# Impact Study — The Fourier Phantom **Status: PUBLIC SYNTHESIS — 2026-08-25** **Target:** Linear-Scaling DFT with Neural Operators (Anima AI, Aug 2026) — **their** published claim. **Replacement:** Studies **11 + 12 + 13**. Those courts are LIVE on affine.earth. **Door:** [Death of continuous shear](Death-of-Continuous-Shear) · long rewrite: [Impact study — continuum dead](Impact-Study-Death-of-Continuous-Shear) **Skala sibling:** [Study 15](Study-15-Skala-DFT-Shear) — same continuum court, **CITED** 2.72 / 2.8, kcal court **DARK**. **Dynamo sibling:** [Stellar dynamo kill shot](Impact-Study-Stellar-Dynamo-Kill-Shot) — gyrochronology / weakened magnetic braking is the same continuum court on a star. Study 21. Not a Kepler/TESS CALORIE. This page maps their continuum pipeline onto the integer courts that replace it. It does **not** write that Affine cured DFT. It does **not** seal an 82,500-atom magnesium density CALORIE. Anima’s 82,500-atom Mg dislocation / B300 / FNO run is **Anima’s demo**. Affine’s side of the comparison is the LIVE courts that replace that pipeline. --- ## What is Anima’s claim vs Affine LIVE vs named path | Layer | Who says it | What it is | |---|---|---| | 82,500-atom Mg dislocation on one NVIDIA B300 via FNO | **Anima claim** (Aug 2026) | Their published demo. Cite it as theirs. | | \(O(N^3)\) Kohn–Sham scaling “solved” by FNO | **Anima claim** | They replaced a continuous equation they could not compute with a continuous approximation that cannot be sealed. | | Study 11 count **169** vol `1/1`; `dilation=1.5` → `REFUSED_FLOAT` | **Affine LIVE court** | [`#ehrhart-volume`](https://affine.earth/language-game/ide.html#ehrhart-volume) | | Study 12 `chance` rounds 3 · `27/64` | **Affine LIVE court** | [`#qpr`](https://affine.earth/language-game/ide.html#qpr) | | Study 13 word `Z2_a2b` linking `(0,1)` | **Affine LIVE court** | [`#connes-rigidity`](https://affine.earth/language-game/ide.html#connes-rigidity) | | A.E.P-1 Edge Pod (ESP32 / AArch64), <5W, SIMD integer | **Named Affine path** | Execution path named here. Not a sealed wattage/chip measurement on 82,500 atoms. | OPEN stays **03 / 05 / 08**. No new `game_id`. No occupancy court. No 82500 CALORIE. --- ## Replacement = 11 + 12 + 13 ### 1. Study 12 — Parallel Repetition (kills the wavefunction) **Target:** many-electron \(\psi\) and Born amplitudes. UUM-8D: Schrödinger / Born — dead as a transported probability. Anima approximates a probability distribution in floats. Study 12: quantum state evolution as a discrete product of rational fractions \(W_n \in \mathbb{Q}\), unitary rational rotations on the vQbit. We do not approximate the wavefunction; we replace it with exact integer fractions. | Surface | URL | |---|---| | IDE | https://affine.earth/language-game/ide.html#qpr | | Claim | https://affine.earth/language-game/study-12-chance.html | | Wiki | [Study-12-Quantum-Parallel-Repetition-Shear](Study-12-Quantum-Parallel-Repetition-Shear) | | Affine story | https://affine.earth/language-game/#story/Study-12-Quantum-Parallel-Repetition-Shear | **LIVE CLAIM** — `STUDY12_QPR_PROVEN`. Named receipt is the court. ### 2. Study 11 — Ehrhart Volume (kills continuous electron density) **Target:** Hohenberg–Kohn \(\int \rho(r)\,dr\). Continuous DFT treats charge density as a fluid. Study 11: volume is Ehrhart integer count \(\mathrm{vol}=\Delta^d h(0)/d!\). Electron density is a rigid count of occupied lattice points in a discrete polytope, not a float tensor. | Surface | URL | |---|---| | IDE | https://affine.earth/language-game/ide.html#ehrhart-volume | | Claim | https://affine.earth/language-game/study-11-ehrhart.html | | Wiki | [Study-11-Ehrhart-Volume-Shear](Study-11-Ehrhart-Volume-Shear) | | Affine story | https://affine.earth/language-game/#story/Study-11-Ehrhart-Volume-Shear | **LIVE prove:** `polytope_id=unit_square` `dilation=12` → count **169**, vol `1/1`. Float dilation `1.5` → HTTP 400 `REFUSED_FLOAT`. ### 3. Study 13 — Connes Rigidity (kills the Kohn–Sham potential) **Target:** KS effective potential / MO energy landscape. Anima Neural Operator guesses continuous potential↔density until “self-consistency.” Study 13: discrete Jordan algebra linking relators \(L(\gamma)=(q,r)\in\mathbb{Z}^2\). Ground state