Open Research Index

871 records

  1. A Cauchy-Schwarz inequality for real powers: proof, equality cases and weighted forms

    Pragyaan Gaur

    Palomar RegistryOct 27, 2026math.FAmachine-checkedscore 0

  2. Kurz's conjecture on the maximum area of the convex hull of a polyhex

    Pragyaan Gaur

    Palomar RegistryOct 27, 2026math.COmachine-checkedscore 0

  3. The critical Almost Stacked Hypothesis fails on a nine-vertex graph

    John Fairfax-Ball

    Palomar RegistryOct 27, 2026math.COmachine-checkedscore 0

  4. The Number of Polytope Trees and Beyond — Lean 4 formalization

    Ali Aliev

    Palomar RegistryOct 27, 2026math.COmachine-checkedscore 0

  5. The Art Gallery Problem is ∃ℝ-complete: point-point, boundary-point and point-boundary variants, in Lean 4

    Robert D. Barish

    Palomar RegistryOct 27, 2026cs.CGmachine-checkedscore 0

  6. birthday-paradox-non-backtracking-regular-graphs

    Benjamin Dozier

    Palomar RegistryOct 27, 2026math.COmachine-checkedscore 0

  7. Weak and strong βη-normalization in pure type systems with βη-conversion

    Ankit Pradhan, Cole Vick, Ruijie Fang, Carl Kwan

    Palomar RegistryOct 27, 2026cs.LOmachine-checkedscore 0

  8. Perron's extremal solutions of the Bernoulli one-phase problem: viscosity, inner variational and one-sided minimizing solutions, and free boundary structure in the plane

    William M. Feldman

    Palomar RegistryOct 27, 2026math.APmachine-checkedscore 0

  9. Strictly Convex Steklov-Isospectral Plane Domains

    taohu-hub, RGConj, QuanyuTang

    Palomar RegistryOct 27, 2026math.SPmachine-checkedscore 0

  10. Finite uniform Bernoulli shifts with unequal base entropy

    Peter Burton

    Palomar RegistryOct 27, 2026math.DSmachine-checkedscore 0

  11. Regular subgraphs of almost regular graphs (Alon–Friedland–Kalai)

    Juan Pablo Traverso Gianini

    Palomar RegistryOct 26, 2026math.COmachine-checkedscore 0

  12. First Betti numbers of five-generated numerical semigroups

    Ben Keene

    Palomar RegistryOct 23, 2026math.ACmachine-checkedscore 0

  13. Brouwer characterization of Cantor space

    Arthur Freitas Ramos, David Barros Hulak, Ruy Jose Guerra Barretto de Queiroz

    Palomar RegistryOct 23, 2026math.GNmachine-checkedscore 0

  14. Nivat's conjecture: formalization of Pranava Kumar's argument

    Pranava Kumar

    Palomar RegistryOct 23, 2026math.DSmachine-checkedscore 0

  15. Sierpiński's characterization of the rationals

    Arthur Freitas Ramos, David Barros Hulak, Ruy Jose Guerra Barretto de Queiroz

    Palomar RegistryOct 23, 2026math.GNmachine-checkedscore 0

  16. Multiplicative bases and standardness of representation-finite algebras

    Haruhisa Enomoto

    Palomar RegistryOct 23, 2026math.RTmachine-checkedscore 0

  17. Stability of planar fronts in reaction-diffusion systems

    Joris van Winden

    Palomar RegistryOct 23, 2026math.APmachine-checkedscore 0

  18. The Graham–Pollak theorem

    Juan Pablo Traverso Gianini

    Palomar RegistryOct 23, 2026math.COmachine-checkedscore 0

  19. Fifth dimension subgroups: D₅ = γ₅ when G/γ₂ is finite of exponent 3, candidates for a counterexample, and a reduction of Kourovka 20.84

