@@ -68,7 +68,7 @@ const RESET = colors.RESET;
6868// =============================================================================
6969
7070const data = @import ("math/sacred_constants_data.zig" );
71- const sacred_formula = @import ("formula.zig" );
71+ const sacred_formula = @import ("math/ formula.zig" );
7272
7373const PHI = data .PHI ;
7474const PHI_SQ = data .PHI_SQ ;
@@ -454,6 +454,8 @@ fn printMathHelp() void {
454454 std .debug .print ("\n {s}TOOLS:{s}\n " , .{ CYAN , RESET });
455455 std .debug .print (" {s}math-verify{s} Trinity identity checks (38 checks)\n " , .{ GREEN , RESET });
456456 std .debug .print (" {s}math-bench{s} Performance benchmark\n " , .{ GREEN , RESET });
457+ std .debug .print (" {s}math compare{s} [n] Sacred Math Comparison Table (phi^n, F(n), L(n))\n " , .{ GREEN , RESET });
458+ std .debug .print (" {s}math compare{s} --pellis Pellis φ⁵ vs Trinity φ²+φ⁻²=3 comparison\n " , .{ GREEN , RESET });
457459 std .debug .print ("\n {s}DIRECT ALIASES:{s}\n " , .{ CYAN , RESET });
458460 std .debug .print (" tri constants | tri phi 10 | tri fib 19\n " , .{});
459461 std .debug .print (" tri lucas 5 | tri spiral 8 | tri math-verify\n " , .{});
@@ -1163,10 +1165,16 @@ fn printBenchResult(name: []const u8, iters: u32, elapsed_ns: u64) void {
11631165}
11641166
11651167// =============================================================================
1166- // COMMAND: tri math-compare [n]
1168+ // COMMAND: tri math-compare [n] OR tri math-compare --pellis
11671169// =============================================================================
11681170
11691171pub fn runMathCompareCommand (args : []const []const u8 ) void {
1172+ // Check for --pellis flag
1173+ if (args .len > 0 and std .mem .eql (u8 , args [0 ], "--pellis" )) {
1174+ displayPellisComparison ();
1175+ return ;
1176+ }
1177+
11701178 const n = parseU32 (args , 12 );
11711179 const max = @min (n , 92 );
11721180
@@ -1202,6 +1210,92 @@ pub fn runMathCompareCommand(args: []const []const u8) void {
12021210 std .debug .print ("\n " , .{});
12031211}
12041212
1213+ // =============================================================================
1214+ // PELLIS φ⁵ vs TRINITY φ² + φ⁻² = 3 Comparison
1215+ // =============================================================================
1216+
1217+ fn displayPellisComparison () void {
1218+ // Pellis formulas (from viXra:2110.0084v5, viXra:2111.0037)
1219+ const pellis_phi_inv_sq = PHI_INV_SQ ; // φ⁻²
1220+ const pellis_phi_inv_cubed = PHI_INV * PHI_INV * PHI_INV ; // φ⁻³
1221+ const pellis_3phi = 3.0 * PHI ;
1222+ const pellis_3phi_inv_5 = 1.0 / (std .math .pow (f64 , pellis_3phi , 5.0 ));
1223+
1224+ // α⁻¹ Pellis: 360·φ⁻² - 2·φ⁻³ + (3·φ)⁻⁵
1225+ const pellis_alpha_inv = 360.0 * pellis_phi_inv_sq - 2.0 * pellis_phi_inv_cubed + pellis_3phi_inv_5 ;
1226+
1227+ // Trinity formulas
1228+ // α⁻¹ Trinity: π⁴φ⁴e²/36
1229+ const trinity_alpha_inv = (std .math .pow (f64 , PI , 4.0 ) * std .math .pow (f64 , PHI , 4.0 ) * std .math .pow (f64 , E , 2.0 )) / 36.0 ;
1230+
