# K — Dendritic Structural Encoding (KDSE) — UHWare

> Official machine-readable map for K — Dendritic Structural Encoding (KDSE). The HTML specification and paper mirrors are the primary retrieval surfaces; consult the typeset PDFs for authoritative page layout and the source repository for implementations.

## Read first: HTML surfaces

- [KDSE technical specification](https://kdse.uhware.com/spec)
- [Introductory paper — HTML mirror](https://kdse.uhware.com/papers/introductory)
- [Instantaneous Jump Magnitude paper — HTML mirror](https://kdse.uhware.com/papers/ijm)
- [KDSE landing page](https://kdse.uhware.com/)

## What KDSE is

K — Dendritic Structural Encoding (KDSE) is UHWare's compact, delimiterless breadth-first encoding of finite full q-ary dendritic structures. Every node is either a terminal or a branch with exactly `q` children. The structural alphabet is binary even when `q` is greater than two.

KDSE defines the structure; an operator defines a particular computation over that structure. The threshold-and-loss response and instantaneous jump magnitude are worked operators, not requirements for structural validity.

## Core structural definition

- `1` denotes a branch; `0` denotes a terminal.
- Explicit node indicators are emitted level by level in breadth-first order.
- If level `ell` has `b_ell` branches, the next level has width `w_(ell+1) = q * b_ell`, with `w_0 = 1`.
- The final all-terminal level is deterministic, implicit, and omitted in minimal form.
- Internal level boundaries are therefore delimiterless; concatenated variable-length KDSE values still require outer framing or a known boundary.
- Values are independent of the structure and are listed in reconstructed breadth-first order, including implicit final leaves.
- Ordered KDSE is a canonical subtype selected by the lowest numerical valid sibling ordering. Valid structural KDSE may be unbalanced or otherwise non-canonical.
- KDSE-8 and KDSE-16 are current binary container classes, not limits on the mathematical construction and not descriptions of branching arity.

## Operator example

Under equal q-way splitting, uniform multiplicative branch retention, and a common terminal threshold `T`, let `c_d` be the number of reconstructed terminals at depth `d`. The grouped instantaneous jump magnitude is `J_d = T * c_d`. Depth and path transfer determine the event location; terminal multiplicity and threshold determine the grouped jump. This identity belongs to the worked operator, not to KDSE payload validity.

## Source and implementation

- [GitHub repository](https://github.com/uhware/kdse)
- [v1.0.3 GitHub release](https://github.com/uhware/kdse/releases/tag/v1.0.3)
- [Introductory paper — PDF](https://kdse.uhware.com/papers/KDSE_Introductory_Paper.pdf)
- [Instantaneous Jump Magnitude paper — PDF](https://kdse.uhware.com/papers/KDSE_Deterministic_Instantaneous_Jump_Magnitude.pdf)
- [Source ZIP](https://kdse.uhware.com/downloads/kdse-main.zip)
- [Source tar.gz](https://kdse.uhware.com/downloads/kdse-main.tar.gz)
- [KDSE structural chart](https://kdse.uhware.com/papers/figures/KDSE_chart.png)
- [KDSE threshold-sweep animation](https://kdse.uhware.com/papers/figures/KDSE_threshold_sweep_1110111.gif)

## Licensing and status

Source code, tests, examples, and command-line tools are licensed AGPL-3.0-or-later. Papers and documentation are licensed CC BY-SA 4.0. The project states: U.S. Patent Pending, Application No. 64/131,240. Public reference implementations are available in ISO C11 and Python.