A paper that claims to state its own weaknesses is worth nothing if the caveats arrive after the reader has already formed an impression. So they are here — before the theory pages, not after them.
These run through the whole programme:
α is a modelling parameter for the price of an unclear boundary, and carries no variational-free-energy or surprise commitment.| # | Limitation | What it costs |
|---|---|---|
| 1 | Not experimentally verified. No real system has been tested; P1–P3 are predictions, not facts. | The empirical layer is empty |
| 2 | Not peer-reviewed. This is a preprint; it has not had independent expert review. | No external certification |
| 3 | Modelling choices versus theorems. κ*, σ*=1, dE/dt≡0 and the convergence results are theorems under stated modelling choices. The logistic core, the cost ∝κ, the capacity ∝1/κ, and the price α are modelling choices whose empirical legitimacy is open. | Half the potential is chosen, not derived — and since this edition, which half is itself machine-checked |
| 4 | The value layer is the logistic instance. The 33 declarations formalise the logistic coordinate instance; general-C_F statements are structural, and their quantitative spectrum is computation, not machine proof. | Do not read the frozen corpus as covering all kernels |
| 5 | The categorical layer does not settle the identification. That a system's attribution structure is such a functor is an assumption; no amount of formalisation removes that. | The central ontological step stays an assumption |
| 6 | Boundary with the free-energy principle. See red line 2. | No borrowing of a neighbouring framework's authority |
| 7 | Ontological neutrality. See red line 1. | No metaphysical claim to defend or attack |
| 8 | The engineering bridge is a mapping hypothesis. The variable identification is assumed, not derived. | The route to measurement rests on an assumption |
"General" is used in two incompatible senses. In ordinary use it means widely applicable. In category theory universal is a technical term: characterised by a universal property, hence unique up to unique isomorphism — which does not imply wide applicability. So the programme states the grade rather than letting "general" do work it cannot do.
| Grade | Name | Meaning | Claimed here |
|---|---|---|---|
| G0 | parametric | a formula with a free parameter | — |
| G1 | equivariant | a definite transformation law under a group action | yes |
| G2 | functorial | commutes with all morphisms of the parameter category | yes |
| G3 | universal | characterised by a universal property | yes |
| G4 | free / 2-universal | every model factors uniquely through it | state layer: yes · kernel layer: no |
The programme holds itself to one discipline, and it is the reason this site looks the way it does:
sorry, or (2) a faithful report of a cited source. Everything else is an interpretation, must carry its tag, and may not appear in a theorem position.
That is why every statement on this site carries one of five labels: Definition Assumption Machine-Checked Conjecture Empirical prediction