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NEW TO E₄₇? BEGIN HERE.

This page gives you one memorable route through the City: Carrier → Selector → Projector → Certificate → Correction.

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The one-sentence mental model

The Mathematical City is a research operating system in which a claim becomes navigable only after its object, operator, kernel, projector, executable witness, evidence class, provenance, correction history, and boundary are all made explicit.

The five-stop memory route

1. Carrier — start with the 125-dimensional space $V_2^{\otimes3}$.
2. Selector — define $K=(C-6I)(C-30I)$.
3. Projector — isolate $E_{47}=\ker K$ with $\dim E_{47}=47$ and $\Omega_c=47/125$.
4. Certificate — reproduce the computation and inspect the machine record.
5. Correction — see how a false transport identity was preserved, diagnosed, replaced, and propagated.

Remember this: 125 → K → 47 → certificate → correction.

Route A · Understand the core in five minutes

• Foundations
• Representation Theory
• Kartekeya — Projection Spine
• Machine Certificates
• Central Citadel

Route B · Reproduce one proof

Proof selected: Dual Horizon complementary projector algebra

The exact objects are

$$ J=\begin{bmatrix}0&1\\1&0\end{bmatrix},\qquad P_+=\frac12(I+J),\qquad P_-=\frac12(I-J). $$