{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:XCX7TJB7AANLAEKP72DEWHHCZQ","short_pith_number":"pith:XCX7TJB7","canonical_record":{"source":{"id":"math/0304021","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2003-04-02T13:53:58Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"cf40eb5ac7b66ceb517924689647db68d863659ebbf72751af691ea0fa4eee6e","abstract_canon_sha256":"d8f947eea485578d405d047993de00d4a6a49483ec1f0b8995f1e231a39d3902"},"schema_version":"1.0"},"canonical_sha256":"b8aff9a43f001ab0114ffe864b1ce2cc2f85d7d79a9d233ef0117a8321d34f26","source":{"kind":"arxiv","id":"math/0304021","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0304021","created_at":"2026-05-18T04:08:43Z"},{"alias_kind":"arxiv_version","alias_value":"math/0304021v1","created_at":"2026-05-18T04:08:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0304021","created_at":"2026-05-18T04:08:43Z"},{"alias_kind":"pith_short_12","alias_value":"XCX7TJB7AANL","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"XCX7TJB7AANLAEKP","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"XCX7TJB7","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:XCX7TJB7AANLAEKP72DEWHHCZQ","target":"record","payload":{"canonical_record":{"source":{"id":"math/0304021","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2003-04-02T13:53:58Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"cf40eb5ac7b66ceb517924689647db68d863659ebbf72751af691ea0fa4eee6e","abstract_canon_sha256":"d8f947eea485578d405d047993de00d4a6a49483ec1f0b8995f1e231a39d3902"},"schema_version":"1.0"},"canonical_sha256":"b8aff9a43f001ab0114ffe864b1ce2cc2f85d7d79a9d233ef0117a8321d34f26","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:43.096184Z","signature_b64":"V5dkMDPCzfaXOA9C6WYQjKZ9ez4u+pJ5yE4ToC6zfgg6GKOGuPQVoOU70F5gTZ/Or28K+xRpeZ2GM3YjprkSAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b8aff9a43f001ab0114ffe864b1ce2cc2f85d7d79a9d233ef0117a8321d34f26","last_reissued_at":"2026-05-18T04:08:43.095746Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:43.095746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0304021","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":"2026-05-18T04:08:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WviPD8m88QOVkKtQTYjaFzB1COEogkdNwWklEeey93he1L3QSS/nGwThBgrQj0nByoVxxZeLw1MzInZiImIwBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T06:08:47.516785Z"},"content_sha256":"0527311326da0a01c715680c884e4ec652dbf98ebe76bfa485fb44774e38132f","schema_version":"1.0","event_id":"sha256:0527311326da0a01c715680c884e4ec652dbf98ebe76bfa485fb44774e38132f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:XCX7TJB7AANLAEKP72DEWHHCZQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Euler's constant, q-logarithms, and formulas of Ramanujan and Gosper","license":"","headline":"","cross_cats":["math.CA"],"primary_cat":"math.NT","authors_text":"Jonathan Sondow (New York), Wadim Zudilin (Moscow)","submitted_at":"2003-04-02T13:53:58Z","abstract_excerpt":"The aim of the paper is to relate computational and arithmetic questions about Euler's constant $\\gamma$ with properties of the values of the $q$-logarithm function, with natural choice of $q$. By these means, we generalize a classical formula for $\\gamma$ due to Ramanujan, together with Vacca's and Gosper's series for $\\gamma$, as well as deduce irrationality criteria and tests and new asymptotic formulas for computing Euler's constant. The main tools are Euler-type integrals and hypergeometric series."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0304021","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":"2026-05-18T04:08:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LLTBvOdBHjxMJeLDYJwc7e2gkS6v6RxzzQvzlQXSoimOY/vym4chZtf0vPmQ/R7Qm/fUlDGYk+e3lBiJHPirAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T06:08:47.517138Z"},"content_sha256":"f673e9d3b0bec3e059f6feaa130efbbb78a5192c1d37550c6fef45c6f9f8a8eb","schema_version":"1.0","event_id":"sha256:f673e9d3b0bec3e059f6feaa130efbbb78a5192c1d37550c6fef45c6f9f8a8eb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XCX7TJB7AANLAEKP72DEWHHCZQ/bundle.json","state_url":"https://pith.science/pith/XCX7TJB7AANLAEKP72DEWHHCZQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XCX7TJB7AANLAEKP72DEWHHCZQ/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":"2026-06-12T06:08:47Z","links":{"resolver":"https://pith.science/pith/XCX7TJB7AANLAEKP72DEWHHCZQ","bundle":"https://pith.science/pith/XCX7TJB7AANLAEKP72DEWHHCZQ/bundle.json","state":"https://pith.science/pith/XCX7TJB7AANLAEKP72DEWHHCZQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XCX7TJB7AANLAEKP72DEWHHCZQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:XCX7TJB7AANLAEKP72DEWHHCZQ","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":"d8f947eea485578d405d047993de00d4a6a49483ec1f0b8995f1e231a39d3902","cross_cats_sorted":["math.CA"],"license":"","primary_cat":"math.NT","submitted_at":"2003-04-02T13:53:58Z","title_canon_sha256":"cf40eb5ac7b66ceb517924689647db68d863659ebbf72751af691ea0fa4eee6e"},"schema_version":"1.0","source":{"id":"math/0304021","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0304021","created_at":"2026-05-18T04:08:43Z"},{"alias_kind":"arxiv_version","alias_value":"math/0304021v1","created_at":"2026-05-18T04:08:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0304021","created_at":"2026-05-18T04:08:43Z"},{"alias_kind":"pith_short_12","alias_value":"XCX7TJB7AANL","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"XCX7TJB7AANLAEKP","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"XCX7TJB7","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:f673e9d3b0bec3e059f6feaa130efbbb78a5192c1d37550c6fef45c6f9f8a8eb","target":"graph","created_at":"2026-05-18T04:08:43Z","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 aim of the paper is to relate computational and arithmetic questions about Euler's constant $\\gamma$ with properties of the values of the $q$-logarithm function, with natural choice of $q$. By these means, we generalize a classical formula for $\\gamma$ due to Ramanujan, together with Vacca's and Gosper's series for $\\gamma$, as well as deduce irrationality criteria and tests and new asymptotic formulas for computing Euler's constant. The main tools are Euler-type integrals and hypergeometric series.","authors_text":"Jonathan Sondow (New York), Wadim Zudilin (Moscow)","cross_cats":["math.CA"],"headline":"","license":"","primary_cat":"math.NT","submitted_at":"2003-04-02T13:53:58Z","title":"Euler's constant, q-logarithms, and formulas of Ramanujan and Gosper"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0304021","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":"sha256:0527311326da0a01c715680c884e4ec652dbf98ebe76bfa485fb44774e38132f","target":"record","created_at":"2026-05-18T04:08:43Z","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":"d8f947eea485578d405d047993de00d4a6a49483ec1f0b8995f1e231a39d3902","cross_cats_sorted":["math.CA"],"license":"","primary_cat":"math.NT","submitted_at":"2003-04-02T13:53:58Z","title_canon_sha256":"cf40eb5ac7b66ceb517924689647db68d863659ebbf72751af691ea0fa4eee6e"},"schema_version":"1.0","source":{"id":"math/0304021","kind":"arxiv","version":1}},"canonical_sha256":"b8aff9a43f001ab0114ffe864b1ce2cc2f85d7d79a9d233ef0117a8321d34f26","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8aff9a43f001ab0114ffe864b1ce2cc2f85d7d79a9d233ef0117a8321d34f26","first_computed_at":"2026-05-18T04:08:43.095746Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:43.095746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V5dkMDPCzfaXOA9C6WYQjKZ9ez4u+pJ5yE4ToC6zfgg6GKOGuPQVoOU70F5gTZ/Or28K+xRpeZ2GM3YjprkSAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:43.096184Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0304021","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0527311326da0a01c715680c884e4ec652dbf98ebe76bfa485fb44774e38132f","sha256:f673e9d3b0bec3e059f6feaa130efbbb78a5192c1d37550c6fef45c6f9f8a8eb"],"state_sha256":"4bd4e4db6eb7e292561fd41c8008330dea1731cc59ce98c3234c8b3c4996b7cb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VGJmbj2cVXvBuXxGo65ow1zm/WDH0Vwv8o6g6NlMKqlvz/IM0j+vsb4PZniJ8Z4iBzoWy6m5q7r/WQRJVTwjBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T06:08:47.519265Z","bundle_sha256":"4f8f21ffc116fcdba0e1f434656f1212adab3569b264797c3be68922eacbf0d9"}}