Graduate Finance · Capital as a Structured State
Mathematical Theory of Capital
Capital represented not as a quantity but as a structured state — the quadruple \(\mathbf{C}=(K,\mathcal{G},Q,\Xi)\) of productive position, transformation architecture, information position, and meta-capacity. Sixteen chapters that prove a scalar cannot carry the theory, and build the mathematics that can.
K→𝒢→Q→Ξ
16 Chapters
16 Lab Engines
128 Validation Checks
3 Companions
Why this course exists
A scalar cannot measure capital
Capital adequacy, valuation, and allocation as practiced are built on projections of the capital system onto a single number: book value, replacement cost, discounted cash flow, market capitalization, regulatory capital. Each is valid on a restricted domain — and each discards the structure that was the economics. This course develops the replacement: capital as a quadruple, the transformation network as the asset, valuation as geometry, and the meta-capacity to make new pathways as the coordinate a scalar can never see. The through-line is a single signature network carried through all sixteen chapters — founded, priced, killed in crisis, and governed — with one set of seeded engines so every number agrees by construction.
The Three Companions
One engine, three ways to use it
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Laboratory Webapp
16 chapter dashboards implementing every Capital Systems Laboratory module of the book — interactive, seeded, and validated.
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Python Notebooks
One rendered notebook per chapter driving the same engine, with charts and the book’s validation checks built in.
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Excel Workbooks
One workbook per chapter — live formulas beside engine values, reproducing the book’s numbers.
All three consume the same Python engine with the book’s seeds (2026CCNN), so the numbers agree by construction — from the miniature’s \(90+10+5.5\) to the fractal dimension \(\log 3/\log 2 \approx 1.585\).
What you will build
By the end of the course
- The habit of representing capital as a structured state, locating every phenomenon in exactly one coordinate of the quadruple \((K,\mathcal{G},Q,\Xi)\)
- A working command of the book’s machinery — the transformation network and its reachability lattice, the algebra and geometry of transformations, valuation on a fixed architecture, architecture value and the Separation Theorem, and the information position
- Hands-on fluency with the companion laboratory: every chapter has a webapp module, a rendered Python notebook, and an Excel workbook, all producing identical numbers on identical seeds
- Verified computational work: every laboratory module carries the book’s validation checks, and passing them (
ALL_PASS) is part of every assignment
Chapters
The Sixteen Chapters · Five Parts