{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:24BQLB3NDCTWAIPNXGQK3YAV6T","short_pith_number":"pith:24BQLB3N","canonical_record":{"source":{"id":"math/0412298","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CV","submitted_at":"2004-12-15T11:25:32Z","cross_cats_sorted":[],"title_canon_sha256":"35a52c56c5c80bb0a36415e2dc2bceb4935879a9e86c7c1e125825fd41094e87","abstract_canon_sha256":"b3146de55a56aa64994094b15269ca9446d4b60c179e092f880a7f82ee511263"},"schema_version":"1.0"},"canonical_sha256":"d70305876d18a76021edb9a0ade015f4eef4daa724bf996f90545d3c0b24f9e0","source":{"kind":"arxiv","id":"math/0412298","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0412298","created_at":"2026-05-18T00:07:44Z"},{"alias_kind":"arxiv_version","alias_value":"math/0412298v1","created_at":"2026-05-18T00:07:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0412298","created_at":"2026-05-18T00:07:44Z"},{"alias_kind":"pith_short_12","alias_value":"24BQLB3NDCTW","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"24BQLB3NDCTWAIPN","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"24BQLB3N","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:24BQLB3NDCTWAIPNXGQK3YAV6T","target":"record","payload":{"canonical_record":{"source":{"id":"math/0412298","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CV","submitted_at":"2004-12-15T11:25:32Z","cross_cats_sorted":[],"title_canon_sha256":"35a52c56c5c80bb0a36415e2dc2bceb4935879a9e86c7c1e125825fd41094e87","abstract_canon_sha256":"b3146de55a56aa64994094b15269ca9446d4b60c179e092f880a7f82ee511263"},"schema_version":"1.0"},"canonical_sha256":"d70305876d18a76021edb9a0ade015f4eef4daa724bf996f90545d3c0b24f9e0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:44.270232Z","signature_b64":"Jyt692Z8CC39zHGVjgEZ1SmNZU05ae3OLVJUSk5wm6wbZM/B8H5m2eo99K52xqK/bWGts8MsnOKYA+tfjMrTBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d70305876d18a76021edb9a0ade015f4eef4daa724bf996f90545d3c0b24f9e0","last_reissued_at":"2026-05-18T00:07:44.269631Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:44.269631Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0412298","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":"2026-05-18T00:07:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zjyu08hssKS6BCmrAVzfXCIC9Y3Fc74p0gU5WfjNxJCSZ3MgILpfxxY+0o3CtyoJ9d8qk95cFWedbNGumUUKCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:15:42.355156Z"},"content_sha256":"978a406e6d1e3e25c17d09d8e71bff5ae2c2335d2c35f1d6f2e659b47c5ad324","schema_version":"1.0","event_id":"sha256:978a406e6d1e3e25c17d09d8e71bff5ae2c2335d2c35f1d6f2e659b47c5ad324"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:24BQLB3NDCTWAIPNXGQK3YAV6T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the convergence of continued fractions at Runckel's points and the Ramanujan conjecture","license":"","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Alexei Tsygvintsev","submitted_at":"2004-12-15T11:25:32Z","abstract_excerpt":"We consider the limit periodic continued fractions of Stieltjes $$ \\frac{1}{1-} \\frac{g_1 z}{1-} \\frac{g_2(1-g_1) z}{1-} \\frac{g_3(1-g_2)z}{1-...,}, z\\in \\mathbb C, g_i\\in(0,1), \\lim\\limits_{i\\to \\infty} g_i=1/2, \\quad (1) $$ appearing as Shur--Wall $g$-fraction representations of certain analytic self maps of the unit disc $|w|< 1$, $w \\in \\mathbb C$. We precise the convergence behavior and prove the general convergence [2, p. 564 ] of (1) at the Runckel's points of the singular line $(1,+\\infty)$ It is shown that in some cases the convergence holds in the classical sense. As a result a count"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0412298","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":"2026-05-18T00:07:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jYpjqWSl0YUmKKWQwK+PAniqM1giPRMthEuzrPqJCX0eBrtuxTGfgz5SOiDVbBghZ7NdBYrOZgf+krB59F4tCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:15:42.355514Z"},"content_sha256":"101ad0b36a0ab945b071ed30dcdef581795f55386aa56e3329ad4cdb5ce4ad5c","schema_version":"1.0","event_id":"sha256:101ad0b36a0ab945b071ed30dcdef581795f55386aa56e3329ad4cdb5ce4ad5c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/24BQLB3NDCTWAIPNXGQK3YAV6T/bundle.json","state_url":"https://pith.science/pith/24BQLB3NDCTWAIPNXGQK3YAV6T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/24BQLB3NDCTWAIPNXGQK3YAV6T/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":"2026-06-02T04:15:42Z","links":{"resolver":"https://pith.science/pith/24BQLB3NDCTWAIPNXGQK3YAV6T","bundle":"https://pith.science/pith/24BQLB3NDCTWAIPNXGQK3YAV6T/bundle.json","state":"https://pith.science/pith/24BQLB3NDCTWAIPNXGQK3YAV6T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/24BQLB3NDCTWAIPNXGQK3YAV6T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:24BQLB3NDCTWAIPNXGQK3YAV6T","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":"b3146de55a56aa64994094b15269ca9446d4b60c179e092f880a7f82ee511263","cross_cats_sorted":[],"license":"","primary_cat":"math.CV","submitted_at":"2004-12-15T11:25:32Z","title_canon_sha256":"35a52c56c5c80bb0a36415e2dc2bceb4935879a9e86c7c1e125825fd41094e87"},"schema_version":"1.0","source":{"id":"math/0412298","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0412298","created_at":"2026-05-18T00:07:44Z"},{"alias_kind":"arxiv_version","alias_value":"math/0412298v1","created_at":"2026-05-18T00:07:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0412298","created_at":"2026-05-18T00:07:44Z"},{"alias_kind":"pith_short_12","alias_value":"24BQLB3NDCTW","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"24BQLB3NDCTWAIPN","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"24BQLB3N","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:101ad0b36a0ab945b071ed30dcdef581795f55386aa56e3329ad4cdb5ce4ad5c","target":"graph","created_at":"2026-05-18T00:07:44Z","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 consider the limit periodic continued fractions of Stieltjes $$ \\frac{1}{1-} \\frac{g_1 z}{1-} \\frac{g_2(1-g_1) z}{1-} \\frac{g_3(1-g_2)z}{1-...,}, z\\in \\mathbb C, g_i\\in(0,1), \\lim\\limits_{i\\to \\infty} g_i=1/2, \\quad (1) $$ appearing as Shur--Wall $g$-fraction representations of certain analytic self maps of the unit disc $|w|< 1$, $w \\in \\mathbb C$. We precise the convergence behavior and prove the general convergence [2, p. 564 ] of (1) at the Runckel's points of the singular line $(1,+\\infty)$ It is shown that in some cases the convergence holds in the classical sense. As a result a count","authors_text":"Alexei Tsygvintsev","cross_cats":[],"headline":"","license":"","primary_cat":"math.CV","submitted_at":"2004-12-15T11:25:32Z","title":"On the convergence of continued fractions at Runckel's points and the Ramanujan conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0412298","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":"sha256:978a406e6d1e3e25c17d09d8e71bff5ae2c2335d2c35f1d6f2e659b47c5ad324","target":"record","created_at":"2026-05-18T00:07:44Z","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":"b3146de55a56aa64994094b15269ca9446d4b60c179e092f880a7f82ee511263","cross_cats_sorted":[],"license":"","primary_cat":"math.CV","submitted_at":"2004-12-15T11:25:32Z","title_canon_sha256":"35a52c56c5c80bb0a36415e2dc2bceb4935879a9e86c7c1e125825fd41094e87"},"schema_version":"1.0","source":{"id":"math/0412298","kind":"arxiv","version":1}},"canonical_sha256":"d70305876d18a76021edb9a0ade015f4eef4daa724bf996f90545d3c0b24f9e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d70305876d18a76021edb9a0ade015f4eef4daa724bf996f90545d3c0b24f9e0","first_computed_at":"2026-05-18T00:07:44.269631Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:44.269631Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jyt692Z8CC39zHGVjgEZ1SmNZU05ae3OLVJUSk5wm6wbZM/B8H5m2eo99K52xqK/bWGts8MsnOKYA+tfjMrTBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:44.270232Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0412298","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:978a406e6d1e3e25c17d09d8e71bff5ae2c2335d2c35f1d6f2e659b47c5ad324","sha256:101ad0b36a0ab945b071ed30dcdef581795f55386aa56e3329ad4cdb5ce4ad5c"],"state_sha256":"5889321a806ee8bcf11f497af5e25623ebfed2a0b7d16bf19f5feacf6a0cd876"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xizNbYasEAZjB2kf9gGEnfdME98A0/UhPQfhNNcv9WpPJ5iUoYeb5MzzU+8+LQOtcG2vw/duc+jXun1vcdQaBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T04:15:42.357404Z","bundle_sha256":"981937c58d97e53e2786af51f0ac1df4b8147e615d0152767e0c6c3e79201e20"}}