Symbolics Lab

Thesis

Every concept draws a line through the world. Where the line falls is governed by an index — scope, locus, resolution, measurement, rules for sameness. What the line captures is a distinction. What it excludes — the remainder — does not disappear, it presses back.

We study the principles that govern this process: how concepts form, what they cost, and what holds them in place.

Framework

Four questions

01

Distinction

How does the first concept appear?

Not in isolation. Every transmissible form begins between two systems under shared pressure. One differentiates; the other reads that differentiation as signal. The first distinction is not made — it is recognized.

02

Index

What determines what it can capture?

Scope, resolution, measurement, locus, rules for sameness — the parameters that make any classification possible are themselves choices. Change the parameters, change what exists.

03

Remainder

What happens to what it excludes?

It doesn't disappear. It accumulates. It presses back. Every system is shaped by what it cannot see — and what it cannot see is shaped by the choices it made to see anything at all.

04

Verification

How do you know any of this holds?

63 theorems. Zero postulates. A pipeline that flows from theory through formal proof to executable runtime, then back through audit. Claims that can be checked are claims that can travel.

Research

The two-body problem

A distinction is not made by a single system. It emerges between two systems under shared pressure. One differentiates; the other reads the differentiation as signal.

System A

Differentiates

Produces a variation in the field — a perturbation, a mark, a pressure differential. Not yet a concept. A difference that has not been read.

distinction

System B

Recognizes

Reads the variation as structure — as something that can be stabilized, repeated, transmitted. The distinction exists only once it is recognized.

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