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This transformation (Eq. 4) is characterized by three Euler angles and two deformation parameters, $\\beta$ (quadrupole) and $\\gamma$ (triaxiality), but does not uniquely define the nuclear shape; rotational averaging over equivalent orientations is "},"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":true,"formal_links_present":true},"canonical_record":{"source":{"id":"2605.17277","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nucl-th","submitted_at":"2026-05-17T06:07:48Z","cross_cats_sorted":["nucl-ex"],"title_canon_sha256":"bf56219d6332e4f6e99dc310f6b2b6af001c7dd92ef841201fffce9103bdc6b6","abstract_canon_sha256":"c9bd9af20bb1f2ff3f0c7edf1da6082c490ca864326633b52ce31b603fca57b7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:03:49.347422Z","signature_b64":"nYSCgebyfHSU10owWsxGEJqY3bkhh2bfcQjpL6d31WnmJpW/24YLTsZA5pueoW7AwZ8EJ2ogGDO8j0L/s+tWDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e0ed4b58d50e7bee6fd9c2bcbcf9b8e8587941d15b173240e7ad3f7a3195da9","last_reissued_at":"2026-05-20T00:03:49.346563Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:03:49.346563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Emergence of Cluster Formation in Light Nuclei","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The non-unique coordinate system with experimental β and γ parameters yields the most probable nuclear shapes where clusters form in light nuclei.","cross_cats":["nucl-ex"],"primary_cat":"nucl-th","authors_text":"Jos\\'e Nicol\\'as Orce, Manfred Jason Jaftha","submitted_at":"2026-05-17T06:07:48Z","abstract_excerpt":"Spherical harmonics form a complete orthonormal basis which allows any function on the sphere to be expanded. 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Only then does cluster formation spatially emerge in light nuclei and the characteristic bowling-pin-like shapes of 10B and 20Ne are reproduced.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The assumption that the three transformation operators in Eq. 6 produce a single intrinsic configuration whose rotational averaging is unnecessary, and that feeding experimental β and γ directly into the non-unique system of Eq. 4 is sufficient to select the most probable shape without further model-dependent corrections.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Using experimental beta and gamma values in a non-unique coordinate system aligned with principal axes produces the most probable nuclear shapes and makes cluster formation visible in light nuclei.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The non-unique coordinate system with experimental β and γ parameters yields the most probable nuclear shapes where clusters form in light nuclei.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"fd4ece064cf68b1697a5d5df02091d3752192c85ed26ea51441fd335115987a4"},"source":{"id":"2605.17277","kind":"arxiv","version":1},"verdict":{"id":"7e8831c6-d078-4427-92c0-d7192f0ac069","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T22:59:13.788185Z","strongest_claim":"Here we show that the non-unique coordinate system of Eq. 4 with β and γ deformation parameters extracted from experimental electric-quadrupole matrix elements actually yields the most probable nuclear shape. Only then does cluster formation spatially emerge in light nuclei and the characteristic bowling-pin-like shapes of 10B and 20Ne are reproduced.","one_line_summary":"Using experimental beta and gamma values in a non-unique coordinate system aligned with principal axes produces the most probable nuclear shapes and makes cluster formation visible in light nuclei.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The assumption that the three transformation operators in Eq. 6 produce a single intrinsic configuration whose rotational averaging is unnecessary, and that feeding experimental β and γ directly into the non-unique system of Eq. 4 is sufficient to select the most probable shape without further model-dependent corrections.","pith_extraction_headline":"The non-unique coordinate system with experimental β and γ parameters yields the most probable nuclear shapes where clusters form in light nuclei."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.17277/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T23:31:20.194936Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T23:13:20.079524Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T22:01:57.830389Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T21:33:23.774514Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"ac86f56642cfba51e9690f42e78173127067f7892086d7b4e24fdcce9e462eec"},"references":{"count":51,"sample":[{"doi":"","year":null,"title":"Motivation This work is motivated by novel research at the Large Hadron Collider (LHC) at CERN probing nuclear geometry via light-ion collisions (LIC). Here, nuclear shapes — includingα- cluster confi","work_id":"6f752d5b-18ea-4df8-84fc-d9c145d1a648","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1952,"title":"To this end, state-of-the-art calculations using nuclear lattice effective field theory (NLEFT) incorporateα-cluster correlations within the minimal nuclear interaction [17]","work_id":"0d00a5ac-b6e7-405d-afbc-46d8ef3e2bd5","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"(4) and (6) with empiricalβandγdeformations are shown in the left and right panels of Fig","work_id":"1b8a778a-0a20-422b-ba94-48e9a6b8877a","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"= 0.08472(56) eb [39], suggests a similarly dominant prolate shape arising from theα+ d +αcluster configuration, in agreement with AMD density distributions [40]. 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