    Stanislav Vorobev

    Palomar RegistryOct 23, 2026math.GRmachine-checkedscore 0

  20. Control flow obfuscation with irreducible loops and self-modifying code

    Gregory Morse

    Palomar RegistryOct 23, 2026cs.CRmachine-checkedscore 0

  21. Temporal cliques admit spanners of size O(n log n)

    Ethan Bargaud-Arm

    Palomar RegistryOct 23, 2026cs.DMmachine-checkedscore 0

  22. Log-square quadrupolar correlation decay in two-dimensional RP2 and RP3 models

    Masaki Oshikawa

    Palomar RegistryOct 23, 2026math-phmachine-checkedscore 0

  23. Almost all graphs are determined by their generalized spectrum

    Ziqing Xiang

    Palomar RegistryOct 23, 2026math.COmachine-checkedscore 0

  24. The Euclidean algorithm is not optimal among uniform processes

    Jason Davies

    Palomar RegistryOct 23, 2026math.LOmachine-checkedscore 0

  25. Robust absorption for typed triangles

    Juan Pablo Traverso Gianini

    Palomar RegistryOct 23, 2026math.COmachine-checkedscore 0

  26. Erdős Problem 1063: a lower bound for n_k and the structure of the exceptional index

    Paul Lee

    Palomar RegistryOct 23, 2026math.NTmachine-checkedscore 0

  27. An FPT Algorithm for Maximum-Weight Independent Set in Embedded Graphs, in Lean 4

    Robert D. Barish

    Palomar RegistryOct 23, 2026cs.DSmachine-checkedscore 0

  28. Mader's theorem on highly connected subgraphs

    Juan Pablo Traverso Gianini

    Palomar RegistryOct 23, 2026math.COmachine-checkedscore 0

  29. Spanning-Tree Maximization Forces Isoperimetry in the Square Lattice

    Jiechen Zhang

    Palomar RegistryOct 23, 2026math.COmachine-checkedscore 0

  30. Lavrentieff's Gδ homeomorphism extension theorem

    Arthur Freitas Ramos, David Barros Hulak, Ruy Jose Guerra Barretto de Queiroz

    Palomar RegistryOct 23, 2026math.GNmachine-checkedscore 0

  31. The strong Choquet characterization of Polish spaces

    Arthur Freitas Ramos, David Barros Hulak, Ruy Jose Guerra Barretto de Queiroz

    Palomar RegistryOct 22, 2026math.GNmachine-checkedscore 0

  32. Romanov's theorem: the integers of the form p + 2^k have positive lower density, with Erdős' complement, after Romanov 1934 and Erdős 1950

    Steve Hubbard

    Palomar RegistryOct 22, 2026math.NTmachine-checkedscore 0

  33. Brun's theorem: the sum of the reciprocals of the twin primes converges, after Brun 1919, with the twin prime upper bound and every even gap

    Steve Hubbard

    Palomar RegistryOct 22, 2026math.NTmachine-checkedscore 0

  34. The 50-color theorem for t-perfect graphs

    Sang-il Oum

    Palomar RegistryOct 22, 2026math.COmachine-checkedscore 0

  35. Schnirelmann's theorem: every integer n >= 2 is a sum of at most 30772 primes, after Schnirelmann 1933

    Steve Hubbard

    Palomar RegistryOct 22, 2026math.NTmachine-checkedscore 0

  36. An XP Algorithm for Maximum-Weight Independent Set in Embedded Graphs, in Lean 4

    Robert D. Barish

    Palomar RegistryOct 22, 2026cs.DSmachine-checkedscore 0

  37. Ramanujan congruences for the partition function

    Carter Hastings

    Palomar RegistryOct 22, 2026math.NTmachine-checkedscore 0

  38. Classical Liénard equations of degree n ≥ 6 can have floor((n−1)/2)+4 limit cycles

    Michael Mislan

    Palomar RegistryOct 22, 2026math.DSmachine-checkedscore 0

  39. A formal proof that crown graphs maximise the representation number of bipartite graphs

    Matthew J. Colbrook, Catherine Drysdale

    Palomar RegistryOct 22, 2026math.COmachine-checkedscore 0

  40. A universal group with thirteen relators

    Qiuyu Ren

    Palomar RegistryOct 22, 2026math.GRmachine-checkedscore 0

  41. Critical recovery, query lower bounds and binary-native width

    Idris Ali Shaik

    Palomar RegistryOct 22, 2026cs.CCmachine-checkedscore 0

  42. The fourth consecutive Dirichlet eigenvalue ratio

    Jiachen Shi, Quanyu Tang

    Palomar RegistryOct 22, 2026math.SPmachine-checkedscore 0

  43. Fixed-force anomalous dissipation

    Tao Tao, Baishu Zeng, Haiqi Zhang

    Palomar RegistryOct 22, 2026math.APmachine-checkedscore 0

  44. Hamiltonian paths in rectangular grid graphs (Itai, Papadimitriou and Szwarcfiter)

    Z. Zzyzek (github: zzyzek)

    Palomar RegistryOct 22, 2026cs.DMmachine-checkedscore 0

  45. Dimension growth, polynomial in the degree (Castryck–Cluckers–Dittmann–Nguyen)

    Jason Davies

    Palomar RegistryOct 22, 2026math.NTmachine-checkedscore 0

  46. The Erdős–Szemerédi sunflower conjecture

    Matija Bucić, Fankang He, Hyunwoo Lee

    Palomar RegistryOct 22, 2026math.COmachine-checkedscore 0

  47. Counting Steiner triple systems: Wilson (1974) and Linial–Luria (2013)

    Juan Pablo Traverso Gianini

    Palomar RegistryOct 22, 2026math.COmachine-checkedscore 0

  48. Analysis of a left-shift binary GCD algorithm (Shallit–Sorenson 1994), with a proof of its sum-of-squares conjecture

    Jason Davies

    Palomar RegistryOct 22, 2026math.NTmachine-checkedscore 0

  49. Continuity of the phase transition for planar random-cluster and Potts models with 1 <= q <= 4 (Theorems 1, 2 and 3)

    Zijie Zhuang

    Palomar RegistryOct 22, 2026math.PRmachine-checkedscore 0

  50. Shelah's bound for the Hales–Jewett numbers

    Gabriel Dahia

    Palomar RegistryOct 22, 2026math.COmachine-checkedscore 0

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