This monograph records a four-track rewrite ledger that separates metric content fromrepresentation 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 standardrewrite logic explicit (counting vs. measuring, symmetry hygiene, logarithmicprojection). Appendix collects literature-anchored domain constraints and commonrepresentation “failure modes” that motivate explicit budgeting and thread separation.