From f734d9082b212504b5c412378e698def098594dc Mon Sep 17 00:00:00 2001 From: Brandon Schneider Date: Thu, 7 May 2026 04:34:19 -0500 Subject: [PATCH] =?UTF-8?q?ingest:=20comprehensive=20Erd=C5=91s=20problems?= =?UTF-8?q?=20collection=20from=20external=20sources?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Ingested 38 Erdős problems from Wikipedia and other sources into local research database. Statistics: - Total unsolved: 13 - Total solved: 19 - Total additional: 6 - Total problems: 38 Domain distribution: - Graph Theory: 6 - Number Theory: 12 - Discrete Geometry: 2 - Additive Number Theory: 3 - Diophantine Equations: 3 - Combinatorics: 3 - Extremal Set Theory: 1 - Ramsey Theory: 1 - Random Graphs: 1 - Linear Algebra: 1 - Additive Combinatorics: 1 - Geometry: 1 - Unknown: 2 Unsolved conjectures include: - Erdős–Gyárfás conjecture - Erdős–Hajnal conjecture - Erdős–Mollin–Walsh conjecture - Erdős–Selfridge conjecture - Erdős–Straus conjecture - Erdős conjecture on arithmetic progressions - Erdős–Szekeres conjecture - Erdős–Turán conjecture on additive bases - Erdős conjecture on quickly growing integer sequences - Erdős–Oler conjecture on circle packing - Minimum overlap problem - Erdős conjecture on ternary expansion of 2^n - Erdős–Moser equation Solved conjectures include: - Erdős–Faber–Lovász conjecture (2021) - Erdős sumset conjecture (2018) - Burr–Erdős conjecture (2015) - Erdős conjecture on equitable colorings (1970) - Erdős–Lovász conjecture (1974) - Erdős–Heilbronn conjecture (1994) - Erdős–Graham conjecture (2000) - Erdős–Stewart conjecture (2001) - Cameron–Erdős conjecture (2003-2004) - Erdős–Menger conjecture (2009) - Erdős distinct distances problem (2010, partially) - Erdős–Rankin conjecture (2014) - Erdős discrepancy problem (2015) - Erdős squarefree conjecture (1996) - Erdős primitive set conjecture (2022) - Erdős–Sauer problem - Erdős problem 728 (2026, AI-assisted) - Erdős problem 347 (2026) - Erdős problem 369 (2026) Additional problems include: - Erdős–Ko–Rado theorem - Erdős–Ginzburg–Ziv theorem - Erdős–Stone theorem - Erdős–Rényi random graph model - Erdős Hadamard conjecture - Erdős–Moser problem Saved to: shared-data/data/germane/research/erdos_problems_comprehensive_v1.json Updated research ingestion index. --- .../shim/ingest_erdos_problems.py | 451 ++++++++++++++++++ 1 file changed, 451 insertions(+) create mode 100644 4-Infrastructure/shim/ingest_erdos_problems.py diff --git a/4-Infrastructure/shim/ingest_erdos_problems.py b/4-Infrastructure/shim/ingest_erdos_problems.py new file mode 100644 index 00000000..9867a23f --- /dev/null +++ b/4-Infrastructure/shim/ingest_erdos_problems.py @@ -0,0 +1,451 @@ +#!/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()