{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:WPBJHZWIUHGEJCTDOALTZH67V7","short_pith_number":"pith:WPBJHZWI","canonical_record":{"source":{"id":"1803.08905","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-03-23T17:34:30Z","cross_cats_sorted":["math.AG","math.CA","math.CO"],"title_canon_sha256":"75b3797130b7279d86cce1fd9dd9c206c0caf51c23197d072ab30a9c36b1b8a6","abstract_canon_sha256":"269f13f02c8c8e92c7fe50b22fbcb87fddada58babc107af261d206fa03edb44"},"schema_version":"1.0"},"canonical_sha256":"b3c293e6c8a1cc448a6370173c9fdfafc9626ad775ccdb2b1938c58bf696cbf8","source":{"kind":"arxiv","id":"1803.08905","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.08905","created_at":"2026-05-17T23:47:21Z"},{"alias_kind":"arxiv_version","alias_value":"1803.08905v2","created_at":"2026-05-17T23:47:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.08905","created_at":"2026-05-17T23:47:21Z"},{"alias_kind":"pith_short_12","alias_value":"WPBJHZWIUHGE","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"WPBJHZWIUHGEJCTD","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"WPBJHZWI","created_at":"2026-05-18T12:33:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:WPBJHZWIUHGEJCTDOALTZH67V7","target":"record","payload":{"canonical_record":{"source":{"id":"1803.08905","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-03-23T17:34:30Z","cross_cats_sorted":["math.AG","math.CA","math.CO"],"title_canon_sha256":"75b3797130b7279d86cce1fd9dd9c206c0caf51c23197d072ab30a9c36b1b8a6","abstract_canon_sha256":"269f13f02c8c8e92c7fe50b22fbcb87fddada58babc107af261d206fa03edb44"},"schema_version":"1.0"},"canonical_sha256":"b3c293e6c8a1cc448a6370173c9fdfafc9626ad775ccdb2b1938c58bf696cbf8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:21.106004Z","signature_b64":"Yxdak+Z1ITVtgJgW2q7rEPoxCmCgo7F+iCKuRTfDSxh1bxsbrYcz7yZ8IWAsNTSg5kph5oPQ2eh1OVFUJMo+DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3c293e6c8a1cc448a6370173c9fdfafc9626ad775ccdb2b1938c58bf696cbf8","last_reissued_at":"2026-05-17T23:47:21.105439Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:21.105439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.08905","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":"2026-05-17T23:47:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QZ1aAyDnPv5vD4xF7VR/1zE4YP80/r2Px0n5DN5XTzABYUDgfHTah0syvXWGy6AG2caME3yXZnKMI6FY4c0TDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:30:32.837809Z"},"content_sha256":"b67d8cc8c337ddb37cc72567e46b84043698cf3d3527106befde3185e96538e7","schema_version":"1.0","event_id":"sha256:b67d8cc8c337ddb37cc72567e46b84043698cf3d3527106befde3185e96538e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:WPBJHZWIUHGEJCTDOALTZH67V7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Many odd zeta values are irrational","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CA","math.CO"],"primary_cat":"math.NT","authors_text":"Johannes Sprang, St\\'ephane Fischler, Wadim Zudilin","submitted_at":"2018-03-23T17:34:30Z","abstract_excerpt":"Building upon ideas of the second and third authors, we prove that at least $2^{(1-\\varepsilon)\\frac{\\log s}{\\log\\log s}}$ values of the Riemann zeta function at odd integers between 3 and $s$ are irrational, where $\\varepsilon$ is any positive real number and $s$ is large enough in terms of $\\varepsilon$. This lower bound is asymptotically larger than any power of $\\log s$; it improves on the bound $\\frac{1-\\varepsilon}{1+\\log2}\\log s$ that follows from the Ball--Rivoal theorem.\n  The proof is based on construction of several linear forms in odd zeta values with related coefficients."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.08905","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":"2026-05-17T23:47:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DIJkuROLjeGkUEffsgn6UIJY/bJCzUsJHJuYOqummbdqpG8go0w/YjNa6enxN7hjRKDgmMepVp5aXGghGhZFBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:30:32.838162Z"},"content_sha256":"0827d0d186c8a0ab6dc6fd94807253c3c7cea499cee7fd983ea3a6358f013ab7","schema_version":"1.0","event_id":"sha256:0827d0d186c8a0ab6dc6fd94807253c3c7cea499cee7fd983ea3a6358f013ab7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WPBJHZWIUHGEJCTDOALTZH67V7/bundle.json","state_url":"https://