{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:BMY2JJ3LZFULXV6A7GTCXZN5EK","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":"3149ed8b675d2d9b9e58e18e11cd4815045dd34e871e96473327b0afd51a2419","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-06-24T13:44:27Z","title_canon_sha256":"c95a23ac311cb7f4ddea246293adc7c21af38da21b52d572b4624f83647fa142"},"schema_version":"1.0","source":{"id":"2606.25825","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.25825","created_at":"2026-06-25T01:18:40Z"},{"alias_kind":"arxiv_version","alias_value":"2606.25825v1","created_at":"2026-06-25T01:18:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.25825","created_at":"2026-06-25T01:18:40Z"},{"alias_kind":"pith_short_12","alias_value":"BMY2JJ3LZFUL","created_at":"2026-06-25T01:18:40Z"},{"alias_kind":"pith_short_16","alias_value":"BMY2JJ3LZFULXV6A","created_at":"2026-06-25T01:18:40Z"},{"alias_kind":"pith_short_8","alias_value":"BMY2JJ3L","created_at":"2026-06-25T01:18:40Z"}],"graph_snapshots":[{"event_id":"sha256:8f8d249821956ce620c774d5bb53801decb11ffe0afe027a2134280ac258371c","target":"graph","created_at":"2026-06-25T01:18:40Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.25825/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It is well known that $F(x)=\\prod_{n=0}^{\\infty}(1-x^{2^n})$ is the generating function of the Prouhet-Thue-Morse sequence $\\{(-1)^{\\sigma_2(n)}\\}_{n=0}^\\infty$, where $\\sigma_2(n)$ is the sum of (binary) digits of $n$. Let $m$ be an integer. In 2018, Gawron, Miska and Ulas initiated the study of arithmetic properties of power series expansion of the function $$F_m(x)=F(x)^m=\\sum_{n=0}^{\\infty}t_m(n) x^n,$$ and proposed a conjecture stating that for any given integer $m\\ge 2$, the sequence $\\{t_m(n)\\}_{n=0}^{\\infty}$ is unbounded. In this paper, we introduce a new method to investigate this co","authors_text":"Jinmin Yu, Shaofang Hong, Wenzhong Lei","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-06-24T13:44:27Z","title":"Proof of the Gawron-Miska-Ulas conjecture concerning unboundedness of coefficients of power series expansion of $\\prod_{n=0}^{\\infty}(1-x^{2^{n}})^m$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.25825","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":"sha256:40d1c603b00f5ff90dcd2485ef9054c32f18bea18261b2b17c36dd4775e01722","target":"record","created_at":"2026-06-25T01:18:40Z","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":"3149ed8b675d2d9b9e58e18e11cd4815045dd34e871e96473327b0afd51a2419","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-06-24T13:44:27Z","title_canon_sha256":"c95a23ac311cb7f4ddea246293adc7c21af38da21b52d572b4624f83647fa142"},"schema_version":"1.0","source":{"id":"2606.25825","kind":"arxiv","version":1}},"canonical_sha256":"0b31a4a76bc968bbd7c0f9a62be5bd22b654e3fec49b2b9227af30561cd554e2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b31a4a76bc968bbd7c0f9a62be5bd22b654e3fec49b2b9227af30561cd554e2","first_computed_at":"2026-06-25T01:18:40.477307Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-25T01:18:40.477307Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7tEQU/9tjCtcqDcJp3F1rG6EGFxXy/sFva7bHvCFSPRTvMpPbhtm1nc2lyca0lihIxWqFaH68rBxyyCqmqcmDA==","signature_status":"signed_v1","signed_at":"2026-06-25T01:18:40.477655Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.25825","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40d1c603b00f5ff90dcd2485ef9054c32f18bea18261b2b17c36dd4775e01722","sha256:8f8d249821956ce620c774d5bb53801decb11ffe0afe027a2134280ac258371c"],"state_sha256":"a3b74dc6174d9ea94f46f4e8444ad9361abaf2252522e2226c79c4b7b8a39af7"}