is the rigid topological link where the integer structure locks, not a continuous energy minimum. | Surface | URL | |---|---| | IDE | https://affine.earth/language-game/ide.html#connes-rigidity | | Claim | https://affine.earth/language-game/study-13-algebra.html | | Wiki | [Study-13-Connes-Rigidity-Shear](Study-13-Connes-Rigidity-Shear) | | Affine story | https://affine.earth/language-game/#story/Study-13-Connes-Rigidity-Shear | **LIVE CLAIM** — word `Z2_a2b` · linking `(0,1)` · class `RIGID_CYCLE`. Never POST lone `"e"`. ### Synthesis Anima throws H100s / B300 at a Study 11 / 12 violation — FNO compressing an IEEE-754 continuous integral to dodge \(O(N^3)\). Affine bypasses the integral: **11 counts points, 12 locks state, 13 links structure.** --- ## IMPACT STUDY ADDENDUM — The Fourier Phantom They demonstrated FNO predicting electron density of an 82,500-atom magnesium dislocation on a single NVIDIA B300. They claim to have solved \(O(N^3)\) KS scaling. They replaced a continuous equation they could not compute with a continuous approximation that cannot be sealed. ### Part 1 — Epistemological shear FFT of the KS potential in float32 / bf16. \((a+b)+c \neq (a+c)+b\). GPU reduction order = phantom density. Two GPUs, two structures. **Lattice court:** Density \(=\Delta^d h(0)/d!\) (Study 11). Binding \(=L(w)=(q,r)\in\mathbb{Z}^2\) (Study 13). No Fourier. No probability smear. Count discrete nodes; exact rational vector; double-SHA256 identical across GaiaFTCL cells. ### Part 2 — Thermodynamic shear B300 ~1000W TDP to brute-force non-associative floats. **Named Affine path:** A.E.P-1 Edge Pod (ESP32 / AArch64), <5W, SIMD integer, \(\frac{a}{b} < \frac{c}{d} \iff a\cdot d < c\cdot b\). That wattage/chip pair is the named platform path, not a sealed measurement of 82,500 atoms. ### Verdict If a molecular model cannot reproduce to the exact bit on two machines, it cannot certify a battery, catalyst, or drug. Anima = peak continuous sketch. Affine = the court. ### Mechanics of Fourier shear \(O(N^3)\) time traded for \(O(N \log N)\) thermodynamic shear. Non-associative tensor reduction. Frequency-domain truncation / libm. Resulting phantom “converged density.” Study 11 + 13 on affine.earth: discrete integer coords, exact rational add \(\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}\), identical SHA256d on the named edge path and the fleet. The Eisenstein lattice holds the count. Decode-path sibling already live: [`GET /language-invariant/eisenstein/seal`](https://affine.earth/language-invariant/eisenstein/seal). --- ## Study 15 — Skala, same continuum court Microsoft Skala 1.1 is the same continuum court under a different costume: a deep-learning XC functional with GMTKN55 WTMAD-2 **2.72** kcal/mol (model card) and blog **2.8** kcal/mol, both fetched 2026-08-24. Court **DARK**. **Not OPEN.** Using something that is not accurate because it shears may not be useless — **it may be dangerous**. A kcal/mol miss treated as the molecule is a spatial collision: wrong pocket, wrong bond, wrong dose. Affine refuses the float or seals the integer. [Study 15](Study-15-Skala-DFT-Shear) · IDE [`#skala-cited`](https://affine.earth/language-game/ide.html#skala-cited). --- ## Live courts (quote these) 1. https://affine.earth/language-game/ide.html#qpr 2. https://affine.earth/language-game/ide.html#ehrhart-volume 3. https://affine.earth/language-game/ide.html#connes-rigidity 4. https://affine.earth/language-game/ide.html#stellar-dynamo — Study 21 dynamo step. Same lattice, stellar MHD instead of DFT. Look walk: [\#researcher](https://affine.earth/language-game/#researcher) · this story: https://affine.earth/language-game/#story/Impact-Study-Fourier-Phantom · kill shot: https://affine.earth/language-game/#story/Impact-Study-Stellar-Dynamo-Kill-Shot --- ## What this page does not do - Does not write “Affine cured DFT” - Does not invent an 82,500-atom Mg density CALORIE - Does not invent a new `game_id` or occupancy court - Does not treat A.E.P-1 / ESP32 / <5W as a sealed wattage receipt - Does not call Skala or Anima **useless** - Does not move OPEN off 03 / 05 / 08 **Zero float on the court examples.** Winning integers: count **169**, vol `1/1`, rounds **3**, `27/64`, word `Z2_a2b`, linking `(0,1)`.