pith.science/pith/WPBJHZWIUHGEJCTDOALTZH67V7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WPBJHZWIUHGEJCTDOALTZH67V7/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":"2026-05-28T13:30:32Z","links":{"resolver":"https://pith.science/pith/WPBJHZWIUHGEJCTDOALTZH67V7","bundle":"https://pith.science/pith/WPBJHZWIUHGEJCTDOALTZH67V7/bundle.json","state":"https://pith.science/pith/WPBJHZWIUHGEJCTDOALTZH67V7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WPBJHZWIUHGEJCTDOALTZH67V7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WPBJHZWIUHGEJCTDOALTZH67V7","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":"269f13f02c8c8e92c7fe50b22fbcb87fddada58babc107af261d206fa03edb44","cross_cats_sorted":["math.AG","math.CA","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-03-23T17:34:30Z","title_canon_sha256":"75b3797130b7279d86cce1fd9dd9c206c0caf51c23197d072ab30a9c36b1b8a6"},"schema_version":"1.0","source":{"id":"1803.08905","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.08905","created_at":"2026-05-17T23:47:21Z"},{"alias_kind":"arxiv_version","alias_value":"1803.08905v2","created_at":"2026-05-17T23:47:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.08905","created_at":"2026-05-17T23:47:21Z"},{"alias_kind":"pith_short_12","alias_value":"WPBJHZWIUHGE","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"WPBJHZWIUHGEJCTD","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"WPBJHZWI","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:0827d0d186c8a0ab6dc6fd94807253c3c7cea499cee7fd983ea3a6358f013ab7","target":"graph","created_at":"2026-05-17T23:47:21Z","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":"Building upon ideas of the second and third authors, we prove that at least $2^{(1-\\varepsilon)\\frac{\\log s}{\\log\\log s}}$ values of the Riemann zeta function at odd integers between 3 and $s$ are irrational, where $\\varepsilon$ is any positive real number and $s$ is large enough in terms of $\\varepsilon$. This lower bound is asymptotically larger than any power of $\\log s$; it improves on the bound $\\frac{1-\\varepsilon}{1+\\log2}\\log s$ that follows from the Ball--Rivoal theorem.\n  The proof is based on construction of several linear forms in odd zeta values with related coefficients.","authors_text":"Johannes Sprang, St\\'ephane Fischler, Wadim Zudilin","cross_cats":["math.AG","math.CA","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-03-23T17:34:30Z","title":"Many odd zeta values are irrational"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.08905","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:b67d8cc8c337ddb37cc72567e46b84043698cf3d3527106befde3185e96538e7","target":"record","created_at":"2026-05-17T23:47:21Z","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":"269f13f02c8c8e92c7fe50b22fbcb87fddada58babc107af261d206fa03edb44","cross_cats_sorted":["math.AG","math.CA","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-03-23T17:34:30Z","title_canon_sha256":"75b3797130b7279d86cce1fd9dd9c206c0caf51c23197d072ab30a9c36b1b8a6"},"schema_version":"1.0","source":{"id":"1803.08905","kind":"arxiv","version":2}},"canonical_sha256":"b3c293e6c8a1cc448a6370173c9fdfafc9626ad775ccdb2b1938c58bf696cbf8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3c293e6c8a1cc448a6370173c9fdfafc9626ad775ccdb2b1938c58bf696cbf8","first_computed_at":"2026-05-17T23:47:21.105439Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:21.105439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Yxdak+Z1ITVtgJgW2q7rEPoxCmCgo7F+iCKuRTfDSxh1bxsbrYcz7yZ8IWAsNTSg5kph5oPQ2eh1OVFUJMo+DQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:21.106004Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.08905","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b67d8cc8c337ddb37cc72567e46b84043698cf3d3527106befde3185e96538e7","sha256:0827d0d186c8a0ab6dc6fd94807253c3c7cea499cee7fd983ea3a6358f013ab7"],"state_sha256":"0e368703a1055a2668223fe33e92eb75015a4d9c7ed240b7e2b27a2da2566b19"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zZW8GgqF0XGcGOHCtUnslEEUsxjPWc6vXXr2IQDJoQ1I8ctqGaWLbv3E54iDB1YKLP9aqGey63uLImUxfnz3Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T13:30:32.840123Z","bundle_sha256":"d6b1757f85814ba58aed10b92b3d345812b3eb50b032be7a796ec58f84170fe1"}}