Michael M. Ross | 2026 Publications
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Cost Viability and Cointegration Are Anti-Correlated in Liquid US ETF Pairs
A ground-truth-validated negative result for daily-frequency statistical arbitrage.
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Triangular FX Residuals on a Retail Feed Are Real, Measurable, and a Fourteenth of Their Cost
A preregistered census, a rejected thin-cross hypothesis, and three unforced choices.
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A Tool for Certifying Exponent Thresholds as Exact Linear-Programming Facets
Turns a published threshold into an executable object and certifies it as the exact facet of a declared linear system.
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Audited Censuses of Two Generalized Fermat Families: Coverage Ledgers and Large Datasets
Exhaustive, machine-auditable censuses of two generalized Fermat families — exactly the seven known coprime solutions to 1016, and none among 193,776 solutions to 1030 — with descent-based closure audits and two disclosed defects.
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Coprimality Density and the Proper-Solution Deficit in the Generalized Fermat Family {2, 3, m}
A closed-form, per-anchor coprimality density and an unconditional 2-descent census of 670 Mordell classes, proving part of the proper-solution deficit dead and locating the remainder on positive-rank curves.
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The Hall Near-Miss Census to 1011: Exact Families, a Depleted Residual Population, and a Preregistered Scaling Test
Ninety billion cubes and their nearest squares resolved into exact parametrized families and a residual population depleted for the second consecutive preregistered decade — real depletion, arriving shallower than the registered law.
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Multiplication Geometry in Square Shells: Finite Coverage, Truncated Legendre Sums, and the Parity Barrier
The multiplication table inside a square shell almost determines its primes: finite overlap geometry gives sharp deterministic coverage, while an exact product cutoff explains much of the apparent parity obstruction.
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The Multiplication Table Near Perfect Squares: Concentration, Typicality, and the Slow Approach to Ford's Exponent
Exact-integer Monte Carlo to N = 21024 and a seam-anchored model of factorizations to N = 21018. The Erdős–Tenenbaum–Ford constant is the true asymptotic exponent, its corrections live on the log log scale, and it is attained at no height that will ever be computed.
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The Jacobian Conjecture Counterexample: Cubic Corollary and Uniqueness of j=1
Two notes on the Jacobian conjecture counterexample of Levent Alpöge (with Claude Fable 5), analyzed through the construction described in Terence Tao's digestion of the counterexample.
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The Semiprimorial Triad: First Prime Offsets, First Semiprime Offsets, and Semiprimes at +1
Semiprimorials exhibit a striking triad of additive phenomena: the first prime shift and first semiprime shift appear always to be prime, while the fixed shift Q_n+1 appears semiprime infinitely often.
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One-Step Fermat Factorization and Goldbach Representations with Almost-Equal Summands in Square-Centered Intervals
Inside the square-centered interval, instant Fermat factorization and near-equal Goldbach representation are the same event — provable on average, open pointwise at window exponent ½, and last absent through 10⁸ at n = 1,884,296.
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Exceptional Sets for Semiprimes in Quadratic Intervals
This note proves three exceptional-set theorems for semiprimes in the intervals (n², (n+1)²) by applying the computational investigation of the companion papers to the analytic findings of Matomäki–Teräväinen and Gafni–Tao.
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Exact Semiprimes in Short Intervals: Prime Supply, Factor-Pair Multiplicity, and the Parity Barrier
A 10¹¹-term computation showing semiprimes are far denser and more evenly spaced than the √x scale would require, reframing "a semiprime between every pair of squares" as a parity problem rather than a Legendre one.
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Semiprimes 2p and 3p in Quadratic Intervals: A Legendre-Class Persistence Problem
Computational and structural verification that every Jn(k) for k ∈ {2, 3} contains a semiprime of the form 2p or 3p; verified through n = 107 with zero failures, framed via a Cramér-gap parsimony argument.
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An Unconditional Golden-Ratio Lower Bound for Coprime Adjacent Divisors of Squarefree Integers
An unconditional proof that the maximum number of coprime adjacent divisor pairs of a squarefree integer with k prime factors grows at least like φ^k/√k, improving the Erdős–Simonovits lower bound (√2 + o(1))^k.
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A Reduction of the Squarefree Coprime Adjacent Divisor Problem and a Conditional Golden-Ratio Lower Bound
A balanced-split identity and Fibonacci layer reduction for Erdős #1100, giving a conditional golden-ratio lower bound g_sf(k) ≥ (φ + o(1))^k that improves the Erdős–Simonovits floor of √2.
