{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:VXVYC5RCJCFBZNXVFAUOU7R2WE","short_pith_number":"pith:VXVYC5RC","canonical_record":{"source":{"id":"1711.02839","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-11-08T05:43:10Z","cross_cats_sorted":[],"title_canon_sha256":"713d16a5378cee536538fc09684604f5aa686c68e6db690ba97c0233c3fa81cb","abstract_canon_sha256":"b79ab2779bdd9b819fe5da3cb2a1a75e15d886495f91f5ed7a66e0eb03ae5762"},"schema_version":"1.0"},"canonical_sha256":"adeb817622488a1cb6f52828ea7e3ab10284091bc5667d7eef277967159f2e39","source":{"kind":"arxiv","id":"1711.02839","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.02839","created_at":"2026-05-18T00:26:36Z"},{"alias_kind":"arxiv_version","alias_value":"1711.02839v2","created_at":"2026-05-18T00:26:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.02839","created_at":"2026-05-18T00:26:36Z"},{"alias_kind":"pith_short_12","alias_value":"VXVYC5RCJCFB","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VXVYC5RCJCFBZNXV","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VXVYC5RC","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:VXVYC5RCJCFBZNXVFAUOU7R2WE","target":"record","payload":{"canonical_record":{"source":{"id":"1711.02839","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-11-08T05:43:10Z","cross_cats_sorted":[],"title_canon_sha256":"713d16a5378cee536538fc09684604f5aa686c68e6db690ba97c0233c3fa81cb","abstract_canon_sha256":"b79ab2779bdd9b819fe5da3cb2a1a75e15d886495f91f5ed7a66e0eb03ae5762"},"schema_version":"1.0"},"canonical_sha256":"adeb817622488a1cb6f52828ea7e3ab10284091bc5667d7eef277967159f2e39","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:36.048149Z","signature_b64":"jomFBpsyL6E/HKwiV4NDnpgmz3kRrGMVnyMZR7PSRkSl2zDEUwQ3rVmc/71Iy3ba5+Srzh88GWbLMwCWtJtMBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"adeb817622488a1cb6f52828ea7e3ab10284091bc5667d7eef277967159f2e39","last_reissued_at":"2026-05-18T00:26:36.047476Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:36.047476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.02839","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":"2026-05-18T00:26:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"61X32VJvJQGBNjfL11uuw0xea/9OwXtfTruJEE5fD4UJzWYHVyK+vPV/7uGVu92tWvHk4ah8hGWJyTAzsXELAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:10:29.579085Z"},"content_sha256":"d9f94884f0b519adc7611c8e07e19f5e7a034e7f27544c130ee59509450e4445","schema_version":"1.0","event_id":"sha256:d9f94884f0b519adc7611c8e07e19f5e7a034e7f27544c130ee59509450e4445"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:VXVYC5RCJCFBZNXVFAUOU7R2WE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Metric discrepancy results for geometric progressions with small ratios","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"K. Fukuyama, M. Tscheckl, O. Shimabe, S. Sakaguchi, T. Toyoda","submitted_at":"2017-11-08T05:43:10Z","abstract_excerpt":"The law of the iterated logarithm for discrepancies of geometric progressions with small ratios is proved."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02839","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":"2026-05-18T00:26:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0jnleTe1mXEB46bJMCQPVTCqx5VjA50Azp7QgSbb6LkKA8rb5DIQMTDHHf0wnOvBMJqceUFTpXi1Yl5ZFrj9BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:10:29.579681Z"},"content_sha256":"ba7624faecba8425dcef2aaf7ae8b434d66b41ee78d9779c96eb073390abf955","schema_version":"1.0","event_id":"sha256:ba7624faecba8425dcef2aaf7ae8b434d66b41ee78d9779c96eb073390abf955"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VXVYC5RCJCFBZNXVFAUOU7R2WE/bundle.json","state_url":"https://pith.science/pith/VXVYC5RCJCFBZNXVFAUOU7R2WE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VXVYC5RCJCFBZNXVFAUOU7R2WE/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":"2026-05-26T22:10:29Z","links":{"resolver":"https://pith.science/pith/VXVYC5RCJCFBZNXVFAUOU7R2WE","bundle":"https://pith.science/pith/VXVYC5RCJCFBZNXVFAUOU7R2WE/bundle.json","state":"https://pith.science/pith/VXVYC5RCJCFBZNXVFAUOU7R2WE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VXVYC5RCJCFBZNXVFAUOU7R2WE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VXVYC5RCJCFBZNXVFAUOU7R2WE","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":"b79ab2779bdd9b819fe5da3cb2a1a75e15d886495f91f5ed7a66e0eb03ae5762","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-11-08T05:43:10Z","title_canon_sha256":"713d16a5378cee536538fc09684604f5aa686c68e6db690ba97c0233c3fa81cb"},"schema_version":"1.0","source":{"id":"1711.02839","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.02839","created_at":"2026-05-18T00:26:36Z"},{"alias_kind":"arxiv_version","alias_value":"1711.02839v2","created_at":"2026-05-18T00:26:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.02839","created_at":"2026-05-18T00:26:36Z"},{"alias_kind":"pith_short_12","alias_value":"VXVYC5RCJCFB","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VXVYC5RCJCFBZNXV","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VXVYC5RC","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:ba7624faecba8425dcef2aaf7ae8b434d66b41ee78d9779c96eb073390abf955","target":"graph","created_at":"2026-05-18T00:26:36Z","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":"The law of the iterated logarithm for discrepancies of geometric progressions with small ratios is proved.","authors_text":"K. Fukuyama, M. Tscheckl, O. Shimabe, S. Sakaguchi, T. Toyoda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-11-08T05:43:10Z","title":"Metric discrepancy results for geometric progressions with small ratios"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02839","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:d9f94884f0b519adc7611c8e07e19f5e7a034e7f27544c130ee59509450e4445","target":"record","created_at":"2026-05-18T00:26:36Z","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":"b79ab2779bdd9b819fe5da3cb2a1a75e15d886495f91f5ed7a66e0eb03ae5762","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-11-08T05:43:10Z","title_canon_sha256":"713d16a5378cee536538fc09684604f5aa686c68e6db690ba97c0233c3fa81cb"},"schema_version":"1.0","source":{"id":"1711.02839","kind":"arxiv","version":2}},"canonical_sha256":"adeb817622488a1cb6f52828ea7e3ab10284091bc5667d7eef277967159f2e39","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"adeb817622488a1cb6f52828ea7e3ab10284091bc5667d7eef277967159f2e39","first_computed_at":"2026-05-18T00:26:36.047476Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:36.047476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jomFBpsyL6E/HKwiV4NDnpgmz3kRrGMVnyMZR7PSRkSl2zDEUwQ3rVmc/71Iy3ba5+Srzh88GWbLMwCWtJtMBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:36.048149Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.02839","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9f94884f0b519adc7611c8e07e19f5e7a034e7f27544c130ee59509450e4445","sha256:ba7624faecba8425dcef2aaf7ae8b434d66b41ee78d9779c96eb073390abf955"],"state_sha256":"bd84104150d418de8c960aebd13ded668c92659467678c74c5ef6ce394cf18ef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ooVX6LLCTZzzDyeEm5bkz3MTs4Ybaq1cSk6ngF8ESdgX66Wj6VjP8c4xyxTsbM7P1f4LBULkPkdDnFKA4HG5AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T22:10:29.582856Z","bundle_sha256":"7929fb590b50cb3f50c080ceb3e9cb1d742384b969fb81e7f1c996161890a288"}}