{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:ZYMA2WJSNRXLVHEDMYUVWKRBFX","short_pith_number":"pith:ZYMA2WJS","schema_version":"1.0","canonical_sha256":"ce180d59326c6eba9c8366295b2a212dd4af7e645a5bb1ad6f6161ce997eb945","source":{"kind":"arxiv","id":"1404.2312","version":1},"attestation_state":"computed","paper":{"title":"Exact solutions for a periodic assembly of bubbles in a Hele-Shaw channel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.PS"],"primary_cat":"physics.flu-dyn","authors_text":"Christopher C. Green, Giovani L. Vasconcelos","submitted_at":"2014-04-08T21:45:52Z","abstract_excerpt":"Exact solutions are reported for a periodic assembly of bubbles steadily co-travelling in a Hele-Shaw channel. The solutions are obtained as conformal mappings from a multiply connected circular domain in an auxiliary complex plane to the flow region in a period cell. The conformal mappings are constructed using the generalized Schwarz-Christoffel formula for multiply connected polygonal domains in terms of products of Schottky-Klein prime functions. It is shown that previous solutions for multiple steady bubbles in a Hele-Shaw cell are all particular cases of the solutions described herein. E"},"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":"1404.2312","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2014-04-08T21:45:52Z","cross_cats_sorted":["math-ph","math.MP","nlin.PS"],"title_canon_sha256":"87421c8348525db34c59d1bdf5b5c29bee44f567a305c6f763c4b3f89a9b8e52","abstract_canon_sha256":"e60a628d1f07be8789115d6c6b942641e13332d1e47b10c8227fa92d68e20bfa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:31.863193Z","signature_b64":"aP8tYOOPxdgUJR5xntpHwbav32Jdlau8a5K72J8ssWb2KZJXEW+ruvjiJiJsbPe01pB4jxaoVevA1Hyonl3iDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce180d59326c6eba9c8366295b2a212dd4af7e645a5bb1ad6f6161ce997eb945","last_reissued_at":"2026-05-18T02:54:31.862715Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:31.862715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exact solutions for a periodic assembly of bubbles in a Hele-Shaw channel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.PS"],"primary_cat":"physics.flu-dyn","authors_text":"Christopher C. Green, Giovani L. Vasconcelos","submitted_at":"2014-04-08T21:45:52Z","abstract_excerpt":"Exact solutions are reported for a periodic assembly of bubbles steadily co-travelling in a Hele-Shaw channel. The solutions are obtained as conformal mappings from a multiply connected circular domain in an auxiliary complex plane to the flow region in a period cell. The conformal mappings are constructed using the generalized Schwarz-Christoffel formula for multiply connected polygonal domains in terms of products of Schottky-Klein prime functions. It is shown that previous solutions for multiple steady bubbles in a Hele-Shaw cell are all particular cases of the solutions described herein. E"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2312","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":"1404.2312","created_at":"2026-05-18T02:54:31.862787+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.2312v1","created_at":"2026-05-18T02:54:31.862787+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.2312","created_at":"2026-05-18T02:54:31.862787+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZYMA2WJSNRXL","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZYMA2WJSNRXLVHED","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZYMA2WJS","created_at":"2026-05-18T12:28:59.999130+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/ZYMA2WJSNRXLVHEDMYUVWKRBFX","json":"https://pith.science/pith/ZYMA2WJSNRXLVHEDMYUVWKRBFX.json","graph_json":"https://pith.science/api/pith-number/ZYMA2WJSNRXLVHEDMYUVWKRBFX/graph.json","events_json":"https://pith.science/api/pith-number/ZYMA2WJSNRXLVHEDMYUVWKRBFX/events.json","paper":"https://pith.science/paper/ZYMA2WJS"},"agent_actions":{"view_html":"https://pith.science/pith/ZYMA2WJSNRXLVHEDMYUVWKRBFX","download_json":"https://pith.science/pith/ZYMA2WJSNRXLVHEDMYUVWKRBFX.json","view_paper":"https://pith.science/paper/ZYMA2WJS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.2312&json=true","fetch_graph":"https://pith.science/api/pith-number/ZYMA2WJSNRXLVHEDMYUVWKRBFX/graph.json","fetch_events":"https://pith.science/api/pith-number/ZYMA2WJSNRXLVHEDMYUVWKRBFX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZYMA2WJSNRXLVHEDMYUVWKRBFX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZYMA2WJSNRXLVHEDMYUVWKRBFX/action/storage_attestation","attest_author":"https://pith.science/pith/ZYMA2WJSNRXLVHEDMYUVWKRBFX/action/author_attestation","sign_citation":"https://pith.science/pith/ZYMA2WJSNRXLVHEDMYUVWKRBFX/action/citation_signature","submit_replication":"https://pith.science/pith/ZYMA2WJSNRXLVHEDMYUVWKRBFX/action/replication_record"}},"created_at":"2026-05-18T02:54:31.862787+00:00","updated_at":"2026-05-18T02:54:31.862787+00:00"}