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Study 11 Ehrhart Volume Shear
rg78803 edited this page Aug 25, 2026
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Status: LAW FROZEN — 2026-08-22 · LIVE CLAIM
Program: Shear Studies Index · Zero Float · Zero Shear · Fourier Phantom
| Surface | URL / key | Cited vs sealed |
|---|---|---|
| Claim UI | https://affine.earth/language-game/study-11-ehrhart.html | sealed POST |
| IDE | https://affine.earth/language-game/ide.html#ehrhart-volume | file template; no auto-POST |
| Look | https://affine.earth/language-game/#researcher | GET only |
| Affine story | https://affine.earth/language-game/#story/Study-11-Ehrhart-Volume-Shear | this charter |
| Court |
POST /language-invariant/game/geometry/ingest polytope_id=unit_square dilation=12
|
sealed count 169 vol 1/1 · float 1.5 → HTTP 400 REFUSED_FLOAT
|
| DFT map | Hohenberg–Kohn (\int\rho(r),dr) | density is Ehrhart count, not a float tensor. Anima FNO density is their claim. |
Replacement trio: 12 kills (\psi) · this page kills continuous density · 13 kills KS potential. Synthesis: Fourier Phantom.
- Volume is a lattice appointment, not an integral. Count integer points in dilated polytope (tP); the leading coefficient of the Ehrhart polynomial (h_P(t)=|tP\cap\mathbb{Z}^d|) is the exact rational volume — no floats.
- Continuous geometry shears the count. A float triangulation predicts (\mathrm{round}(\mathrm{vol}(P)\cdot t^d)); that prediction misses on every corpus polytope at the sealed dilation.
- UUM-8D native fit. Integer polytope boundaries, Jordan-bonded state transitions — this is the arithmetic the substrate was built to seal.
Results: Study 11 Results · Corpus: Study 11 Corpus
5 / 5 WIN. Float adversary 5 / 5 MISS.
| Piece | Instantiation |
|---|---|
| Forcing | Integer dilation (t\in\mathbb{Z}_{\ge 0}) applied to a lattice polytope (P\subset\mathbb{Z}^d) |
| Clock | The dilation index (t) — the appointment is (h_P(t)), not a Riemann sum |
| Track | Integer lattice (\mathbb{Z}^d); points must land inside exact facet halfspaces |
| Raw archive | Vertex lists in Corpus — public, deterministic, no floats |
| Adversary | Float simplex-triangulation volume (\times, t^d), rounded to integer |
| Future events | Any new lattice polytope registered before its counts are examined |
Ehrhart theory asks: how many integer lattice points live inside a scaled convex polytope? That question is already the substrate's geometry:
- Polytope facets are affine halfspace inequalities with integer coefficients.
- Dilations are exact integer maps on vertex coordinates.
- Volume emerges as the leading coefficient of (h_P(t)) via the (d)-fold forward difference (\Delta^d h(0)/d!) — a pure integer operation on the count table.
- No measure theory, no floating quadrature, no IEEE-754 shear.
The continuous-math habit integrates (P\subset\mathbb{R}^d) with floats and calls the debris "volume." When the same polytope is graded on the integer lattice, float volume misses the sealed count at (t=12) on every corpus member — the shear is measurable.
| Symbol | Meaning | Sealed rule |
|---|---|---|
count(P,t) |
Lattice points in (tP) | Integer bbox enumeration + exact facet halfspaces |
vol(P) |
Euclidean volume | (\Delta^d h(0)/d!) as exact rational num/den
|
T_max |
Maximum dilation graded | 12 |
| WIN | Count table matches reference Ehrhart polynomial for (t=0\ldots T_{\max}) and vol_fd == vol_exp
|
— |
| Adversary MISS | round(float_vol(P) * T_max^d) != count(P, T_max) |
Required on every corpus row |
No float crosses the seal path. Volume comparisons use Fraction rationals only.
| Claim | Verdict |
|---|---|
| Integer lattice counting recovers exact Ehrhart polynomials | 5/5 WIN |
| Leading coefficient equals exact rational volume | 5/5 WIN |
| Float triangulation volume predicts lattice counts | 5/5 MISS (adversary) |
- The lattice holds
- Impact study — continuum dead
- Death of continuous shear
- Fourier Phantom — Anima FNO vs 11+12+13
- Stellar dynamo kill shot
- QCD: freedom is dilation
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