Total progress across all work types.
Swept 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. Status: this queue is retired — ratio recovery at this spectral density was shown indistinguishable from null spectra (April 2026), so "hits" below are recorded candidates, not evidence. Data retained for the record.
| # | 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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This panel presented finite-level spectral-dimension estimates (1.32, 1.88, 2.14) as a sequence converging toward the Hausdorff dimension, with each level refining constant predictions by 10×. Direct measurement contradicts the premise: the sponge's spectral dimension is ds ≈ 2.45, flat across levels L2–L5 (three independent methods), and the constant-prediction framing was withdrawn after null testing (April/August 2026). Retained below for the record.
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.