1231+ // μ Trinity: 6π⁵ (proton-electron mass ratio)
1232+ const trinity_mu = 6.0 * std .math .pow (f64 , PI , 5.0 );
1233+
1234+ // Ω_Λ Trinity: 3⁸φ⁻³/(π⁵e²) = 6561·φ⁻³/(π⁵e²)
1235+ const trinity_omega_lambda = 6561.0 * pellis_phi_inv_cubed / (std .math .pow (f64 , PI , 5.0 ) * std .math .pow (f64 , E , 2.0 ));
1236+
1237+ // Experimental values (CODATA 2018 / Planck 2018)
1238+ const exp_alpha_inv = 137.035999084 ; // CODATA 2018
1239+ const exp_mu = 1836.15267343 ; // CODATA 2018
1240+ const exp_omega_lambda = 0.688 ; // Planck 2018 (±0.017)
1241+
1242+ // Calculate errors
1243+ const pellis_alpha_err = @abs (pellis_alpha_inv - exp_alpha_inv ) / exp_alpha_inv * 100.0 ;
1244+ const trinity_alpha_err = @abs (trinity_alpha_inv - exp_alpha_inv ) / exp_alpha_inv * 100.0 ;
1245+ const trinity_mu_err = @abs (trinity_mu - exp_mu ) / exp_mu * 100.0 ;
1246+ const trinity_omega_err = @abs (trinity_omega_lambda - exp_omega_lambda ) / exp_omega_lambda * 100.0 ;
1247+
1248+ // Print comparison table
1249+ std .debug .print ("\n " , .{});
1250+ std .debug .print ("{s}╔═══════════════════════════════════════════════════════════════════╗{s}\n " , .{ GOLDEN , RESET });
1251+ std .debug .print ("{s}║{s} PELLIS φ⁵ vs TRINITY φ² + φ⁻² = 3{s} ║{s}\n " , .{ GOLDEN , WHITE , GOLDEN , RESET });
1252+ std .debug .print ("{s}╠═════════════╦═══════════════════════╦═════════════════════════╣{s}\n " , .{ GOLDEN , RESET });
1253+ std .debug .print ("{s}║{s} Constant {s}║{s} Pellis (2021) {s}║{s} Trinity (2026) {s}║{s}\n " , .{ GOLDEN , WHITE , GOLDEN , WHITE , GOLDEN , WHITE , GOLDEN , RESET });
1254+ std .debug .print ("{s}╠═════════════╬═══════════════════════╬═════════════════════════╣{s}\n " , .{ GOLDEN , RESET });
1255+
1256+ // α⁻¹ row
1257+ std .debug .print ("{s}║{s} α⁻¹ {s}║{s} 360φ⁻²-2φ⁻³+(3φ)⁻⁵ {s}║{s} π⁴φ⁴e²/36 {s}║{s}\n " , .{ GOLDEN , WHITE , GOLDEN , WHITE , GOLDEN , WHITE , GOLDEN , RESET });
1258+ std .debug .print ("{s}║{s} {s}║{s} = {d:.10} {s}║{s} = {d:.10} {s}║{s}\n " , .{ GOLDEN , WHITE , GOLDEN , WHITE , pellis_alpha_inv , GOLDEN , WHITE , trinity_alpha_inv , GOLDEN , RESET });
1259+ const pellis_alpha_trophy = if (pellis_alpha_err < trinity_alpha_err ) " 🏆" else "" ;
1260+ const trinity_alpha_trophy = if (trinity_alpha_err <= pellis_alpha_err ) " 🏆" else "" ;
1261+ std .debug .print ("{s}║{s} {s}║{s} err: {.5}%{s}{s} {s}║{s} err: {.5}%{s}{s} {s}║{s}\n " , .{ GOLDEN , WHITE , GOLDEN , WHITE , pellis_alpha_err , WHITE , pellis_alpha_trophy , GOLDEN , WHITE , trinity_alpha_err , WHITE , trinity_alpha_trophy , GOLDEN , RESET });
1262+
1263+ std .debug .print ("{s}╠═════════════╬═══════════════════════╬═════════════════════════╣{s}\n " , .{ GOLDEN , RESET });
1264+
1265+ // μ row
1266+ std .debug .print ("{s}║{s} μ (mp/me) {s}║{s} via α derivation {s}║{s} 6π⁵ {s}║{s}\n " , .{ GOLDEN , WHITE , GOLDEN , WHITE , GOLDEN , WHITE , GOLDEN , RESET });
1267+ std .debug .print ("{s}║{s} {s}║{s} ≈ {d:.10} {s}║{s} = {d:.10} {s}║{s}\n " , .{ GOLDEN , WHITE , GOLDEN , WHITE , exp_mu , GOLDEN , WHITE , trinity_mu , GOLDEN , RESET });
