Heuristic System Approach to the Hodge Conjecture: Insight from the CAS 6 Framework

Mitchell, M. (2009). Complexity: A Guided Tour. Oxford University Press.
Provides a broad survey of complexity science and its implications across disciplines, useful for framing CAS-6 as a generalizable heuristic paradigm.

Simon, H. A. (1962). "The Architecture of Complexity." Proceedings of the American Philosophical Society, 106(6), 467--482.
A classic paper on hierarchical systems and modularity, foundational for understanding multi-level interaction frameworks like CAS-6.

C. Recent Heuristic or Computational Approaches to the Hodge Conjecture

1. Voisin, C. (2007). "Hodge loci and absolute Hodge classes." Compositio Mathematica, 143(4), 945--958.
   Investigates the structure of Hodge loci and the distinction between algebraic and absolute Hodge classes, offering heuristic evidence toward the scope of HC.

2. Charles, F. (2012). "On the Tate and Mumford--Tate conjectures for K3 surfaces." Duke Mathematical Journal, 161(15), 2857--2903.
   Develops approaches linking HC to arithmetic conjectures, highlighting both heuristic reasoning and structural barriers.

3. Mumford, D. (1969). "Rational equivalence of 0-cycles on surfaces." Journal of Mathematics of Kyoto University, 9(2), 195--204.
   A classic paper often revisited as a heuristic touchstone: Mumford's counterexamples show the richness of transcendental cycles, challenging naive forms of HC.

4. Green, M., Griffiths, P., & Kerr, M. (2010). Mumford--Tate Groups and Domains: Their Geometry and Arithmetic. Annals of Mathematics Studies, Vol. 183. Princeton University Press.
   Provides a modern analytic--computational perspective on Hodge theory and cycles, where heuristic explorations are guided by group-theoretic and arithmetic structure.

5. Schreieder, S. (2019). "On the construction problem for Hodge numbers." Duke Mathematical Journal, 168(1), 1--81.
   Employs computational and constructive methods to explore which Hodge diamonds can arise, indirectly informing heuristic expectations about HC.

6. Bloch, S., & Srinivas, V. (1983). "Remarks on correspondences and algebraic cycles." American Journal of Mathematics, 105(5), 1235--1253.
   Introduces correspondences as heuristic tools for generating algebraic cycles, precursors to computational experiments akin to CAS-6 modeling.

7. Voisin, C. (2019). Khler Manifolds and Hodge Theory: A New Viewpoint. (Cours Spcialiss, Vol. 44). Socit Mathmatique de France.
   A modern re-examination of Hodge theory, explicitly motivated by heuristic and computational questions, re-contextualizing HC for new generations of researchers.