mirror of
https://github.com/allaunthefox/Research-Stack.git
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451 lines
19 KiB
Python
451 lines
19 KiB
Python
#!/usr/bin/env python3
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"""
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Ingest Erdős Problems from External Sources
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=========================================
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Pull in Erdős problems from external sources and ingest into local research database.
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"""
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import json
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from pathlib import Path
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from datetime import datetime
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RESEARCH_STACK = Path("/home/allaun/Documents/Research Stack")
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RESEARCH_DIR = RESEARCH_STACK / "shared-data/data/germane/research"
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# Erdős problems from Wikipedia and other sources
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ERDOS_PROBLEMS = {
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"unsolved_conjectures": [
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{
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"name": "Erdős–Gyárfás conjecture",
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"description": "On cycles with lengths equal to a power of two in graphs with minimum degree 3.",
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"domain": "Graph Theory",
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"status": "Unsolved",
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"source": "Wikipedia: List of conjectures by Paul Erdős",
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"url": "https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Gy%C3%A1rf%C3%A1s_conjecture"
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},
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{
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"name": "Erdős–Hajnal conjecture",
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"description": "In a family of graphs defined by an excluded induced subgraph, every graph has either a large clique or a large independent set.",
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"domain": "Graph Theory",
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"status": "Unsolved",
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"source": "Wikipedia: List of conjectures by Paul Erdős",
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"url": "https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Hajnal_conjecture"
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},
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{
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"name": "Erdős–Mollin–Walsh conjecture",
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"description": "On consecutive triples of powerful numbers.",
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"domain": "Number Theory",
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"status": "Unsolved",
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"source": "Wikipedia: List of conjectures by Paul Erdős",
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"url": "https://en.wikipedia.org/wiki/Powerful_number"
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},
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{
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"name": "Erdős–Selfridge conjecture",
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"description": "A covering system with distinct moduli contains at least one even modulus.",
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"domain": "Number Theory",
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"status": "Unsolved",
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"source": "Wikipedia: List of conjectures by Paul Erdős",
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"url": "https://en.wikipedia.org/wiki/Covering_system"
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},
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{
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"name": "Erdős–Straus conjecture",
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"description": "For every integer n ≥ 2, the equation 4/n = 1/x + 1/y + 1/z has a solution in positive integers x, y, z.",
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"domain": "Diophantine Equations",
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"status": "Unsolved",
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"source": "Wikipedia: List of conjectures by Paul Erdős",
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"url": "https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Straus_conjecture"
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},
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{
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"name": "Erdős conjecture on arithmetic progressions",
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"description": "If Σ_{a∈A} 1/a diverges, then A contains arbitrarily long arithmetic progressions.",
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"domain": "Additive Number Theory",
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"status": "Unsolved",
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"source": "Wikipedia: List of conjectures by Paul Erdős",
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"url": "https://en.wikipedia.org/wiki/Erd%C5%91s_conjecture_on_arithmetic_progressions"
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},
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{
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"name": "Erdős–Szekeres conjecture",
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"description": "On the number of points needed to ensure that a point set contains a large convex polygon.",
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"domain": "Discrete Geometry",
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"status": "Unsolved",
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"source": "Wikipedia: List of conjectures by Paul Erdős",
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"url": "https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Szekeres_conjecture"
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},
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{
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"name": "Erdős–Turán conjecture on additive bases",
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"description": "If A is an additive basis of order 2 for the natural numbers, then the sum of reciprocals diverges: Σ_{a∈A} 1/a = ∞.",
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"domain": "Additive Number Theory",
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"status": "Unsolved",
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"source": "Wikipedia: List of conjectures by Paul Erdős",
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"url": "https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Tur%C3%A1n_conjecture_on_additive_bases"
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},
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{
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"name": "Erdős conjecture on quickly growing integer sequences",
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"description": "On integer sequences with rational reciprocal series (Sylvester's sequence).",
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"domain": "Number Theory",
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"status": "Unsolved",
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"source": "Wikipedia: List of conjectures by Paul Erdős",
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"url": "https://en.wikipedia.org/wiki/Sylvester%27s_sequence"
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},
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{
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"name": "Erdős–Oler conjecture on circle packing",
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"description": "On circle packing in an equilateral triangle with a number of circles one less than a triangular number.",
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"domain": "Geometry",
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"status": "Unsolved",
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"source": "Wikipedia: List of conjectures by Paul Erdős",
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"url": "https://en.wikipedia.org/wiki/Circle_packing_in_an_equilateral_triangle"
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},
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{
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"name": "Minimum overlap problem",
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"description": "To estimate the limit of M(n).",
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"domain": "Combinatorics",
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"status": "Unsolved",
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"source": "Wikipedia: List of conjectures by Paul Erdős",
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"url": "https://en.wikipedia.org/wiki/Minimum_overlap_problem"
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},
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{
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"name": "Erdős conjecture on ternary expansion of 2^n",
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"description": "The ternary expansion of 2^n contains at least one digit 2 for every n > 8.",
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"domain": "Number Theory",
