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To the third order, the zero-energy result S_11(0) and the first energy derivative S'_11(0) are found to be (3.99 \\pm 0.14)* 10^-25 MeV b and S_11(0)*(11.3 \\pm 0.1) MeV^-1, respectively; both consistent with the current adopted values. The second energy derivative is also calculated for the first time, and the result S\"_11(0) = S_11(0)*(170 \\pm 2) MeV^-2 contributes at the level of 0.5% to the fusion rate at the solar center, whic"},"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":"1209.2552","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nucl-th","submitted_at":"2012-09-12T10:34:08Z","cross_cats_sorted":[],"title_canon_sha256":"ecb21a4e2c19ceb546e7730028e733f56b69de666f9e54256dc65c0454bc0fc3","abstract_canon_sha256":"741d59fa7f21019b6484b51fd547499cf16591c7773324c0fe36e118eb963b6f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:54:30.058197Z","signature_b64":"YIAL2ELFBzFRBxA3KmApPgdbjGcKAMfJmLjDF9UJSmw2gwB5qmD7+/lH3KPYNQ6OKo7s4b0NidMpIDD2kSlvDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78c755dd37ac2a252c916fa84940537c106a1bdb2344a11dd1efbac06154fd28","last_reissued_at":"2026-05-18T01:54:30.057760Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:54:30.057760Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Near Threshold Proton-Proton Fusion in Effective Field Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nucl-th","authors_text":"C.-P. Liu, Jiunn-Wei Chen, Shen-Hsi Yu","submitted_at":"2012-09-12T10:34:08Z","abstract_excerpt":"The astrophysical S-factor for proton-proton fusion, S_11(E), is obtained with the nuclear matrix element analytically calculated in pionless effective field theory. To the third order, the zero-energy result S_11(0) and the first energy derivative S'_11(0) are found to be (3.99 \\pm 0.14)* 10^-25 MeV b and S_11(0)*(11.3 \\pm 0.1) MeV^-1, respectively; both consistent with the current adopted values. 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