Research guide: mathematics, physics and computation from minimal change

[bookwormseagull1980]

The research portal connects nine papers, a book, the Lean proof library and V5 calculations.

The common question is what can be generated from minimal unbiased compositional change, and what information must remain available when the generated system is observed at finite resolution.

Mathematics. Generated arithmetic and histories develops native arithmetic, finite expression fibres, conditional readout and history-dependent response. Prime operators connects irreducibility, cotangent directions, Hodge localization and occupation traces.

Physics. Gauge structure and the Yang-Mills spectral gap follows the source into the generated action and its complete differential Hessian. Gravity and cosmology treats long-range source response, retained memory and finite-window cosmic structure.

Computation. Certified computation and P vs NP explains finite rational records, residual checking, polynomial bit-cost theorems and the uniform-generation interface to computational complexity.

The proofs and calculations guide links theorem mappings, formal audits, interval certificates and numerical comparisons.

Use mathematics and physics Q&A for questions about the constructions and mechanisms. Reproduction help has a separate form for the source record, procedure, environment and result. A question is most useful when it names the article and passage, declaration or numerical record involved. The issue forms are intended for concrete corrections and failed reproductions. Each article retains its own citation and rights record.