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"status": "Unsolved",
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"source": "Wikipedia: List of conjectures by Paul Erdős",
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"url": ""
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},
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{
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"name": "Erdős–Moser equation",
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"description": "The equation 1^k + 2^k + ... + (m-1)^k = m^k has no solutions except 1^1 + 2^1 = 3^1.",
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"domain": "Diophantine Equations",
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"status": "Unsolved",
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"source": "Wikipedia: List of conjectures by Paul Erdős",
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"url": "https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Moser_equation"
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}
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],
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"solved_conjectures": [
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{
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"name": "Erdős–Faber–Lovász conjecture",
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"description": "On coloring unions of cliques.",
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"domain": "Graph Theory",
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"status": "Solved (2021)",
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"solved_by": "Dong Yeap Kang, Tom Kelly, Daniela Kühn, Abhishek Methuku, and Deryk Osthus",
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"source": "Wikipedia: List of conjectures by Paul Erdős",
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"url": "https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Faber%E2%80%93Lov%C3%A1sz_conjecture"
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},
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{
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"name": "Erdős sumset conjecture",
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"description": "On sets.",
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"domain": "Additive Combinatorics",
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"status": "Solved (2018)",
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"solved_by": "Joel Moreira, Florian Karl Richter, Donald Robertson",
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"source": "Wikipedia: List of conjectures by Paul Erdős",
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"url": "https://en.wikipedia.org/wiki/Erd%C5%91s_sumset_conjecture"
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},
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{
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"name": "Burr–Erdős conjecture",
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"description": "On Ramsey numbers of graphs.",
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"domain": "Ramsey Theory",
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"status": "Solved (2015)",
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"solved_by": "Choongbum Lee",
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"source": "Wikipedia: List of conjectures by Paul Erdős",
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"url": "https://en.wikipedia.org/wiki/Burr%E2%80%93Erd%C5%91s_conjecture"
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},
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{
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"name": "Erdős conjecture on equitable colorings",
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"description": "Now known as the Hajnal–Szemerédi theorem.",
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"domain": "Graph Theory",
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"status": "Solved (1970)",
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"solved_by": "András Hajnal and Endre Szemerédi",
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"source": "Wikipedia: List of conjectures by Paul Erdős",
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"url": ""
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},
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{
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"name": "Erdős–Lovász conjecture on weak/strong delta-systems",
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"description": "On delta-systems.",
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"domain": "Combinatorics",
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"status": "Solved (1974)",
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"solved_by": "Michel Deza",
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"source": "Wikipedia: List of conjectures by Paul Erdős",
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"url": ""
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},
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{
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"name": "Erdős–Heilbronn conjecture",
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"description": "In combinatorial number theory on the number of sums of two sets of residues modulo a prime.",
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"domain": "Number Theory",
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"status": "Solved (1994)",
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"solved_by": "Dias da Silva and Hamidoune",
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"source": "Wikipedia: List of conjectures by Paul Erdős",
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"url": ""
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},
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{
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"name": "Erdős–Graham conjecture",
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"description": "In combinatorial number theory on monochromatic Egyptian fraction representations of unity.",
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"domain": "Number Theory",
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"status": "Solved (2000)",
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"solved_by": "Ernie Croot",
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"source": "Wikipedia: List of conjectures by Paul Erdős",
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"url": ""
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},
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{
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"name": "Erdős–Stewart conjecture",
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"description": "On the Diophantine equation n! + 1 = p^k_a p_{k+1}^b.",
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"domain": "Number Theory",
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"status": "Solved (2001)",
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"solved_by": "Florian Luca",
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"source": "Wikipedia: List of conjectures by Paul Erdős",
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"url": ""
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},
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{
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"name": "Cameron–Erdős conjecture",
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"description": "On sum-free sets of integers.",
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"domain": "Number Theory",
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"status": "Solved (2003-2004)",
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"solved_by": "Ben Green and Alexander Sapozhenko",
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"source": "Wikipedia: List of conjectures by Paul Erdős",
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"url": ""
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},
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{
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"name": "Erdős–Menger conjecture",
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"description": "On disjoint paths in infinite graphs.",
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"domain": "Graph Theory",
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"status": "Solved (2009)",
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"solved_by": "Ron Aharoni and Eli Berger",
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"source": "Wikipedia: List of conjectures by Paul Erdős",
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"url": ""
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},
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{
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"name": "Erdős distinct distances problem",
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"description": "The correct exponent was proved in 2010 by Larry Guth and Nets Katz, but the correct power of log n is still undetermined.",
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"domain": "Discrete Geometry",
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"status": "Partially Solved (2010)",
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"solved_by": "Larry Guth and Nets Katz",
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"source": "Wikipedia: List of conjectures by Paul Erdős",
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"url": "https://en.wikipedia.org/wiki/Erd%C5%91s_distinct_distances_problem"
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},
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{
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"name": "Erdős–Rankin conjecture on prime gaps",
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"description": "On prime gaps.",
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"domain": "Number Theory",
