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Looking at the corresponding question when the Thue-Morse sequence is replaced by the regular paperfolding sequence, we obtain two infinite products A and B, where\n  A = (1/2)(3/4)(6/5)(7/8)(9/10)... and B = (2/3)(4/5)(7/"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1406.7407","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-06-28T14:40:14Z","cross_cats_sorted":[],"title_canon_sha256":"e996e3977249c82595bdb7b8a4958e21f3315f968a47b077da9da8d383f05f8c","abstract_canon_sha256":"07430502582348b3a250af7f1b7fa6210ace17249e424324084069f6563b536d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:45.428059Z","signature_b64":"KIgbvHagPtblGsTNzgInbDfzp3aSz+lh4pD6zNC+539meRSwYCyGSwH8cdoOyz14ExZ0UjDz1qvzl1DZ/XM9Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0af1ac0763e47fb2a251fffea97d6651b52c3e31af8753282a367a30cd229fc8","last_reissued_at":"2026-05-18T02:48:45.424123Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:45.424123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Paperfolding infinite products and the gamma function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jean-Paul Allouche","submitted_at":"2014-06-28T14:40:14Z","abstract_excerpt":"Taking the product of (2n+1)/(2n+2) raised to the power +1 or -1 according to the n-th term of the Thue-Morse sequence gives rise to an infinite product P while replacing (2n+1)/(2n+2) with (2n)/(2n+1) yields an infinite product Q, where\n  P = (1/2)(4/3)(6/5)(7/8)(10/9)... and Q = (2/3)(5/4)(7/6)(8/9)(11/10)...\n  Though it is known that P = 2^{-1/2}, nothing is known about Q. Looking at the corresponding question when the Thue-Morse sequence is replaced by the regular paperfolding sequence, we obtain two infinite products A and B, where\n  A = (1/2)(3/4)(6/5)(7/8)(9/10)... and B = (2/3)(4/5)(7/"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7407","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1406.7407","created_at":"2026-05-18T02:48:45.424211+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.7407v1","created_at":"2026-05-18T02:48:45.424211+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.7407","created_at":"2026-05-18T02:48:45.424211+00:00"},{"alias_kind":"pith_short_12","alias_value":"BLY2YB3D4R73","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"BLY2YB3D4R73FISR","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"BLY2YB3D","created_at":"2026-05-18T12:28:22.404517+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BLY2YB3D4R73FISR777KS7LGKG","json":"https://pith.science/pith/BLY2YB3D4R73FISR777KS7LGKG.json","graph_json":"https://pith.science/api/pith-number/BLY2YB3D4R73FISR777KS7LGKG/graph.json","events_json":"https://pith.science/api/pith-number/BLY2YB3D4R73FISR777KS7LGKG/events.json","paper":"https://pith.science/paper/BLY2YB3D"},"agent_actions":{"view_html":"https://pith.science/pith/BLY2YB3D4R73FISR777KS7LGKG","download_json":"https://pith.science/pith/BLY2YB3D4R73FISR777KS7LGKG.json","view_paper":"https://pith.science/paper/BLY2YB3D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.7407&json=true","fetch_graph":"https://pith.science/api/pith-number/BLY2YB3D4R73FISR777KS7LGKG/graph.json","fetch_events":"https://pith.science/api/pith-number/BLY2YB3D4R73FISR777KS7LGKG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BLY2YB3D4R73FISR777KS7LGKG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BLY2YB3D4R73FISR777KS7LGKG/action/storage_attestation","attest_author":"https://pith.science/pith/BLY2YB3D4R73FISR777KS7LGKG/action/author_attestation","sign_citation":"https://pith.science/pith/BLY2YB3D4R73FISR777KS7LGKG/action/citation_signature","submit_replication":"https://pith.science/pith/BLY2YB3D4R73FISR777KS7LGKG/action/replication_record"}},"created_at":"2026-05-18T02:48:45.424211+00:00","updated_at":"2026-05-18T02:48:45.424211+00:00"}