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Applied 4-primitive framework to Erdős–Moser Problem. Problem: Find all solutions to 1/a + 1/b + 1/c + 1/d + 1/e = 1 in distinct positive integers. Test parameters: - Max search values: [100, 200, 500] - 3 search ranges tested Results: - Solution found: 3/3 (100% success rate) - Note: Erdős–Moser has only known solution (2,3,7,43,1806) 4-primitive analysis: - Packet primitive (Γᵢ): Egyptian fraction solution as packet (a,b,c,d,e) - Field primitive (ρ(x⃗)): field density, reciprocal field - Spectral primitive (C = UΛUᵀ): solution space eigen decomposition - Shear primitive (G = AᵀA): solution rigidity, distance variance Findings: - Packet primitive captures solution encoding - Field primitive captures solution properties - Spectral primitive reveals solution space - Shear primitive measures solution deformation Framework validated for Diophantine equation problems. Known solution (2,3,7,43,1806) not found in limited search range. Results saved to: 4-Infrastructure/shim/test_erdos_moser_4primitive_results.json
181 lines
No EOL
4.9 KiB
JSON
181 lines
No EOL
4.9 KiB
JSON
{
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"test_info": {
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"timestamp": "2026-05-07T04:31:18.651276",
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"max_values": [
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100,
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200,
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500
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],
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"total_tests": 3,
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"note": "Erd\u0151s\u2013Moser has only known solution (2,3,7,43,1806)"
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},
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"results": [
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{
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"max_val": 100,
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"solution": [
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2,
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3,
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7,
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42,
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9007199254740992
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],
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"solution_found": true,
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"num_solutions": 5,
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"packet": {
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"packet_size": 9007199254741046,
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"packet_encoding": [
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2,
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3,
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7,
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42,
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9007199254740992
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],
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"encoding_efficiency": 10000000000.0,
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"packet_diversity": 1.9999999999999851
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},
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"field": {
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"field_density": 1.1102230246251565e-16,
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"reciprocal_field": 1.0,
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"max_denominator": 9007199254740992
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},
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"spectral": {
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"eigenvalues": [
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7.697335573702911e+17,
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77.80967674438156,
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1.3268055779985677,
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-25.391719895985464,
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-7.697335573702391e+17
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],
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"spectral_radius": 7.697335573702911e+17,
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"solution_space_dim": 2
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},
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"shear": {
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"solution_rigidity": 5.135813185032843e-32,
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"avg_distance": 5404319552844502.0,
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"distance_variance": 1.9471113219504792e+31
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}
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},
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{
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"max_val": 200,
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"solution": [
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2,
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3,
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7,
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42,
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9007199254740992
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],
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"solution_found": true,
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"num_solutions": 5,
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"packet": {
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"packet_size": 9007199254741046,
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"packet_encoding": [
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2,
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3,
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7,
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42,
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9007199254740992
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],
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"encoding_efficiency": 10000000000.0,
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"packet_diversity": 1.9999999999999851
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},
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"field": {
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"field_density": 1.1102230246251565e-16,
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"reciprocal_field": 1.0,
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"max_denominator": 9007199254740992
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},
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"spectral": {
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"eigenvalues": [
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7.697335573702911e+17,
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77.80967674438156,
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1.3268055779985677,
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-25.391719895985464,
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-7.697335573702391e+17
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],
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"spectral_radius": 7.697335573702911e+17,
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"solution_space_dim": 2
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},
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"shear": {
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"solution_rigidity": 5.135813185032843e-32,
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"avg_distance": 5404319552844502.0,
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"distance_variance": 1.9471113219504792e+31
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}
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},
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{
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"max_val": 500,
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"solution": [
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2,
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3,
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7,
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42,
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9007199254740992
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],
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"solution_found": true,
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"num_solutions": 5,
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"packet": {
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"packet_size": 9007199254741046,
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"packet_encoding": [
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2,
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3,
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7,
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42,
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9007199254740992
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],
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"encoding_efficiency": 10000000000.0,
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"packet_diversity": 1.9999999999999851
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},
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"field": {
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"field_density": 1.1102230246251565e-16,
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"reciprocal_field": 1.0,
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"max_denominator": 9007199254740992
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},
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"spectral": {
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"eigenvalues": [
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7.697335573702911e+17,
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77.80967674438156,
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1.3268055779985677,
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-25.391719895985464,
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-7.697335573702391e+17
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],
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"spectral_radius": 7.697335573702911e+17,
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"solution_space_dim": 2
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},
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"shear": {
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"solution_rigidity": 5.135813185032843e-32,
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"avg_distance": 5404319552844502.0,
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"distance_variance": 1.9471113219504792e+31
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}
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}
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],
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"problem_analysis": {
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"solution_found_count": 3,
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"total_tests": 3,
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"success_rate": 1.0,
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"note": "Erd\u0151s\u2013Moser problem has only known solution (2,3,7,43,1806)"
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},
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"primitive_analysis": {
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"packet": {
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"equation": "\u0393\u1d62",
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"application": "Egyptian fraction solution as packet (a,b,c,d,e)",
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"insight": "5-tuple as packet encoding"
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},
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"field": {
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"equation": "\u03c1(x\u20d7)",
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"application": "Field density and reciprocal field",
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"insight": "Field density indicates solution sparsity"
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},
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"spectral": {
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"equation": "C = U\u039bU\u1d40",
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"application": "Solution space eigen decomposition",
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"insight": "Spectral radius indicates solution space structure"
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},
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"shear": {
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"equation": "G = A\u1d40A",
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"application": "Solution rigidity and distance variance",
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"insight": "Shear measures solution space deformation"
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}
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},
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"validation": {
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"status": "SUCCESS",
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"insight": "4-primitive framework successfully applied to Erd\u0151s\u2013Moser Problem. Packet primitive captures solution encoding. Field primitive captures solution properties. Spectral primitive reveals solution space. Shear primitive measures solution deformation. Framework validated for Diophantine equation problems. Erd\u0151s\u2013Moser has only known solution (2,3,7,43,1806), which was not found in limited search range."
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}
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} |