IndisputableMonolith.Meta.LedgerUniqueness
The Meta.LedgerUniqueness module collects definitions and uniqueness results centered on the golden ratio φ together with gray-code cycle properties for hypercubes. Researchers verifying the meta foundations of the Recognition Science ledger would cite it when checking fixed-point and dimension-uniqueness claims. The module is organized as a sequence of definitions imported from Constants and GrayCode followed by targeted uniqueness lemmas.
claimThe golden ratio satisfies $\phi = \frac{1 + \sqrt{5}}{2}$. The module also records uniqueness of the linking dimension on the 3-cube and minimality of the eight-tick gray-code cycle length.
background
The module sits in the meta domain and imports the RS time quantum $\tau_0 = 1$ tick from Constants together with the binary-reflected Gray code construction from GrayCode. The latter supplies the recursive definition BRGC(0) = [0] that yields a Hamiltonian cycle on the d-dimensional hypercube $Q_d$. Sibling declarations inside the module introduce $\phi$, linkingNumber, H_LinkingDimensionUniqueness, Q3_unique_linking_dimension, cube_uniqueness, grayCodeCycleLength, eight_tick_minimal and related statements.
proof idea
This is a definition module containing multiple definitions and lemmas; individual uniqueness statements are proved by algebraic verification of the fixed-point equation for $\phi$ and by direct appeal to the cycle-length properties supplied by the imported GrayCode construction.
why it matters in Recognition Science
The module supplies the uniqueness ingredients required by the phi-ladder and the eight-tick octave (T6 and T7 of the forcing chain). It therefore underpins later claims that rely on a unique self-similar fixed point and a minimal gray-code period of length $2^3$.
scope and limits
- Does not derive the forcing chain from T0 to T8.
- Does not compute numerical values inside the alpha inverse band.
- Does not treat the mass formula or Berry creation threshold.
- Does not supply physical interpretations of the constants.
depends on (2)
declarations in this module (17)
-
def
phi -
theorem
phi_satisfies_fixed_point -
theorem
phi_unique_fixed_point -
theorem
cost_fixed_point_is_phi -
def
linkingNumber -
def
H_LinkingDimensionUniqueness -
theorem
Q3_unique_linking_dimension -
theorem
cube_uniqueness -
def
grayCodeCycleLength -
theorem
eight_tick_minimal -
theorem
no_shorter_cycle -
theorem
eight_tick_is_minimal -
structure
RSLedger -
structure
DiscreteConservativeSystem -
theorem
ledger_structure_unique -
theorem
complete_ledger_uniqueness -
theorem
rs_ledger_is_unique