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"status": "Solved (2014)",
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"solved_by": "Ford, Green, Konyagin, and Tao",
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"source": "Wikipedia: List of conjectures by Paul Erdős",
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"url": ""
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},
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{
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"name": "Erdős discrepancy problem",
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"description": "On partial sums of ±1-sequences.",
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"domain": "Number Theory",
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"status": "Solved (2015)",
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"solved_by": "Terence Tao",
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"source": "Wikipedia: List of conjectures by Paul Erdős",
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"url": ""
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},
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{
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"name": "Erdős squarefree conjecture",
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"description": "Central binomial coefficients C(2n, n) are never squarefree for n > 4.",
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"domain": "Number Theory",
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"status": "Solved (1996)",
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"solved_by": "Various",
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"source": "Wikipedia: List of conjectures by Paul Erdős",
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"url": ""
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},
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{
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"name": "Erdős primitive set conjecture",
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"description": "The sum Σ_{n∈A} 1/(n log n) for any primitive set A attains its maximum at the set of prime numbers.",
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"domain": "Number Theory",
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"status": "Solved (2022)",
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"solved_by": "Jared Duker Lichtman",
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"source": "Wikipedia: List of conjectures by Paul Erdős",
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"url": ""
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},
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{
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"name": "Erdős–Sauer problem",
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"description": "About maximum number of edges an n-vertex graph can have without containing a k-regular subgraph.",
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"domain": "Graph Theory",
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"status": "Solved",
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"solved_by": "Oliver Janzer and Benny Sudakov",
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"source": "Wikipedia: List of conjectures by Paul Erdős",
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"url": ""
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},
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{
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"name": "Erdős problem 728",
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"description": "Solved in 2026 using AI assistance.",
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"domain": "Unknown",
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"status": "Solved (2026)",
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"solved_by": "Kevin Barreto and Liam Price with ChatGPT 5.2 and Aristotle Lean API",
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"source": "Wikipedia: List of conjectures by Paul Erdős",
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"url": ""
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},
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{
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"name": "Erdős problem 347",
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"description": "On subset sums of sequences with ratio limit 2.",
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"domain": "Combinatorics",
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"status": "Solved (2026)",
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"solved_by": "Enrique Barschkis",
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"source": "Wikipedia: List of conjectures by Paul Erdős",
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"url": ""
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},
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{
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"name": "Erdős problem 369",
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"description": "Solved in March 2026 by 17-year-old Sky Yang (Yueer Yang).",
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"domain": "Unknown",
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"status": "Solved (2026)",
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"solved_by": "Sky Yang (Yueer Yang)",
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"source": "Wikipedia: List of conjectures by Paul Erdős",
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"url": ""
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}
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],
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"additional_problems": [
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{
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"name": "Erdős–Ko–Rado theorem",
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"description": "Maximum size of intersecting families of k-subsets of {1,...,n} is C(n-1, k-1) for n ≥ 2k.",
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"domain": "Extremal Set Theory",
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"status": "Solved",
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"source": "Standard theorem",
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"url": ""
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},
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{
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"name": "Erdős–Ginzburg–Ziv theorem",
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"description": "Any 2n-1 integers contain n whose sum is divisible by n.",
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"domain": "Additive Number Theory",
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"status": "Solved",
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"source": "Standard theorem",
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"url": ""
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},
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{
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"name": "Erdős–Stone theorem",
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"description": "For any graph H, ex(n,H) = (1 - 1/χ(H)-1 + o(1))n²/2 where χ(H) is chromatic number.",
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"domain": "Extremal Graph Theory",
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"status": "Solved",
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"source": "Standard theorem",
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"url": ""
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},
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{
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"name": "Erdős–Rényi random graph model",
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"description": "Study properties of G(n,p) random graphs. Threshold phenomena for connectivity, giant component, Hamiltonicity.",
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"domain": "Random Graphs",
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"status": "Standard model",
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"source": "Standard model",
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"url": ""
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},
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{
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"name": "Erdős Hadamard conjecture",
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"description": "There exist Hadamard matrices of order 4k for all k.",
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"domain": "Linear Algebra",
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"status": "Unsolved",
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"source": "Standard conjecture",
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"url": ""
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},
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{
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"name": "Erdős–Moser problem",
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"description": "Find all solutions to 1/a + 1/b + 1/c + 1/d + 1/e = 1 in distinct positive integers.",
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"domain": "Diophantine Equations",
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"status": "Solved (only known solution)",
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"source": "Standard problem",
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"url": ""
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}
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]
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}
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def create_erdos_problems_document():
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"""Create a comprehensive Erdős problems document."""
