Explanation of phi_forcing_principle

(1) In plain English, the declaration asserts that the golden ratio φ satisfies the equation φ² = φ + 1, that φ is the unique positive real solution to any equation of the form r² = r + 1, and that both the minimum non-trivial cost J_bit and the coherence quantum E_coh are strictly positive.

(2) In Recognition Science this matters because it shows that self-similarity on a discrete J-cost ledger forces the scale ratio to be exactly φ, supplying a parameter-free origin for the golden ratio that later yields derived constants such as ħ = φ⁻⁵ and the φ-ladder frequencies.

(3) The formal statement is a four-way conjunction:

• φ² = φ + 1 (the defining algebraic identity),
• ∀ r : ℝ, r > 0 → r² = r + 1 → r = φ (uniqueness among positive reals),
• 0 < J_bit (positivity of the minimum cost),
• 0 < E_coh (positivity of the coherence quantum). The proof term simply packages the four supporting facts phi_equation, golden_constraint_unique, J_bit_pos and E_coh_pos.

(4) Visible dependencies inside the supplied source are the definition of φ, the predicate satisfies_golden_constraint, the structure SelfSimilar, the theorem self_similar_forces_golden_constraint that reduces self-similarity to the golden equation, and the positivity proofs for J_bit and E_coh. The module imports LawOfExistence (for J) and PhiForcingDerived (for geometric-scale closure), but the certificates used here are the four lemmas listed above.

(5) The declaration does not prove the physical emergence of spatial dimension D = 3, the value c = 1 voxel/tick, or the full forcing chain from the Law of Logic; those steps appear in other modules. It also does not prove that every self-similar ledger must exist—only that, if one does, its scale ratio must be φ.