Rigidity in Rational Exponent Systems Bounded Diophantine Constraints, Minimality, and Base Invariance

This monograph records a four-track rewrite ledger that separates metric content from
representation artefacts. A recurring lesson in the historical record is that apparent
“transcendental difficulty” can be a by-product of domain and tool constraints (e.g.
ruler–compass constructibility, or an implicit restriction to real-plane constructions),
rather than an arithmetic necessity.
All statements are representation-level identities and convention-scoped ledger rules.
No microscopic dynamics, physical law, or ontological claim is asserted. Appendix 
rewrites the canonical derivation of classical statistical mechanics to make the standard
rewrite logic explicit (counting vs. measuring, symmetry hygiene, logarithmic
projection). Appendix  collects literature-anchored domain constraints and common
representation “failure modes” that motivate explicit budgeting and thread separation.