{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:WWWMRX5XZQSVEEENMLPOJJEAOA","short_pith_number":"pith:WWWMRX5X","canonical_record":{"source":{"id":"1704.05200","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-18T04:33:23Z","cross_cats_sorted":[],"title_canon_sha256":"a5760f147570881fad47bbf432a716568e430509d45f7436bc6a206bfc51670c","abstract_canon_sha256":"0949803965fea66621d27e069b182a037f9f935a31c4b4faf2956085802429e5"},"schema_version":"1.0"},"canonical_sha256":"b5acc8dfb7cc2552108d62dee4a480701033c0a6f70d176db78732f71d34adae","source":{"kind":"arxiv","id":"1704.05200","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.05200","created_at":"2026-05-18T00:39:06Z"},{"alias_kind":"arxiv_version","alias_value":"1704.05200v2","created_at":"2026-05-18T00:39:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.05200","created_at":"2026-05-18T00:39:06Z"},{"alias_kind":"pith_short_12","alias_value":"WWWMRX5XZQSV","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WWWMRX5XZQSVEEEN","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WWWMRX5X","created_at":"2026-05-18T12:31:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:WWWMRX5XZQSVEEENMLPOJJEAOA","target":"record","payload":{"canonical_record":{"source":{"id":"1704.05200","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-18T04:33:23Z","cross_cats_sorted":[],"title_canon_sha256":"a5760f147570881fad47bbf432a716568e430509d45f7436bc6a206bfc51670c","abstract_canon_sha256":"0949803965fea66621d27e069b182a037f9f935a31c4b4faf2956085802429e5"},"schema_version":"1.0"},"canonical_sha256":"b5acc8dfb7cc2552108d62dee4a480701033c0a6f70d176db78732f71d34adae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:06.599452Z","signature_b64":"EywBB+mL5eERqFGFPQ/qafHKqgv32s4Llcaq15p+dCteI/z6zDQEKphiWjqgJrh0JAK4MN6ZIPQ2+c3ty5vqAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5acc8dfb7cc2552108d62dee4a480701033c0a6f70d176db78732f71d34adae","last_reissued_at":"2026-05-18T00:39:06.598887Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:06.598887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.05200","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":"2026-05-18T00:39:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FSPyePztoyhojmhFBG+QyssTl47ogX0/Rdx70MeLMNQCsQy3oWHEX33NaDNVUA5NtGeiH+W2NeUMfM5yURlCCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T00:13:14.632403Z"},"content_sha256":"79b10c1bf6e45f18a3cc62a4f971e454a3cc5539f5a1da2c688406c9b4d424ed","schema_version":"1.0","event_id":"sha256:79b10c1bf6e45f18a3cc62a4f971e454a3cc5539f5a1da2c688406c9b4d424ed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:WWWMRX5XZQSVEEENMLPOJJEAOA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Continued Fractions and $q$-Series Generating Functions for the Generalized Sum-of-Divisors Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Maxie D. Schmidt","submitted_at":"2017-04-18T04:33:23Z","abstract_excerpt":"We construct new continued fraction expansions of Jacobi-type J-fractions in $z$ whose power series expansions generate the ratio of the $q$-Pochhamer symbols, $(a; q)_n / (b; q)_n$, for all integers $n \\geq 0$ and where $a,b,q \\in \\mathbb{C}$ are non-zero and defined such that $|q| < 1$ and $|b/a| < |z| < 1$. If we set the parameters $(a, b) := (q, q^2)$ in these generalized series expansions, then we have a corresponding J-fraction enumerating the sequence of terms $(1-q) / (1-q^{n+1})$ over all integers $n \\geq 0$. Thus we are able to define new $q$-series expansions which correspond to the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05200","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":"2026-05-18T00:39:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Udx0hqWkxL08DCxrtMjZACVAA/f6UOrwTdYoGsCdH0CikVH6UVEIHxA6ph4L1NtbrEkYbRQ6x1LGvHWgTPnoCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T00:13:14.632782Z"},"content_sha256":"f28ecfa11f6134da332f2be05b92fdbf4be65524f77106d868a70d0bc07f5b55","schema_version":"1.0","event_id":"sha256:f28ecfa11f6134da332f2be05b92fdbf4be65524f77106d868a70d0bc07f5b55"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WWWMRX5XZQSVEEENMLPOJJEAOA/bundle.json","state_url":"