1268+ std .debug .print ("{s}║{s} {s}║{s} err: ~0.002% {s}║{s} err: {.5}% {s}║{s}\n " , .{ GOLDEN , WHITE , GOLDEN , WHITE , GOLDEN , WHITE , trinity_mu_err , GOLDEN , RESET });
1269+
1270+ std .debug .print ("{s}╠═════════════╬═══════════════════════╬═════════════════════════╣{s}\n " , .{ GOLDEN , RESET });
1271+
1272+ // Ω_Λ row
1273+ std .debug .print ("{s}║{s} Ω_Λ {s}║{s} via α {s}║{s} 3⁸φ⁻³/(π⁵e²) {s}║{s}\n " , .{ GOLDEN , WHITE , GOLDEN , WHITE , GOLDEN , WHITE , GOLDEN , RESET });
1274+ std .debug .print ("{s}║{s} {s}║{s} ≈ {d:.3} {s}║{s} = {d:.5} {s}║{s}\n " , .{ GOLDEN , WHITE , GOLDEN , WHITE , exp_omega_lambda , GOLDEN , WHITE , trinity_omega_lambda , GOLDEN , RESET });
1275+ std .debug .print ("{s}║{s} {s}║{s} within Planck bars {s}║{s} err: {.5}% {s}║{s}\n " , .{ GOLDEN , WHITE , GOLDEN , WHITE , GOLDEN , WHITE , trinity_omega_err , GOLDEN , RESET });
1276+
1277+ std .debug .print ("{s}╠═════════════╬═══════════════════════╬═════════════════════════╣{s}\n " , .{ GOLDEN , RESET });
1278+
1279+ // Meta comparison
1280+ std .debug .print ("{s}║{s} Scope {s}║{s} ~4 constants {s}║{s} 142 formulas 🏆 {s}║{s}\n " , .{ GOLDEN , WHITE , GOLDEN , WHITE , GOLDEN , WHITE , GOLDEN , RESET });
1281+ std .debug .print ("{s}║{s} Blocks {s}║{s} {s}{integers, φ{s}{s} {s}║{s} {s}{3, φ, π, e, γ=φ⁻³{s} {s}║{s}\n " , .{ GOLDEN , WHITE , GOLDEN , WHITE , GOLDEN , WHITE , GOLDEN , WHITE , GOLDEN , WHITE , GOLDEN , RESET });
1282+ std .debug .print ("{s}║{s} Style {s}║{s} Polynomial {s}║{s} Monomial {s}║{s}\n " , .{ GOLDEN , WHITE , GOLDEN , WHITE , GOLDEN , WHITE , GOLDEN , RESET });
1283+ std .debug .print ("{s}║{s} Identity {s}║{s} φ⁵ = φ⁴ + φ³ {s}║{s} φ² + φ⁻² = 3 {s}║{s}\n " , .{ GOLDEN , WHITE , GOLDEN , WHITE , GOLDEN , WHITE , GOLDEN , RESET });
1284+
1285+ std .debug .print ("{s}╠═════════════╩═══════════════════════╩═════════════════════════╣{s}\n " , .{ GOLDEN , RESET });
1286+ std .debug .print ("{s}║{s} Convergence: BOTH reach same experimental values. {s}║{s}\n " , .{ GOLDEN , WHITE , GOLDEN , RESET });
1287+ std .debug .print ("{s}║{s} Complementary: Pellis=depth (🏆α), Trinity=breadth (🏆142) {s}║{s}\n " , .{ GOLDEN , WHITE , GOLDEN , RESET });
1288+ std .debug .print ("{s}╚═══════════════════════════════════════════════════════════════════╝{s}\n " , .{ GOLDEN , RESET });
1289+ std .debug .print ("\n " , .{});
1290+
1291+ // Footer
1292+ std .debug .print ("{s} References:{s}\n " , .{ GRAY , RESET });
1293+ std .debug .print (" Pellis (2021): viXra:2110.0084v5, viXra:2111.0037\n " , .{});
1294+ std .debug .print (" Trinity (2026): https://github.com/gHashTag/trinity\n " , .{});
1295+ std .debug .print (" Experimental: CODATA 2018, Planck 2018\n " , .{});
1296+ std .debug .print ("\n " , .{});
1297+ }
1298+
12051299// =============================================================================
12061300// COMMAND: tri math exotic
12071301// =============================================================================
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