A Parameter–Free Deductive Measurement of Physical Reality

We present a deductive framework for fundamental physics grounded in a single mechanised logical axiom: the impossibility of self-referential non-existence. In this Part I we restrict attention to the formal core, deriving three key results: (i) existence and uniqueness (up to order isomorphism) of a positive double-entry ledger with an immutable generator, establishing the necessity of tracked alterations with finite cost; (ii) uniqueness of the symmetric cost functional J(x) = (1/2)(x + x^(-1)) - 1 under explicit assumptions of symmetry, analyticity, locality, and periodicity (S/A/L/P), yielding the golden ratio phi as the universal scaling constant; and (iii) a minimal three-dimensional spatial embedding that forces a Hamiltonian 8-tick recognition cycle, providing the unique stable topology for recognition events. Results are status-labelled [T] for mechanised theorems, [R] for rigorous but unmechanised results, and [P] for phenomenology; only [T]/[R] are essential to Part I. A comprehensive public artifact index (Lean 4 proofs, Python notebooks, pinned toolchains, and SHA-256 checksums) ensures complete reproducibility. Dimensionless outputs from the proof layer are mapped to SI units via an audited, anchor-invariant bridge functor. Bridge-level phenomenology (including fine-structure constant alpha, particle mass ladder, information-limited gravity, and cosmological parameters) is quarantined behind a compile-time toggle and deferred to Part II, maintaining focus on the parameter-free formal foundations.