{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:OW3MLYNMEWHA6I2YEWGMQZBAQD","short_pith_number":"pith:OW3MLYNM","canonical_record":{"source":{"id":"1807.09646","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-07-25T14:56:07Z","cross_cats_sorted":[],"title_canon_sha256":"fca4d6e239e7a022ba71b6b4333c4abac06eff6a63b9f83110e4f4e3c0936b55","abstract_canon_sha256":"a8ac3ee9199288f917bc525ba4a4ce6a02f2918e7a4109888363dfdbf18fd7cc"},"schema_version":"1.0"},"canonical_sha256":"75b6c5e1ac258e0f2358258cc8642080d79e24995ff3a70dcf2014e98ce064b1","source":{"kind":"arxiv","id":"1807.09646","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.09646","created_at":"2026-05-17T23:45:37Z"},{"alias_kind":"arxiv_version","alias_value":"1807.09646v1","created_at":"2026-05-17T23:45:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.09646","created_at":"2026-05-17T23:45:37Z"},{"alias_kind":"pith_short_12","alias_value":"OW3MLYNMEWHA","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OW3MLYNMEWHA6I2Y","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OW3MLYNM","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:OW3MLYNMEWHA6I2YEWGMQZBAQD","target":"record","payload":{"canonical_record":{"source":{"id":"1807.09646","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-07-25T14:56:07Z","cross_cats_sorted":[],"title_canon_sha256":"fca4d6e239e7a022ba71b6b4333c4abac06eff6a63b9f83110e4f4e3c0936b55","abstract_canon_sha256":"a8ac3ee9199288f917bc525ba4a4ce6a02f2918e7a4109888363dfdbf18fd7cc"},"schema_version":"1.0"},"canonical_sha256":"75b6c5e1ac258e0f2358258cc8642080d79e24995ff3a70dcf2014e98ce064b1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:37.386533Z","signature_b64":"iDr5/n1ZIt8Pm8B7k8BEx0rcHqxvXNdCA9tVz0VII2cDc1CGFF3eTfRcat9W0oWSDvQgEgpXPYLE4oQQXCrbAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75b6c5e1ac258e0f2358258cc8642080d79e24995ff3a70dcf2014e98ce064b1","last_reissued_at":"2026-05-17T23:45:37.385822Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:37.385822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.09646","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":"2026-05-17T23:45:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hXHJrQknFJ1cN9a0eZsCuBVffzNfWaM+C3qLjBYdBtK8fdwEIpHxDvXpHMV/J3ziTCj86YxJE2RUONGGF+ByAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T00:30:31.060714Z"},"content_sha256":"e6cf7cfe2510e41b45ceb60f387af0b4d3ccba4c9dedb7dcaa680b586c4d3785","schema_version":"1.0","event_id":"sha256:e6cf7cfe2510e41b45ceb60f387af0b4d3ccba4c9dedb7dcaa680b586c4d3785"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:OW3MLYNMEWHA6I2YEWGMQZBAQD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the transcendence of certain real numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Bill Mance, Veekesh Kumar","submitted_at":"2018-07-25T14:56:07Z","abstract_excerpt":"In this article we discuss the transcendence of certain infinite sums and products by using the Subspace theorem. In particular we improve the result of Han\\v{c}l and Rucki \\cite{hancl3}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.09646","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":"2026-05-17T23:45:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GbWq7rF1Mp7MwuNuFSw5zx7p/a5oGXn1yagLSiLqlMRfkBpYv6qoZAhwQK7RCg1d8hmGaJkreau2bnvONb6aDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T00:30:31.061222Z"},"content_sha256":"30de7d55c3bacb027d248e3512b7dcf7a7c5f68e9378af231441d7bcf5780917","schema_version":"1.0","event_id":"sha256:30de7d55c3bacb027d248e3512b7dcf7a7c5f68e9378af231441d7bcf5780917"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OW3MLYNMEWHA6I2YEWGMQZBAQD/bundle.json","state_url":"https://pith.