Experiment E · Substrate independence · the H5 test
Silicon. Quartz. Granite.
Same geometry. One ratio?
If the antisymmetric-mode protection ratio is geometry-derived, it should survive a change of material. We hold the cavity shape fixed and re-run the closed-form mode analysis for three substrates whose dielectric loss tangents span four orders of magnitude.
EXPLAIN LIKE I'M 10
· everyday-language one-paragraph version
We've designed a special cavity shape. The question this page answers: does it still work if you build it out of granite, a common rock that exists in every country, instead of silicon, which only a handful of fabs in the world can make pure enough? Same shape. Three materials side by side. If the geometric advantage survives, quantum hardware could be built with materials a village already has.
WHAT YOU ARE LOOKING AT
The Dhara cavity's mode-Q numbers, symmetric vs antisymmetric, recomputed for three different materials of construction. Silicon at semiconductor purity. Crystalline quartz. Common granite. Same geometry, different ε and tan δ.
WHY THIS MATTERS FOR QUANTUM
The simulator's central claim is that the geometric advantage, the ratio of antisymmetric to symmetric mode Q, survives the substrate change. If true, the same Dhara geometry implemented in granite at room temperature gives the same protection ratio as silicon at millikelvin, just at a lower absolute Q and a different operating frequency. That is the meta-hypothesis (H5) that turns the simulator's output from a fab design into a deployment-anywhere design.
WHAT TO WATCH
The right-most column. The absolute Q drops by orders of magnitude from silicon to granite, as expected. The ratio Q_anti / Q_sym should stay roughly constant across all three substrates. If it does, the natural-resource pathway claim has its quantitative basis. If it collapses for granite, H5 is falsified and we retract.
Geometry under test
Dhara composite
base ratio Q_anti/Q_sym = 2.75×
Ratio range across substrates
2.58× → 2.75×
mean = 2.69× · drift 6.3%
Frequency span
876.47 MHz → 1.28 GHz
cavity scale L = 5.0 cm
Verdict (current geometry)
preserved
Ratio is preserved across substrates. H5 stands at this geom…
Silicon
Semiconductor-grade Si · the fab incumbent
ε_r
11.7
tan δ
1.0e-5
Q_max ceiling
1.0e+5
f_mode
876.47 MHz
Q_sym (eff)
4.00
Q_anti (eff)
11.00
Ratio (anti / sym)
2.75×
99.9999% intrinsic Si at 4K, isotopically purified. Reference standard.
Deployable: lab only
Deployable: lab only
Crystalline Quartz
Natural mineral · low-loss insulator
ε_r
4.5
tan δ
1.0e-4
Q_max ceiling
1.0e+4
f_mode
1.41 GHz
Q_sym (eff)
4.00
Q_anti (eff)
10.99
Ratio (anti / sym)
2.75×
Natural single-crystal SiO₂. Used in oscillators since 1920s.
Deployable: any workshop
Deployable: any workshop
Granite
Natural rock · the village-scale substrate
ε_r
5.5
tan δ
1.0e-2
Q_max ceiling
1.0e+2
f_mode
1.28 GHz
Q_sym (eff)
3.85
Q_anti (eff)
9.91
Ratio (anti / sym)
2.58×
Common natural rock. Available everywhere. tan δ varies with composition; pegmatitic granite gives lowest loss.
Deployable: globally accessible
Deployable: globally accessible
Q-bars across substrates · log scale
copper = ratio · steel/sand/biege = Q-sym, Q-anti, Q-max
Cross-geometry · ratio drift across substrates (same geometry, three substrates)
| Geometry | Silicon | Crystalline Quartz | Granite | Drift |
|---|---|---|---|---|
| Dhara composite | 2.75× | 2.75× | 2.58× | 6.3% |
| Sphere | 0.94× | 0.94× | 0.95× | 1.5% |
| Cube | 1.17× | 1.17× | 1.13× | 3.1% |
| Pyramid | 1.22× | 1.22× | 1.18× | 3.3% |
| Cylinder | 1.19× | 1.19× | 1.15× | 3.8% |
Drift < 10% (green) = substrate-independent at this geometry. Drift between 10–25% (amber) = moderate. Drift > 25% (red) = geometry's protection ratio collapses under material change, geometry alone is not enough; H5 fails for that geometry.
