ACE Foundations: A Comprehensive Paper

This paper consolidates the foundational layer of the Akṣara Cosmos Engine (ACE) into one comprehensive document. It (1) defines what "foundation" means in ACE and how it differs from phenomenology; (2) states the minimal axiom set (Axioms 0–5) with pointers to full derivations; (3) surveys where foundation already appears across existing ACE papers; (4) develops five foundation strands in full: F2 Ledger Grammar and the 1/4 code-rate (formal statement, LAP-1, Perron–Frobenius, proof sketch, numerical verification); F3 Abhinavagupta–ACE mapping (fidelity and limits); F4 Kalā–Niyati geometric-mean renormalisation lemma (AG-1); F5 Planck closure lemma and resolution saturation; F6 Two-kernel admissibility (compression vs propagation); (5) clarifies foundation vs phenomenology with a quick-reference table; (6) gives the suggested order for the foundation programme and ties all strands to the axiom set