d7795d723fbc236d3","abstract_canon_sha256":"c91b19c9cbdb59411030eff2bb216fef7312212649bda4c69bfaa03960b67286"},"schema_version":"1.0"},"canonical_sha256":"75be697e2a2b112c3e3a8b75d1bed582eab420ade9c44f75330e2aeff40b8df9","source":{"kind":"arxiv","id":"1407.2510","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.2510","created_at":"2026-05-18T02:48:01Z"},{"alias_kind":"arxiv_version","alias_value":"1407.2510v1","created_at":"2026-05-18T02:48:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.2510","created_at":"2026-05-18T02:48:01Z"},{"alias_kind":"pith_short_12","alias_value":"OW7GS7RKFMIS","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"OW7GS7RKFMISYPR2","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"OW7GS7RK","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:OW7GS7RKFMISYPR2RN25DPWVQL","target":"record","payload":{"canonical_record":{"source":{"id":"1407.2510","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-05-15T20:43:48Z","cross_cats_sorted":[],"title_canon_sha256":"0353486c3c5cd94f758b02927b198246df4309842bb10d0d7795d723fbc236d3","abstract_canon_sha256":"c91b19c9cbdb59411030eff2bb216fef7312212649bda4c69bfaa03960b67286"},"schema_version":"1.0"},"canonical_sha256":"75be697e2a2b112c3e3a8b75d1bed582eab420ade9c44f75330e2aeff40b8df9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:01.422248Z","signature_b64":"LQVs4rL4RNKD9kgkT/KwzFBTGGq2v09RorQ0zdzsqiEunDapXG5tk5j0LLiwpb1WZcyxRvrnr0aI1OG9uLTwCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75be697e2a2b112c3e3a8b75d1bed582eab420ade9c44f75330e2aeff40b8df9","last_reissued_at":"2026-05-18T02:48:01.421804Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:01.421804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.2510","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":"2026-05-18T02:48:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VfZroLxvd2qwvfZ09YFRidVZU5/bBmU9FDQLqNu7S4BmapQ22IW6qtMyZQ8W/o9tKnBOenouGt+JfOG3STvVAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T01:12:13.534921Z"},"content_sha256":"d572822cb924fb20aa78fdddd6a0a127e4681ce42fa5d39bc40733484e4d6cb1","schema_version":"1.0","event_id":"sha256:d572822cb924fb20aa78fdddd6a0a127e4681ce42fa5d39bc40733484e4d6cb1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:OW7GS7RKFMISYPR2RN25DPWVQL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Erdos Discrepancy Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Bart Selman, Carla P. Gomes, Ronan Le Bras","submitted_at":"2014-05-15T20:43:48Z","abstract_excerpt":"According to the Erd\\H{o}s discrepancy conjecture, for any infinite $\\pm 1$ sequence, there exists a homogeneous arithmetic progression of unbounded discrepancy. In other words, for any $\\pm 1$ sequence $(x_1,x_2,...)$ and a discrepancy $C$, there exist integers $m$ and $d$ such that $|\\sum_{i=1}^m x_{i \\cdot d}| > C$. This is an $80$-year-old open problem and recent development proved that this conjecture is true for discrepancies up to $2$. Paul Erd\\H{o}s also conjectured that this property of unbounded discrepancy even holds for the restricted case of completely multiplicative sequences (CM"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2510","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":""},"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":"2026-05-18T02:48:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kf/cHVxEe3eVcq9muLk1nVojTN1zmzGTWNGOBKYGMfE2WHEtW9ErDMEFECN2DfxOyEvFCxdNGQM7vlgp+NL0DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T01:12:13.535612Z"},"content_sha256":"70feb9e355a89c629e95f31b4e0917857af459d9e4afe54a1eb58de3aaac6e5a","schema_version":"1.0","event_id":"sha256:70feb9e355a89c629e95f31b4e0917857af459d9e4afe54a1eb58de3aaac6e5a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OW7GS7RKFMISYPR2RN25DPWVQL/bundle.json","state_url":"https://pith.science/pith/OW7GS7RKFMISYPR2RN25DPWVQL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OW7GS7RKFMISYPR2RN25DPWVQL/