On Continuation and Permission
I have been working on a set of mathematical ideas for a long time, mostly in private. This site exists to make that work visible in a form that can be read, checked, cited, and argued with.
At a high level, the work is concerned with continuation. That is, what it means for a process, argument, or construction to be allowed to proceed, and what it means for that permission to fail. From that starting point come related ideas such as admissibility, capacity, exhaustion, and collapse. These ideas cut across mathematics, computation, and physics in ways I did not initially expect.
I am less interested in how systems evolve once they are running than in the conditions under which they are permitted to keep running at all.
How to Read What Is Here
This is not a blog in the usual sense. I am not writing to persuade, advertise, or speculate in public. The posts here are closer to notebook entries or short papers. They are focused, self contained, and written with the assumption that the reader is willing to slow down.
Some posts contain complete proofs. Others contain definitions, structural observations, or partial results. In every case, I try to be explicit about what is established, what is assumed, and what remains open.
If something is tentative, I say so. If something is firm, I try to make it checkable.
Structure of the Work
Most of what appears here falls into one of three categories.
Foundational pieces
Clarifying terms such as admissibility, continuation, capacity, and collapse, and fixing their relationships.
Structural results
Statements about what can or cannot persist under explicit constraints, often without reference to dynamics or probabilistic models.
Interpretive notes
Connections to familiar problems in mathematics, physics, and computation, written carefully and without assuming agreement.
Posts are versioned. When something changes, the change is noted.
Relation to Existing Mathematics
Some of these ideas overlap with established areas of mathematics, but the framework itself is not standard. I am not trying to force it into an existing category.
This site is, in part, an attempt to make that difference precise enough that it can be evaluated on its own terms.
Readers are encouraged to treat the work as a proposal. It is something to be tested, stressed, and possibly rejected, but not skimmed.
Status
This is an ongoing project. Definitions may sharpen, proofs may simplify, and some directions may turn out to be dead ends.
What will not change is the intent to be clear about what I know, what I think I know, and what I do not.
Nothing here is presented as final.