{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XZP5TZ6L3JOUUKBCFMXOMS7K7T","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":"222cb8cb238e60df9cb743dc0c923067f4f97e74b328d0716214b78e283d137d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-02-29T12:38:53Z","title_canon_sha256":"c9fce9edbfc9d5bc4fe939db9975ae8c67cd8778915bfea356175b1ac26db1b3"},"schema_version":"1.0","source":{"id":"1602.08937","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.08937","created_at":"2026-05-17T23:46:42Z"},{"alias_kind":"arxiv_version","alias_value":"1602.08937v1","created_at":"2026-05-17T23:46:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.08937","created_at":"2026-05-17T23:46:42Z"},{"alias_kind":"pith_short_12","alias_value":"XZP5TZ6L3JOU","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XZP5TZ6L3JOUUKBC","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XZP5TZ6L","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:453f8d865635dc8451ec583a00e60a7dd612c65866b4b20269bc882731ba30a2","target":"graph","created_at":"2026-05-17T23:46:42Z","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 partial theta function $\\theta (q,x):=\\sum_{j=0}^{\\infty}q^{j(j+1)/2}x^j$, where $x\\in \\mathbb{C}$ is a variable and $q\\in \\mathbb{C}$, $0<|q|<1$, is a parameter. We show that, for any fixed $q$, if $\\zeta$ is a multiple zero of the function $\\theta (q,.)$, then $|\\zeta |\\leq 8^{11}$.","authors_text":"Vladimir Petrov Kostov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-02-29T12:38:53Z","title":"On the multiple zeros of a partial theta function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.08937","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":"sha256:2ef5de53e4771451dbde7f1dbf123584cc541db21e89e58184d1f4f0cdc092ec","target":"record","created_at":"2026-05-17T23:46:42Z","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":"222cb8cb238e60df9cb743dc0c923067f4f97e74b328d0716214b78e283d137d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-02-29T12:38:53Z","title_canon_sha256":"c9fce9edbfc9d5bc4fe939db9975ae8c67cd8778915bfea356175b1ac26db1b3"},"schema_version":"1.0","source":{"id":"1602.08937","kind":"arxiv","version":1}},"canonical_sha256":"be5fd9e7cbda5d4a28222b2ee64beafcceb20929bf860ba4480fd6f8fed48be2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be5fd9e7cbda5d4a28222b2ee64beafcceb20929bf860ba4480fd6f8fed48be2","first_computed_at":"2026-05-17T23:46:42.286723Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:42.286723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IbDIf353k4XipUlazWFmBGtWYB9j13yjEwFBsHz4oFnc9puhVCY8gsgoMYGJwBo02mJBoC0Wp0IENeKolrpdAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:42.287574Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.08937","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ef5de53e4771451dbde7f1dbf123584cc541db21e89e58184d1f4f0cdc092ec","sha256:453f8d865635dc8451ec583a00e60a7dd612c65866b4b20269bc882731ba30a2"],"state_sha256":"aea318c96df3157cf8e293e776e412e5d383ab8047255eedcc12179baba75f6d"}