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Proximate-Prime Quadratics: Forced Local Obstruction and a Conditioned Null Model
Quadratics through four consecutive primes with gaps in arithmetic progression are prime-rich because four prime values prohibit roots in four residue classes modulo every prime. A conditioned random quadratic reproduces their nonresidue distribution to 1010, and Bateman–Horn gives their density to 1% per curve. However, the construction misses the best curves in every range.
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Stacked Prime-Rich Quadratics and the Covering of Square Intervals
Stacking prime-rich quadratics covers the square intervals up to M with K(M) ≈ 2(log M)2/C̄ curves when the stack’s constants are spread over many band-widths — and the dependence when they aren’t is the pair singular series at the landing offset, predicted pair by pair with no free parameter. No finite stack covers every band.
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An Explicit Semiprime-Tail Bound in Square-Root Intervals and a One-Hypothesis Reduction for Primes in [4n²−n, 4n²+n]
An unconditional bound is proved for the semiprime tail by pushing the linear sieve to the Fouvry–Iwaniec level x^{5/8} against prime moduli exceeding x^{1/2}. Reduces the existence of primes in [4n²−n, 4n²+n] to a single medium-range Buchstab lower bound at any cutoff beyond (2n)^{0.9393}.
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Triprime Contributions and Signed Remainders in Square-Root Intervals
Proves an unconditional one-sided cancellation for rough triprime contributions in square-root intervals, together with explicit remainder reductions and uniform variance bounds. Isolates the sharp signed comparison that remains open in the program to prove H(ϑ), the rough-number hypothesis underlying the companion prime-existence reduction.
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Factor Rays and the Self-Conjugate Parabola: Deterministic Coverage Geometry in Square Intervals
Geometric coverage analysis of factor rays and the parabola n=k2 in the square-interval setting.
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Rough and Smooth Numbers in Square-Centered Intervals: First-Order Structure and Second-Order Genericity
Places Jn at the high-threshold endpoint of the rough-numbers-in-short-interval spectrum, where roughness and primality coincide — yet is invisible to the second-order statistics of the prime count.
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Primes in Square Intervals: A Structural Audit of the Square-Centered Dispersion Route
A structural audit of the square-centered dispersion method shows exactly where the perfect-square geometry survives—and where the analytic route loses traction. The obstruction is not the absence of structure, but the form in which that structure reaches the second-level exponential sum.
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A Modified Legendre Product for Primes in Consecutive Square Intervals
A modified Legendre product for primes in consecutive square intervals: a two-term Mertens-type expansion predicts the mean count ratio out-of-sample to 1.8×10⁻⁵ at n = 10⁹, and an exhaustive census locates the last pointwise violation of the mean-level upper bound at n = 77,433.
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Empirical Diagnostics for the Shadow-Sieve Model in Square-Centered Intervals
A computational study of a shadow-sieve framework for primes in the quadratic intervals Jn = [4n2 - n, 4n2 + n], in which π(Jn) is expressed exactly as the difference between B-rough survivors and composites caught by a bilinear "shadow" map.
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Two-Sided Fortunate Numbers and Goldbach Amplification for Primorial Multiples
Prime complements of primorial multiples up to 7,482 digits arrive as an exponential model predicts—except over a range corresponding roughly to 4,182–6,355-digit primorials, where they arrive about 6% too soon.
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Sifted Symmetry and Sieve Structures of Primorial Goldbach Complements
Shows that primorial Goldbach representations with a summand below pk+12 ≍ (log N)2 correspond exactly to primes in an interval below N, while divisor-sum sieve tests below pk+1 are constant on the complements.
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Loop Structure of Collatz-Type Functions 3x+n: A Conjugacy Theorem and Powers of Three
Shows how prescribed exponent patterns become loops across the 3x+n family, and proves that every 3x+3k orbit eventually reduces to a rescaled 3x+1 orbit.
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Spike Structures and 2-adic Transition Laws in the Accelerated Collatz Map
Builds a 2-adic and modulo-24 model of accelerated Collatz spikes, proving that every finite exponent pattern is locally realizable and that finite residue quotients alone cannot exclude cycles.
Empirical Structure of the Gilbreath Decay Constants
Exact values of c₄–c₆ and a binary digit-sum decay law for the Gilbreath constants of Chase, Hunter & Tao (arXiv:2607.08712), with Monte Carlo evidence that the growth threshold is exponential rather than linear.
BTW Is Gilbreath’s conjecture garden-variety numerology?
Supersedes...