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timestamp = datetime.now().isoformat()
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document = {
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"document_id": "erdos_problems_comprehensive_v1",
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"title": "Comprehensive Erdős Problems Collection",
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"created": timestamp,
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"source": "Wikipedia and other sources",
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"unsolved_conjectures": ERDOS_PROBLEMS["unsolved_conjectures"],
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"solved_conjectures": ERDOS_PROBLEMS["solved_conjectures"],
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"additional_problems": ERDOS_PROBLEMS["additional_problems"],
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"statistics": {
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"total_unsolved": len(ERDOS_PROBLEMS["unsolved_conjectures"]),
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"total_solved": len(ERDOS_PROBLEMS["solved_conjectures"]),
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"total_additional": len(ERDOS_PROBLEMS["additional_problems"]),
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"total_problems": len(ERDOS_PROBLEMS["unsolved_conjectures"]) + len(ERDOS_PROBLEMS["solved_conjectures"]) + len(ERDOS_PROBLEMS["additional_problems"])
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},
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"domains": {
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"Graph Theory": 0,
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"Number Theory": 0,
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"Discrete Geometry": 0,
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"Additive Number Theory": 0,
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"Diophantine Equations": 0,
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"Combinatorics": 0,
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"Extremal Set Theory": 0,
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"Ramsey Theory": 0,
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"Random Graphs": 0,
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"Linear Algebra": 0,
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"Additive Combinatorics": 0,
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"Geometry": 0,
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"Unknown": 0
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}
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}
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# Count domains
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all_problems = ERDOS_PROBLEMS["unsolved_conjectures"] + ERDOS_PROBLEMS["solved_conjectures"] + ERDOS_PROBLEMS["additional_problems"]
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for problem in all_problems:
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domain = problem["domain"]
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if domain in document["domains"]:
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document["domains"][domain] += 1
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return document
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def main():
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print("=" * 70)
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print(" INGESTING ERDŐS PROBLEMS INTO LOCAL RESEARCH DATABASE")
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print("=" * 70)
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# Create document
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document = create_erdos_problems_document()
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print(f"\nStatistics:")
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print(f" Total unsolved: {document['statistics']['total_unsolved']}")
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print(f" Total solved: {document['statistics']['total_solved']}")
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print(f" Total additional: {document['statistics']['total_additional']}")
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print(f" Total problems: {document['statistics']['total_problems']}")
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print(f"\nDomain distribution:")
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for domain, count in document["domains"].items():
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if count > 0:
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print(f" {domain}: {count}")
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# Save to research directory
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output_file = RESEARCH_DIR / "erdos_problems_comprehensive_v1.json"
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with open(output_file, 'w') as f:
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json.dump(document, f, indent=2)
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print(f"\n✓ Erdős problems saved to: {output_file}")
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# Update research ingestion index
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index_file = RESEARCH_DIR / "research_ingestion_index.json"
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if index_file.exists():
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with open(index_file, 'r') as f:
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index = json.load(f)
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else:
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index = []
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# Add new entry
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new_entry = {
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"id": "erdos-problems-comprehensive-v1",
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"title": "Comprehensive Erdős Problems Collection",
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"date": datetime.now().isoformat(),
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"source": "Wikipedia and other sources",
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"ingested_at": datetime.now().timestamp(),
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"tags": ["erdos", "conjectures", "problems", "graph-theory", "number-theory", "combinatorics"]
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}
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index.append(new_entry)
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with open(index_file, 'w') as f:
|
||
json.dump(index, f, indent=2)
|
||
|
||
print(f"✓ Research ingestion index updated")
|
||
|
||
return document
|
||
|
||
|
||
if __name__ == "__main__":
|
||
main()
|