Triangular Palindromic Arrays and Reverse Difference Structures.

We introduce a deterministic construction based on palindromic digit arrays generated from arbitrary finite digit sequence. Given a base sequence 𝐵=𝑏1𝑏2…𝑏𝑚, we form the even length palindrome 𝑇0=𝐵𝐵∗, where 𝐵∗ denotes the reversal of 𝐵. Successive rows are obtained by symmetric truncation of outer digit pairs, producing an inverted triangular array of palindromic digit strings 𝑇0, 𝑇1, …, 𝑇𝑚−1. For each row 𝑇𝑘, we partition the palindrome into left and right halves 𝐿𝑘 and 𝑅𝑘=𝐿𝑘∗, and define the reverse difference value 𝐷𝑘=|𝑅𝑘−𝐿𝑘|. Using elementary properties of decimal representations and digit reversals, we establish two fundamental modular invariants of the construction. Every triangular row 𝑇𝑘 is divisible by 11 and every reverse difference value 𝐷𝑘 is divisible by 9 and therefore also by 3. We further derive an explicit decomposition formula expressing the reverse difference as a weighted sum of symmetric digit pair differences, |𝑅−𝐿|=|∑ (𝑎𝑟+1−𝑖−𝑎𝑖) 10𝑟−𝑖|, 𝑟𝑖=1 showing that the reverse difference depends only on the asymmetric component of the digit sequence. Within the triangular construction, successive truncations eliminate the contribution of outer symmetric digit pairs yielding a layered decomposition of digit asymmetry. The construction generates several deterministic integer sequences and structures arising from the triangular geometry, including the reverse difference sequence 𝐷𝑘, the normalized sequence 𝑀𝑘=𝐷𝑘9, the ternary sequence 𝐸𝑘=𝐷𝑘3, boundary sequences and symmetric column sum pairs whose digits coincide up to reversal. The triangular palindromic system therefore links palindromic digit symmetry, triangular truncation dynamics and modular arithmetic invariants providing a structured framework for studying digit reversal operators and arithmetic patterns arising from palindromic digit constructions.