Information-Theoretic Identifiability of Split-Mark Diagnostic Posets, L1 Micro-Syntax Transfer Independence, and Sentence-Level Propositional Conservation in English Prose (1818-2026)

This monograph establishes four interconnected results across cognitive diagnostic psychometrics, second-language acquisition (SLA) corpus linguistics, and quantitative diachronic philology: Split-Mark Poset Identifiability: In Cambridge C1/C2 Key Word Transformation (Part 4) testing, each item awards up to 2 marks across two syntactic loci, yet standard reporting collapses the ordered binary vector (m_L, m_R) in {0,1}^2 into the scalar sum S = m_L + m_R in {0,1,2}. Over a 5-attribute hierarchical syntactic poset with |S| = 10 permissible mastery states (prior Shannon entropy log_2(10) = 3.3219 bits), we prove that ordered Split-Mark vector scoring achieves full poset identifiability in N_min(V) = 3 static items (and 2.3000 expected items adaptively), compared with N_min(S) = 4 for scalar sums and N_min(D) = 5 for dichotomous scoring. The Macro/Micro Decoupling Paradox: Auditing N = 80 Cambridge C2 Proficiency Part 4 items and 14 longitudinal C1/C2 scripts (3,886 words across 322 sentences) from zero-article Slavic/Baltic (Russian, Ukrainian, Lithuanian) and Romance (Italian, French) L1 learners reveals that candidates attain 96.9% accuracy on C1 macro-syntactic frames while remaining capped at a 21.4% Error-Free Sentence Ratio (EFSR) by deterministic L1 micro-syntax transfer (50.8% determiner errors in Slavic/Baltic vs 26.8% in Romance), while macro-frame deployment is statistically invariant to L1 family (chi^2 = 0.3113, p = 0.7258). Closed-Class Syntactic Cadence Entropy: Combining Clause-Initial Opener Shannon Entropy (H_opener) and Punctuation Markov Transition Entropy (H_punct) separates authentic C1/C2 prose from formulaic template prose with ROC AUC = 1.000 (Mann-Whitney p = 1.08e-5). Sentence-Level Propositional Conservation (1800-2026): Across a balanced 36-text diachronic corpus (5,296 words), while finite subordination density decayed by 52.6% (p = 1.98e-5), nominal-participial compression surged by 240.0% (p = 1.43e-8), holding total propositions per sentence invariant across two centuries (2.70 to 2.92, p = 0.4778). Interactive browser verifiers and corpus diagnostics are hosted at https://garethenglish.com/sprucefield-research.html and https://garethenglish.com/c1-syntactic-research-lab.html.