Timeline

Version 4 submitted as a Research Paper to JPDC (Elsevier, Q1), manuscript JPDC-D-26-01392, assigned to an editor the same day — the venue whose scope is the theory, design, and evaluation of parallel computing, and the first to receive the work in its generator-first form. Verification and benchmark scripts, with fixed seeds and complete raw outputs, were published alongside the manuscript at detsignper.org and archived on Zenodo.

Complete rework: meryemPer presented as, to our knowledge, the first inherently data-parallel lexicographic permutation generator; streaming execution under a provable block-size overflow law; exact big-integer reduction; honest LU and Bareiss baselines. Zenodo record (DOI 10.5281/zenodo.21709734).

On a single NVIDIA B300, the fused streaming kernel summed all 20,922,789,888,000 Leibniz terms of a 16×16 matrix exactly in 361 s at a flat 57.9 billion lines/s — every value certified against the independent exact Bareiss computation. Measured horizons: n=17 in 1.7 h, n=18 in 30.7 h, n=19 in 584 h.

The streaming pipeline (rank-locality windows + block-size law + exact reduction) computed the exact 14×14 determinant — 87.2 billion terms — on a free Tesla T4 inside 194 MB of working memory, where materialization would need 1.2 TB: a ~6,300× reduction.

Science China Information Sciences returned the manuscript without review after a five-day prescreen — stating explicitly no implication on scientific quality or merit. The quick turnaround freed the work for a parallel-computing venue, where its strongest contribution belongs.

Version 3 submitted as a Research Paper (manuscript SCIS-2026-2299) — the paper's strongest form, led by the parallel-structure contribution, meeting its natural readership.

After 96 days without editorial movement, the authors formally withdrew manuscript DA19757 (final disposition: Withdrawn, by author request) to submit the substantially stronger Version 3 to a venue matching its computer-science identity.

Complete rewrite with three pillars: isolated sign benchmarks, formal parallel-complexity analysis (factorial tree, span $O(n)$ vs the chains' $\Omega(n!)$ critical path), and vectorized implementations with benchmarks. Zenodo record (DOI 10.5281/zenodo.21326563).

Vectorized meryemPer generates all permutations up to 6× faster than the C-implemented itertools chain; all 479,001,600 signs of S₁₂ in 0.19 seconds; exact vectorized 10×10 determinant 15× faster than SJT — the serial n=10 crossover explained and resolved.

Component-isolated benchmarks: ~100× faster than inversion counting, 350–400× faster than merge-based parity, and 15–18× faster than the strongest classical baseline (Narayana stepping with O(1) parity updates). Verified element-by-element through order 10.

Manuscript DA19757 submitted to Discrete Applied Mathematics (Elsevier) as a Note.

New title (“Block Replication and Index Mapping”); strengthened sort-free analysis of meryemPer against naive (suffix sort) and Narayana Pandita (suffix reversal) generators. Zenodo v2.

The Monthly's board judged the work algorithmic rather than pure-mathematical — out of scope for their venue. The feedback redirected berkeDet to algorithms journals, where it belongs.

ORCID profile created (0009-0002-8017-5400); work shared with the community.

Submitted to The American Mathematical Monthly (submission ID 265600446).

detsignper.org launched; video presentation published on YouTube; preprint v1 archived on Zenodo (DOI 10.5281/zenodo.19115506), establishing priority.

The dual iterative algorithm — meryemSign and meryemPer — completed, with the first manuscript and the visual presentation of the meryemPer patterns (orders 2 through 9). The idea itself traces back more than twenty years, to a young student who saw the pattern before knowing its name.