Total progress across all work types.
Sweeping lambda from 0.4 to 0.6 in 200,000 steps. Each step: build the W-operator on a Menger sponge contact graph, solve eigenvalues, compare ratios against known physical constants.
| # | Worker | Jobs | Hours | Hits | W | Trust | Status |
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If the Menger sponge's physical constant predictions are mere numerology, other fractals should produce similar matches. We test every threshold-based 3D fractal from base 3 to base 21 (odd bases only). Each is defined by removing subcubes with ≥P center coordinates from a b×b×b grid.
| Base (b) | Threshold (P) | S | Δ | Kept (k) | Removed (r) | Constants Matched |
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If physical constants come from Menger spectral invariants, the residuals between predicted and measured values decrease geometrically with iteration depth. The convergence ratio P/k = 2/20 = 0.1 means each Menger level refines predictions by 10×.
Eigenvalue-2 multiplicity: m(n) = (18n + 153·4n + 1155) / 357
| Level | Multiplicity | dS | Gap Ratio | Residual vs dH |
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High-precision eigenvalue extraction on dedicated GPU hardware (NVIDIA GH200 480GB). 94 physical constants matched at L5 (3.2M vertices) and L6 (64M vertices). L7 (1.28 billion vertices) is currently running.
Sorted by L6 precision. Sub-ppb matches highlighted green. All 94 constants found at both levels.
| Constant | Target Value | L5 Match | L5 Error (ppm) | L6 Match | L6 Error (ppm) | Improvement |
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Extracted via thick-restart Lanczos with deflation on an NVIDIA GH200. GPU at 100%, 96.7GB VRAM. Every probe converges to delta=0.00. Updates live via the L7 bridge.
94 out of 94 physical constants emerge from the Menger sponge eigenvalue spectrum with zero free parameters. Precision improves geometrically with iteration depth: L5 median error ? ppm → L6 median error ? ppm. The convergence pattern is identical for known and unknown ratios — consistent with standing waves on a self-similar fractal structure.
L7 (1.28 billion vertices) is the largest Menger eigenvalue computation in history. Currently extracting interior eigenvalues via 50 sigma sweeps. Hardware: NVIDIA GH200 480GB, ~$40 total cost.