Closure, Admissibility, and the Area Law: A Structural Framework for Horizon Entropy and Singularity Resolution

A finite-state grammar (LAP-1) over the classical Sanskrit 51-akṣara partition (SVARA,CORE, BRIDGE, GATE) with a 4-phase ledger closure rule yields an e􀆯ective code-rateof 1/4: we prove ℎe􀆯 = ℎ/4 and verify 𝑅e􀆯 ≈ 0.2499 for the 30-state LAP-1 v0.2automaton. Under a Closure Principle (admissibility forbids unbounded compressionand unbounded ledger streaming), we derive: (1) a closure kernel 𝑊(𝑟) = 𝑒􀬿􀰒/􀯥 thatsuppresses sub-𝜆 structure and forces bulk degrees of freedom onto the boundary asan information ledger; (2) an area-law 𝑁􀭫􀭟􀭶~𝐴/𝜆􀬶, 𝑆􀭫􀭟􀭶 ∝ 𝐴/𝜆􀬶, with explicit falsifiers(F1–F3); (3) black-hole application—horizon as information ledger, Bekenstein–Hawking entropy and its 1/4 coe􀆯icient from the same 4-phase redundancy; (4) horizontemperature and radiation (Hawking/Unruh scaling) from area law plus velocityadmissibility; (5) singularity resolution—non-singular cores, “singularity” ascompression failure; (6) nature of the universe—permission landscape, sub-Planck asoperator/admissibility logic. The paper states the full chain of progress and falsificationcriteria. It does not provide a full quantum theory; it provides a structural kernel (closure+ ledger + boundary encoding) intended to constrain a future completion.