Let \(M\) be the largest size of a subset with the stated property. The current certified bounds are \[ \boxed{13\leq M\leq14}. \] The lower bound is attained by \[ A=\{8,13,18,28,29,47,68,71,82,83,91,95,99\}. \] For this set, the 99 nonzero ordered-difference multiplicities have histogram \[ 12\text{ zeros},\qquad18\text{ ones},\qquad69\text{ twos}. \] Their sum is \(13\cdot12=156\), and their maximum is two. The executable record checks every ordered pair directly. It also checks that adjoining any of the other 87 residues violates the bound, so this particular 13-set is inclusion-maximal.

For the upper bound, a \(k\)-set has \(k(k-1)\) ordered pairs of distinct elements. All of their differences lie in the 99 nonzero residues, each with capacity two. Hence \[ k(k-1)\leq2\cdot99=198. \] Since \(15\cdot14=210\), one has \(k\leq14\). This counting proof leaves the candidate size 14 undecided.

A seeded one-swap simulated-annealing run evaluated 600,000,000 proposals. A separate conflict-directed tabu run was capped after reaching the same best score. Neither run found a feasible 14-set. The best retained near miss was \[ \{0,5,7,31,43,58,61,62,63,72,80,84,91,97\}. \] Its only overloaded ordered residues are 19 and 81, each with multiplicity three. These are the two orientations of one overloaded circular distance class.

This evidence explains why simple greedy searches may stall one step short. It carries no upper-bound force. The exact continuation is the binary model in the artifact. Solving it with proof logging, followed by independent proof checking, would settle the candidate.

For a support set \(A\subseteq\mathbb Z_v\), the off-peak periodic autocorrelation at shift \(t\) is \[ |A\cap(A+t)|=|\{(a,b)\in A^2:a-b=t\}|. \] Thus the candidate asks whether a binary sequence of length 100 and weight 14 can have every off-peak autocorrelation at most two. This is exactly the autocorrelation condition for one codeword of a \((100,14,2)\) optical orthogonal code.

Chung, Salehi, and Wei introduced the standard OOC framework and its counting bounds. Swanson studied the adjacent multiplicity-one case under the name planar cyclic difference packing and reported exact computations through modulus 144 for that case. Baicheva and Topalova give a modern exact backtracking treatment of autocorrelation two, with complete small-length classifications for weights 6 and 7. Their definition explicitly identifies repeated differences with autocorrelation.

The located tables and constructions do not include weight 14 at length 100. The generalized-Sidon name also has competing sum-representation conventions, so searches using only `B_2[2]` can mix different finite problems. This record uses the ordered-difference definition in the candidate and states every multiplicity convention explicitly.

The first part computes all 156 ordered differences of the 13-set. It checks the full 99-entry multiplicity vector, the special self-inverse residue 50, and every possible one-point extension. The second part builds a complete binary linear model for a 14-set.

The model uses membership variables \(x_i\) and pair variables \(y_{ij}\) for \(0\leq i<j<100\). Three inequalities impose \(y_{ij}=x_ix_j\). For each circular distance \(d=1,\ldots,49\), the sum of the corresponding pair variables is at most two. At distance 50 it is at most one, since one antipodal unordered pair contributes both ordered representations of residue 50. The constraints \(\sum_i x_i=14\) and \(x_0=1\) complete the formulation. Fixing zero loses no solution because any nonempty set can be translated.

The generated LP has 5,050 binary variables, 14,850 linearization constraints, and 50 distance constraints. Its SHA-256 digest is `d0f0125ef4b783aaec55d868884c1ef99e7434bc667b544623389db15ac000a5`. The model has not been solved in this record. A feasible solution supplies the desired 14-set. An infeasibility result needs a retained, independently checked proof trace before it can lower the upper bound.