Atlas v3 → substrate · anomaly-proximity axis
Source-region matters.
Cratonic baseline vs anomaly-zone variants.
The Atlas v3 meta-origin landed at Hudson Bay Low to 5.4°. If that finding is engineering-relevant, substrates sourced near published geophysical anomalies carry a measurable Q-factor signature distinct from cratonic-stable counterparts. The hypothesis encodes as a single tunable α (Q-multiplier); the test is whether α ≠ 1 survives a head- to-head loss-tangent measurement.
Substrate
Source region · anomaly proximity
mass-deficit lithosphere → lower defect density (predicted)
Q_max · cratonic baseline
100.0
tan δ = 1.0e-2
Q_max · Hudson Bay Low zone
153.8
tan δ × α = 6.5e-3
Q advantage · zone / baseline
1.54×
anomaly zone wins
Geometry × zone · antisymmetric-mode advantage shift
| geometry | Q_sym baseline | Q_anti baseline | ratio baseline | Q_sym zone | Q_anti zone | ratio zone | Δ ratio |
|---|---|---|---|---|---|---|---|
| Sphere | 23.66 | 22.48 | 0.95 | 25.80 | 24.40 | 0.95 | -0.00 |
| Cube | 19.35 | 21.88 | 1.13 | 20.76 | 23.69 | 1.14 | +0.01 |
| Pyramid | 15.25 | 18.03 | 1.18 | 16.11 | 19.25 | 1.19 | +0.01 |
| Cylinder | 20.63 | 23.66 | 1.15 | 22.24 | 25.80 | 1.16 | +0.01 |
| Dhara composite | 3.85 | 9.91 | 2.58 | 3.90 | 10.27 | 2.63 | +0.06 |
The antisymmetric-mode advantage (Q_anti / Q_sym) is by construction a geometry-derived ratio, but the absolute Q values both shift under anomaly-zone material. If α < 1 (anomaly zone has lower defect density), the absolute Qs rise and the Dhara-composite's containment improves linearly. The geometry-rank ordering survives, the antisymmetric-mode hypothesis is robust to source-region, but the ABSOLUTE manufacturable performance window shifts.
Buildable test
Procure granite samples from three geological source regions matched for petrologic composition: one cratonic-stable (Karelian or Canadian Shield interior), one Hudson Bay zone (Quebec / Nunavut margins), one Indian Geoid Low zone (Deccan Trap basalt margin near the geoid minimum at 3°N, 79°E). Measure tan δ at 1 GHz on three samples of each. The hypothesis predicts:
- cratonic tan δ ≈ baseline
- Hudson zone tan δ ≈ 0.65 × baseline (within ±30%)
- Indian Geoid Low tan δ ≈ 0.55 × baseline (within ±30%)
If any of those three relationships hold up at p < 0.05 across the sample set, the Atlas v3 finding has its first engineering-side replication.
Catalogued anomalies used in this hypothesis
| anomaly | lat / lon | type | note |
|---|---|---|---|
| South Atlantic Anomaly | -27°, -45° | geomagnetic | weakest surface geomagnetic field |
| Hudson Bay Low | 60°, -85° | gravimetric | largest negative gravity anomaly · post-glacial rebound |
| Bangui Magnetic Anomaly | 5°, 18° | geomagnetic | largest crustal magnetic anomaly |
| Indian Ocean Geoid Low | 3°, 79° | gravimetric | deepest geoid low · 106 m below reference |
| Kursk Magnetic Anomaly | 52°, 36° | geomagnetic | 4500 km² iron-ore magnetic signature |
| Pacific LLSVP · Tuzo | -10°, -160° | mantle | deep-mantle dome under Pacific |
| African LLSVP · Jason | 0°, 20° | mantle | deep-mantle dome under Africa |
| Caroline Plate gravity high | 5°, 140° | gravimetric | western Pacific positive gravity anomaly |