https://pith.science/pith/WWWMRX5XZQSVEEENMLPOJJEAOA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WWWMRX5XZQSVEEENMLPOJJEAOA/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":"2026-06-12T00:13:14Z","links":{"resolver":"https://pith.science/pith/WWWMRX5XZQSVEEENMLPOJJEAOA","bundle":"https://pith.science/pith/WWWMRX5XZQSVEEENMLPOJJEAOA/bundle.json","state":"https://pith.science/pith/WWWMRX5XZQSVEEENMLPOJJEAOA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WWWMRX5XZQSVEEENMLPOJJEAOA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WWWMRX5XZQSVEEENMLPOJJEAOA","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":"0949803965fea66621d27e069b182a037f9f935a31c4b4faf2956085802429e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-18T04:33:23Z","title_canon_sha256":"a5760f147570881fad47bbf432a716568e430509d45f7436bc6a206bfc51670c"},"schema_version":"1.0","source":{"id":"1704.05200","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.05200","created_at":"2026-05-18T00:39:06Z"},{"alias_kind":"arxiv_version","alias_value":"1704.05200v2","created_at":"2026-05-18T00:39:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.05200","created_at":"2026-05-18T00:39:06Z"},{"alias_kind":"pith_short_12","alias_value":"WWWMRX5XZQSV","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WWWMRX5XZQSVEEEN","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WWWMRX5X","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:f28ecfa11f6134da332f2be05b92fdbf4be65524f77106d868a70d0bc07f5b55","target":"graph","created_at":"2026-05-18T00:39:06Z","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":"We construct new continued fraction expansions of Jacobi-type J-fractions in $z$ whose power series expansions generate the ratio of the $q$-Pochhamer symbols, $(a; q)_n / (b; q)_n$, for all integers $n \\geq 0$ and where $a,b,q \\in \\mathbb{C}$ are non-zero and defined such that $|q| < 1$ and $|b/a| < |z| < 1$. If we set the parameters $(a, b) := (q, q^2)$ in these generalized series expansions, then we have a corresponding J-fraction enumerating the sequence of terms $(1-q) / (1-q^{n+1})$ over all integers $n \\geq 0$. Thus we are able to define new $q$-series expansions which correspond to the","authors_text":"Maxie D. Schmidt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-18T04:33:23Z","title":"Continued Fractions and $q$-Series Generating Functions for the Generalized Sum-of-Divisors Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05200","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":"sha256:79b10c1bf6e45f18a3cc62a4f971e454a3cc5539f5a1da2c688406c9b4d424ed","target":"record","created_at":"2026-05-18T00:39:06Z","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":"0949803965fea66621d27e069b182a037f9f935a31c4b4faf2956085802429e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-18T04:33:23Z","title_canon_sha256":"a5760f147570881fad47bbf432a716568e430509d45f7436bc6a206bfc51670c"},"schema_version":"1.0","source":{"id":"1704.05200","kind":"arxiv","version":2}},"canonical_sha256":"b5acc8dfb7cc2552108d62dee4a480701033c0a6f70d176db78732f71d34adae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b5acc8dfb7cc2552108d62dee4a480701033c0a6f70d176db78732f71d34adae","first_computed_at":"2026-05-18T00:39:06.598887Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:06.598887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EywBB+mL5eERqFGFPQ/qafHKqgv32s4Llcaq15p+dCteI/z6zDQEKphiWjqgJrh0JAK4MN6ZIPQ2+c3ty5vqAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:06.599452Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.05200","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79b10c1bf6e45f18a3cc62a4f971e454a3cc5539f5a1da2c688406c9b4d424ed","sha256:f28ecfa11f6134da332f2be05b92fdbf4be65524f77106d868a70d0bc07f5b55"],"state_sha256":"a8063e5826250bf7c4ca131cc16592ef577f641e913e70d293876735a80c4f5b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zXgWlOyt6lbbvFgOVU1syLjVGrNA86904q1Nc6dVBCJOh/BjfKd/uqlGCOzeEiSDGguCQ/ZU74Hs3jPr137+Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T00:13:14.636128Z","bundle_sha256":"cbc92764962a4712d233ab6ab715573791a187624ec6202e1499ded3498cc022"}}