{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:Q5QM2CHMES7IL7XV3FI4D66M4G","short_pith_number":"pith:Q5QM2CHM","canonical_record":{"source":{"id":"0705.2802","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.CA","submitted_at":"2007-05-19T08:10:31Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"9697129f0706df9a3a924152710853aed6e4387c19a25bd33e5a360f350b2cd2","abstract_canon_sha256":"b13193b5aa25fdd784b912ca8504b3244601d9b958c3848e1e2c56020b07ac28"},"schema_version":"1.0"},"canonical_sha256":"8760cd08ec24be85fef5d951c1fbcce18c666339cac2b15b3ad527c9bb5edda4","source":{"kind":"arxiv","id":"0705.2802","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0705.2802","created_at":"2026-05-18T02:16:30Z"},{"alias_kind":"arxiv_version","alias_value":"0705.2802v3","created_at":"2026-05-18T02:16:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0705.2802","created_at":"2026-05-18T02:16:30Z"},{"alias_kind":"pith_short_12","alias_value":"Q5QM2CHMES7I","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"Q5QM2CHMES7IL7XV","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"Q5QM2CHM","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:Q5QM2CHMES7IL7XV3FI4D66M4G","target":"record","payload":{"canonical_record":{"source":{"id":"0705.2802","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.CA","submitted_at":"2007-05-19T08:10:31Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"9697129f0706df9a3a924152710853aed6e4387c19a25bd33e5a360f350b2cd2","abstract_canon_sha256":"b13193b5aa25fdd784b912ca8504b3244601d9b958c3848e1e2c56020b07ac28"},"schema_version":"1.0"},"canonical_sha256":"8760cd08ec24be85fef5d951c1fbcce18c666339cac2b15b3ad527c9bb5edda4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:16:30.836433Z","signature_b64":"hRn3uYwtbnuiV+zdzL07Cg52p1174yz4oBQxZk/tZ34wQjshQJ8Z1J51Q/f1LyoyRo98b7ghWkA9XUb2HqVAAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8760cd08ec24be85fef5d951c1fbcce18c666339cac2b15b3ad527c9bb5edda4","last_reissued_at":"2026-05-18T02:16:30.835804Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:16:30.835804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0705.2802","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:16:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qVMAYO/+Je5dGjO6qy3cjSicDyw2mbxP2bfWvg/9d3d6j84WBwkC+bVD7OqYxM5w1oMXsD6OnQ9rcKRg5Ug/BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T21:59:45.796831Z"},"content_sha256":"8dd4301f0cf007a31adc74f47977dbf8e890524131ccbb968c8e84466dfd1eae","schema_version":"1.0","event_id":"sha256:8dd4301f0cf007a31adc74f47977dbf8e890524131ccbb968c8e84466dfd1eae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:Q5QM2CHMES7IL7XV3FI4D66M4G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Asymptotics of $q$-Gamma Functions","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CA","authors_text":"Ruiming Zhang","submitted_at":"2007-05-19T08:10:31Z","abstract_excerpt":"In this paper we derive some asymptotic formulas for the $q$-Gamma function $\\Gamma_{q}(z)$ for $q$ tending to 1."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.2802","kind":"arxiv","version":3},"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":"2026-05-18T02:16:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DmqsMvJN1flpHoGXLoZgkXaKylF2P3h3bz3fBG/Oz2Jyw9eixbuTG1YjBFaE7z75SCBRSSjZzckCuKPOJo/pDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T21:59:45.797176Z"},"content_sha256":"7dd1fc6e9bbc0a453a1acc69563544ad0a3731410cc47c39874180f4e5472209","schema_version":"1.0","event_id":"sha256:7dd1fc6e9bbc0a453a1acc69563544ad0a3731410cc47c39874180f4e5472209"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q5QM2CHMES7IL7XV3FI4D66M4G/bundle.json","state_url":"https://pith.science/pith/Q5QM2CHMES7IL7XV3FI4D66M4G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q5QM2CHMES7IL7XV3FI4D66M4G/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":"2026-06-21T21:59:45Z","links":{"resolver":"https://pith.science/pith/Q5QM2CHMES7IL7XV3FI4D66M4G","bundle":"https://pith.science/pith/Q5QM2CHMES7IL7XV3FI4D66M4G/bundle.json","state":"https://pith.science/pith/Q5QM2CHMES7IL7XV3FI4D66M4G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q5QM2CHMES7IL7XV3FI4D66M4G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:Q5QM2CHMES7IL7XV3FI4D66M4G","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":"b13193b5aa25fdd784b912ca8504b3244601d9b958c3848e1e2c56020b07ac28","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.CA","submitted_at":"2007-05-19T08:10:31Z","title_canon_sha256":"9697129f0706df9a3a924152710853aed6e4387c19a25bd33e5a360f350b2cd2"},"schema_version":"1.0","source":{"id":"0705.2802","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0705.2802","created_at":"2026-05-18T02:16:30Z"},{"alias_kind":"arxiv_version","alias_value":"0705.2802v3","created_at":"2026-05-18T02:16:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0705.2802","created_at":"2026-05-18T02:16:30Z"},{"alias_kind":"pith_short_12","alias_value":"Q5QM2CHMES7I","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"Q5QM2CHMES7IL7XV","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"Q5QM2CHM","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:7dd1fc6e9bbc0a453a1acc69563544ad0a3731410cc47c39874180f4e5472209","target":"graph","created_at":"2026-05-18T02:16:30Z","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 paper we derive some asymptotic formulas for the $q$-Gamma function $\\Gamma_{q}(z)$ for $q$ tending to 1.","authors_text":"Ruiming Zhang","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"math.CA","submitted_at":"2007-05-19T08:10:31Z","title":"On Asymptotics of $q$-Gamma Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.2802","kind":"arxiv","version":3},"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":"sha256:8dd4301f0cf007a31adc74f47977dbf8e890524131ccbb968c8e84466dfd1eae","target":"record","created_at":"2026-05-18T02:16:30Z","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":"b13193b5aa25fdd784b912ca8504b3244601d9b958c3848e1e2c56020b07ac28","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.CA","submitted_at":"2007-05-19T08:10:31Z","title_canon_sha256":"9697129f0706df9a3a924152710853aed6e4387c19a25bd33e5a360f350b2cd2"},"schema_version":"1.0","source":{"id":"0705.2802","kind":"arxiv","version":3}},"canonical_sha256":"8760cd08ec24be85fef5d951c1fbcce18c666339cac2b15b3ad527c9bb5edda4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8760cd08ec24be85fef5d951c1fbcce18c666339cac2b15b3ad527c9bb5edda4","first_computed_at":"2026-05-18T02:16:30.835804Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:16:30.835804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hRn3uYwtbnuiV+zdzL07Cg52p1174yz4oBQxZk/tZ34wQjshQJ8Z1J51Q/f1LyoyRo98b7ghWkA9XUb2HqVAAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:16:30.836433Z","signed_message":"canonical_sha256_bytes"},"source_id":"0705.2802","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8dd4301f0cf007a31adc74f47977dbf8e890524131ccbb968c8e84466dfd1eae","sha256:7dd1fc6e9bbc0a453a1acc69563544ad0a3731410cc47c39874180f4e5472209"],"state_sha256":"1f6fa2308fea07af8760667141f3e4a86c72f04b5ff5b22135a6447c810c38d9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AGW9fodu2gkWTWLBYLCU7ZJhu9MIfVJDteTYqiFTgp6V/mwp+y1bcPYTZrQKdRXeXjxQVsZjXssVqMrlrcFBDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T21:59:45.799058Z","bundle_sha256":"f91ba50132d9fa54451644cb2fbfbccaf41fb3227952d2d74d61e13a94c951dd"}}