Sequential Structure Analysis of the Ramanujan Mathematical Notebooks: A Hierarchical Inference Assessment (1903-1920)

This report presents a sequential structure analysis of Srinivasa Ramanujan's mathematical notebooks (1903-1920), reconstructed at chapter level from Berndt (1985-1998) and Andrews-Berndt (2005-2018), comprising 49 chapter-level domain-type observations across 8 mathematical domain classes. The analysis applies a validated sequential structure scoring algorithm with formal hierarchical inference level classification (the Markov Decomposition Layer protocol, FMX-IP-2026). Three results are reported. First, the Ramanujan corpus is correctly classified as Level 1 (clustering confirmed): strong domain clustering is confirmed and taxonomy-robust across 4-, 8-, and 12-class representations (structural scores 0.464-0.504, z = +3.88 to +6.59 vs. uniform null, stable across 3 seeds), and the structure is fully accounted for by first-order Markov dynamics (z_markov = +0.27). Second, the framework demonstrates correct inference ceiling detection: Level 2 and Level 3 tests are correctly identified as underpowered at n=49 chapter-level transitions, and no escalation is made. Third, a formally demonstrated methodological finding: chapter-level corpus expansion induces Hurst exponent saturation and inflated self-transitions that are fully explained by representation structure rather than generative dynamics — a measurable artifact confirmed by five independent controls. Cognitive grammar, mental navigation rules, and path dependence as cognitive structure are explicitly excluded from all claims. The primary contribution is the hierarchical inference framework itself, which is domain-general for discrete symbolic corpora (Type B/D/F). Full reproducibility materials in companion private deposit. Algorithm code available to qualified institutional reviewers under IP agreement: [email protected].