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