science/pith/OW3MLYNMEWHA6I2YEWGMQZBAQD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OW3MLYNMEWHA6I2YEWGMQZBAQD/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":"2026-06-05T00:30:31Z","links":{"resolver":"https://pith.science/pith/OW3MLYNMEWHA6I2YEWGMQZBAQD","bundle":"https://pith.science/pith/OW3MLYNMEWHA6I2YEWGMQZBAQD/bundle.json","state":"https://pith.science/pith/OW3MLYNMEWHA6I2YEWGMQZBAQD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OW3MLYNMEWHA6I2YEWGMQZBAQD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:OW3MLYNMEWHA6I2YEWGMQZBAQD","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":"a8ac3ee9199288f917bc525ba4a4ce6a02f2918e7a4109888363dfdbf18fd7cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-07-25T14:56:07Z","title_canon_sha256":"fca4d6e239e7a022ba71b6b4333c4abac06eff6a63b9f83110e4f4e3c0936b55"},"schema_version":"1.0","source":{"id":"1807.09646","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.09646","created_at":"2026-05-17T23:45:37Z"},{"alias_kind":"arxiv_version","alias_value":"1807.09646v1","created_at":"2026-05-17T23:45:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.09646","created_at":"2026-05-17T23:45:37Z"},{"alias_kind":"pith_short_12","alias_value":"OW3MLYNMEWHA","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OW3MLYNMEWHA6I2Y","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OW3MLYNM","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:30de7d55c3bacb027d248e3512b7dcf7a7c5f68e9378af231441d7bcf5780917","target":"graph","created_at":"2026-05-17T23:45:37Z","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":"In this article we discuss the transcendence of certain infinite sums and products by using the Subspace theorem. In particular we improve the result of Han\\v{c}l and Rucki \\cite{hancl3}.","authors_text":"Bill Mance, Veekesh Kumar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-07-25T14:56:07Z","title":"On the transcendence of certain real numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.09646","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:e6cf7cfe2510e41b45ceb60f387af0b4d3ccba4c9dedb7dcaa680b586c4d3785","target":"record","created_at":"2026-05-17T23:45:37Z","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":"a8ac3ee9199288f917bc525ba4a4ce6a02f2918e7a4109888363dfdbf18fd7cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-07-25T14:56:07Z","title_canon_sha256":"fca4d6e239e7a022ba71b6b4333c4abac06eff6a63b9f83110e4f4e3c0936b55"},"schema_version":"1.0","source":{"id":"1807.09646","kind":"arxiv","version":1}},"canonical_sha256":"75b6c5e1ac258e0f2358258cc8642080d79e24995ff3a70dcf2014e98ce064b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"75b6c5e1ac258e0f2358258cc8642080d79e24995ff3a70dcf2014e98ce064b1","first_computed_at":"2026-05-17T23:45:37.385822Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:37.385822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iDr5/n1ZIt8Pm8B7k8BEx0rcHqxvXNdCA9tVz0VII2cDc1CGFF3eTfRcat9W0oWSDvQgEgpXPYLE4oQQXCrbAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:37.386533Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.09646","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6cf7cfe2510e41b45ceb60f387af0b4d3ccba4c9dedb7dcaa680b586c4d3785","sha256:30de7d55c3bacb027d248e3512b7dcf7a7c5f68e9378af231441d7bcf5780917"],"state_sha256":"073142c4bbc6771d7a6f08062fe02e5b63a3ca86c362e0725ccb8eca58288d3f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m3M9n5oWRRj1Mf1AOS23jW0iwLZxb5YN68Uf3vBYLC3rKn6XNcdaTsSw0S1kRxUQ7Ew358P+9as05fJ7eviLDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T00:30:31.064284Z","bundle_sha256":"4893ca721e82dbe5f53269dcef3bc9edf252e8ac8083db70208ff14759fc8e36"}}