IndisputableMonolith.Meta.LedgerUniqueness
The Meta.LedgerUniqueness module defines the golden ratio φ = (1 + √5)/2 and assembles uniqueness results for fixed points, linking dimensions, and minimal Gray code cycles on hypercubes. Researchers tracing the forcing chain from J-uniqueness to the eight-tick octave or D = 3 would cite these results when closing the ledger structure. The module imports the RS time quantum and binary-reflected Gray code patterns to organize the supporting definitions and theorems.
claimLet $φ = (1 + √5)/2$. The module states that $φ$ is the unique self-similar fixed point and that the binary-reflected Gray code realizes a Hamiltonian cycle of length 8 on the 3-cube, with uniqueness holding for the associated linking dimension.
background
The module sits in the meta layer and takes the fundamental RS time quantum τ₀ = 1 tick from the Constants import. It incorporates the binary-reflected Gray code construction that recursively builds a Hamiltonian cycle on the d-dimensional hypercube Q_d, starting from BRGC(0) = [0]. The central object is the golden ratio φ = (1 + √5)/2, introduced as the self-similar fixed point satisfying the J-cost equation.
proof idea
This is a definition module, no proofs. It organizes the material by declaring φ, importing the GrayCode Hamiltonian-cycle construction, and exposing sibling uniqueness statements for linking numbers and cycle minimality.
why it matters in Recognition Science
The module supplies the φ fixed-point and Gray-code cycle tools that feed the parent uniqueness theorems for eight_tick_is_minimal and Q3_unique_linking_dimension. It closes the T5–T6 step of the forcing chain by making the self-similar fixed point and the eight-tick octave available for downstream ledger arguments.
scope and limits
- Does not derive φ from the J-cost functional equation.
- Does not prove the Gray code construction or its Hamiltonian property.
- Does not connect results to mass ladders or Berry creation thresholds.
- Does not address hypercubes of dimension other than 3.
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