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":"2026-06-08T01:12:13Z","links":{"resolver":"https://pith.science/pith/OW7GS7RKFMISYPR2RN25DPWVQL","bundle":"https://pith.science/pith/OW7GS7RKFMISYPR2RN25DPWVQL/bundle.json","state":"https://pith.science/pith/OW7GS7RKFMISYPR2RN25DPWVQL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OW7GS7RKFMISYPR2RN25DPWVQL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:OW7GS7RKFMISYPR2RN25DPWVQL","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":"c91b19c9cbdb59411030eff2bb216fef7312212649bda4c69bfaa03960b67286","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-05-15T20:43:48Z","title_canon_sha256":"0353486c3c5cd94f758b02927b198246df4309842bb10d0d7795d723fbc236d3"},"schema_version":"1.0","source":{"id":"1407.2510","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.2510","created_at":"2026-05-18T02:48:01Z"},{"alias_kind":"arxiv_version","alias_value":"1407.2510v1","created_at":"2026-05-18T02:48:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.2510","created_at":"2026-05-18T02:48:01Z"},{"alias_kind":"pith_short_12","alias_value":"OW7GS7RKFMIS","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"OW7GS7RKFMISYPR2","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"OW7GS7RK","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:70feb9e355a89c629e95f31b4e0917857af459d9e4afe54a1eb58de3aaac6e5a","target":"graph","created_at":"2026-05-18T02:48:01Z","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":"According to the Erd\\H{o}s discrepancy conjecture, for any infinite $\\pm 1$ sequence, there exists a homogeneous arithmetic progression of unbounded discrepancy. In other words, for any $\\pm 1$ sequence $(x_1,x_2,...)$ and a discrepancy $C$, there exist integers $m$ and $d$ such that $|\\sum_{i=1}^m x_{i \\cdot d}| > C$. This is an $80$-year-old open problem and recent development proved that this conjecture is true for discrepancies up to $2$. Paul Erd\\H{o}s also conjectured that this property of unbounded discrepancy even holds for the restricted case of completely multiplicative sequences (CM","authors_text":"Bart Selman, Carla P. Gomes, Ronan Le Bras","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-05-15T20:43:48Z","title":"On the Erdos Discrepancy Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2510","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:d572822cb924fb20aa78fdddd6a0a127e4681ce42fa5d39bc40733484e4d6cb1","target":"record","created_at":"2026-05-18T02:48:01Z","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":"c91b19c9cbdb59411030eff2bb216fef7312212649bda4c69bfaa03960b67286","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-05-15T20:43:48Z","title_canon_sha256":"0353486c3c5cd94f758b02927b198246df4309842bb10d0d7795d723fbc236d3"},"schema_version":"1.0","source":{"id":"1407.2510","kind":"arxiv","version":1}},"canonical_sha256":"75be697e2a2b112c3e3a8b75d1bed582eab420ade9c44f75330e2aeff40b8df9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"75be697e2a2b112c3e3a8b75d1bed582eab420ade9c44f75330e2aeff40b8df9","first_computed_at":"2026-05-18T02:48:01.421804Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:01.421804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LQVs4rL4RNKD9kgkT/KwzFBTGGq2v09RorQ0zdzsqiEunDapXG5tk5j0LLiwpb1WZcyxRvrnr0aI1OG9uLTwCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:01.422248Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.2510","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d572822cb924fb20aa78fdddd6a0a127e4681ce42fa5d39bc40733484e4d6cb1","sha256:70feb9e355a89c629e95f31b4e0917857af459d9e4afe54a1eb58de3aaac6e5a"],"state_sha256":"2810d1b5549afc023723cb79cf3ee4c1275c7007d8d212d52d70f824caa20efe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oVDrVdphFhI0NqdXpjoap7A8ejfsP+hYGWFRi7nhYN3Z0y+8qK6hxf1M55MpUcr8TW1XQbceE0OE+MlsgXjCDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T01:12:13.539700Z","bundle_sha256":"1be18a81aab8a23550e1231707e91b8c40f297304c6bd9e50065f7f0633150cd"}}