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We show explicitly that only the moduli associated to the supersymmetry breaking may give relevant contributions. All other spectator moduli \\mu_I give exponentially suppressed contributions for relatively small (as compared to the string scale) temperature, T, and supersymmetry breaking scale, M. More concisely, for \\mu_I > T and M, F takes the form\n  F(T,M; \\mu_I)=F(T,M)+O[exp(- {\\mu_I\\over T}), exp(- {\\mu_I\\over M"},"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":"0908.1881","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-08-13T12:21:15Z","cross_cats_sorted":[],"title_canon_sha256":"2eaa9fe8c667a208368409543046082d6481e0e1009e41260f196ea10439b59f","abstract_canon_sha256":"9e654bcb4e580cf750e71ae62a657fa002b02a4fdae0a026a896238715a7dbb7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:34:37.874705Z","signature_b64":"R0xuDRbDh+L/xQ6pH+BOaVWqMlZMiwiTLl1cueZedoYu9eMl5rpBaUP6vh8kFtqqk9JPNyyXcYklgWJro/65CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"560cbe0cdd82043f3ad6232c0aba0ff2af1947fa04b77df4363cf43a2449b215","last_reissued_at":"2026-05-18T02:34:37.874197Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:34:37.874197Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cosmological Phases of the String Thermal Effective Potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Costas Kounnas, Francois Bourliot, Herve Partouche, John Estes","submitted_at":"2009-08-13T12:21:15Z","abstract_excerpt":"In a superstring framework, the free energy density, F, can be determined unambiguously at the full string level once supersymmetry is spontaneously broken via geometrical fluxes. 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