Mathematical papers by lmtlssss🜐.
Definition, theorem, paper and exact verifier
8 November 2026 · Version 1.0.0 · DOI: 10.5281/zenodo.24054438
An observation-relative state quotient preserves finite traces. Retained affine costs compose with their complete cross-terms. The paper proposes ᑕ. as a term for the exact contraction contract.
Exact nonnegative rank of a twelve-state composition tensor
26 October 2026 · Version 1.0.0
The nonnegative rank of a specified twelve-element monoid's composition tensor is 35. The paper gives the decomposition, matching lower bounds, and an exact verifier.
A three-bit boundary for cyclic Boolean–modular inversion
27 October 2026 · Version 1.0.0
Three initial bits determine every preimage of a cyclic Boolean–modular map. The complete inverse uses at most eight boundary assignments and 8w local bit updates. An explicit periodic family proves the eight-preimage bound sharp.
Twenty Signed Products for a Twelve-State Composition Tensor
27 October 2026 · Version 1.0.0
An explicit twenty-term signed construction for the twelve-state tensor. The real rank lies between 18 and 20. The exact nonnegative tensor-power rank is 35^q, and the signed construction uses at most 20^q products. DOI: 10.5281/zenodo.23695066.
Exact Counting for a Boolean–Modular Equation with Bounded Tap Span
27 October 2026 · Version 1.0.0 · DOI: 10.5281/zenodo.23697063
A fixed tap span gives a finite nonlinear frontier for exact count-and-witness solving. The manuscript proves the state bound and cyclic closure, with a 256-bit example containing 5,784,112,988,160 solutions.
Affine Fibers and a Fibonacci Bound for Boolean–Modular Inversion
27 October 2026 · Version 1.0.0 · DOI: 10.5281/zenodo.23697726
For any invertible binary-linear map, the complete Boolean–modular inverse is a disjoint union of affine cells. Two carry automata give a Fibonacci signature bound and exact one-cell families.
Exact State Complexity of Two-Stage Addition
27 October 2026 · Version 1.0.0 · DOI: 10.5281/zenodo.23698617
Three fixed radix-B operands define exactly 5B-4 complete two-carry response functions. Explicit normal forms attain the optimal fixed-length code, with a 35-bit code for 32-bit words and a distinct 42-bit independently queryable byte-stage contract.
Exact Counts of Sum-and-Carry Functions for Cascaded Addition
27 October 2026 · Version 1.0.0 · DOI: 10.5281/zenodo.23700193
An exact all-stage, arbitrary-radix count and constructive minimum-length function code. Three 32-bit additions retain every incoming-carry response in exactly 36 bits.
Two Sparse Binary Operators with Optimal Generating Length
27 October 2026 · Version 1.0.0 · DOI: 10.5281/zenodo.23701587
Two sparse binary operators span the full 32-by-32 matrix algebra with products of length at most ten. Ten is the minimum possible bound. A polynomial rank-one identity gives a second constructive proof.
Ordered Carry Frontiers for Parallel Addition
27 October 2026 · Version 1.0.0 · DOI: 10.5281/zenodo.23702847
Shared-input sums have a sharp ordered carry frontier of at most m+1 states. Exact residual minimality and a linear-layer construction give an exact counter and least witness for arbitrary input and output bit masks.
Paper and exact source · DOI · Release
A cyclotomic divisibility criterion decides equality in an integer-occupancy spectral bound. At prime periods, algebraic norms yield a quantitative positive gap for nonflat spectra. The bound is attained at exactly five occupancies in a complete 210-state example. Minimal linear state and retained-potential identities supply the representation framework.
Paper and exact source · DOI · Release
A complete exact selection law for a translating common lattice reduces finite robust designs to residue cells and affine envelopes. It gives rational selection probabilities, expected optima and boundary decisions. A four-design example separates the continuous winner from the phase-selection probabilities. A second theorem proves persistent reversal under arbitrarily fine lattice refinement.
Paper and exact source · DOI · Release
Exact coefficient inequalities classify the stable conjugate-root recurrences with minimal uniform peak horizon two or three. A symmetric observation hexagon supplies necessity and sufficiency. An explicit rational boundary example has shortest uniform horizon three. Sharp observation constants, rational adaptive certificates and exact Stein sums accompany the new coefficient-region result.
Paper and exact source · DOI · Release
A transported cyclic cut changes the accumulated affine cost by the prefix-cost row applied to the full-cycle displacement. Exact rank formulas give the minimum linear summaries for all cut defects and all transported cut totals. An affine consistency criterion includes cut-invariant cycles without fixed points. Polynomial derivative coefficients extend the minimum-state result.
Each file is the full 3840 × 2705 native PNG, also archived on Zenodo.
- Cyclic-Shift Energies: Minimal State and Cyclotomic Gaps — full 4K PNG · Zenodo
- Robust Amplitude Elimination and Exact Lattice-Phase Selection — full 4K PNG · Zenodo
- Sharp Observation Bounds and Minimal Peak Horizons for Damped Recurrences — full 4K PNG · Zenodo
- Affine Cycles: Exact Cut Defects and Minimal Retained State — full 4K PNG · Zenodo
