Two inputs only
A seam normalisation constant c₃ = 1/(8π) and a carrier rank
g_car = 5 (a five slot carrier, 3 plus 2). On the dimensionless axis
essentially only π is primitive, so there are
no free load bearing numbers.
What this page claims
A measurable gap, not a proof of intelligence.
The homepage introduces the hypothesis. This page outlines its scientific framing and measurement principles. Stable field mechanics alone does not establish semantic understanding or general intelligence.
The real contribution is to pin down the minimal gap between stable field mechanics and semantic generalisation, and, crucially, how to measure it.
The laws force the system to settle into one stable attractor, not necessarily the meaning correct one. That exact gap is called grounding.
01 · The foundation
One physics discipline, eight information laws.
TFPT (Topological Fixed-Point Theory) treats physics like a small deterministic compiler: two boundary inputs plus a few typed anchors become read outs as projections rather than fitted parameters. Hylaean does not use the physics predictions. It borrows the structural discipline and vocabulary, and nothing else. The theory itself lives at fixpoint-theory.com.
Honestly typed
TFPT is split into a closed dimensionless compiler, protected physics, declared anchors and open interfaces. It is explicitly not a certified theory of everything, and Hylaean inherits the same honesty about its own limits.
Three operative moves
What falls out of the borrowed structure is a very small runtime grammar: K twists, L binds, T transports. Everything the field does is composed from those three, plus one energy that all of them descend.
| TFPT motif | Hylaean runtime | What it gives the AI |
|---|---|---|
| Field state on a carrier | state.S [N,d] on the unit sphere | One live cognitive substrate, the brain |
| Seam even and odd, involution | SeamOperator, microcell sheet pair | Double cover, chirality, admissibility |
| Carrier, five slot | C5Carrier, two point algebra | An explore and commit algebra, no semantics baked in |
| Antisymmetric torsion | K [N,d,d] (Hebbian) | Field memory: twist within a place |
| Symmetric metric | L [N,d,d] (PSD) | Binding, complementary to the twist |
| Cross position holonomy | FieldTransport T [N,N] | Moving content between positions |
| Gapped transport to attractor | Energy minimisation, cavity relax | The answer is a settled state |
Deliberately left out: the Standard Model masses, the full lattice compiler as a runtime, hypergraph rewriting as the substrate, and the cosmology read outs. None of that is needed to run a field.
The eight laws, and where each one stands
These principles describe the research proposal. They are not a published assessment of the current implementation.
Unity, one field
Exactly one field state.S on a sphere. Question, answer, world model and regions are deformations of the same field.
One energy
Every behavioural force is one additive term of a single master energy. A question is a boundary condition, the answer is an energy minimum, thinking is relaxation.
Selector is not dynamics
After each step an algebraic selector projects onto the admissible sector. Closed form selection, never a second optimizer.
Attractors and stability
The proposal studies conditions under which dynamics converge. Stable convergence alone does not establish a semantically correct answer.
Memory as geometry
Memory changes geometry (Hebbian ΔK and ΔL, basins deepen). There is no back propagation anywhere on the answer path.
Composition and transport
A per node move can only recolour. Moving content or relations between positions needs a shared operator: transport T, or a norm preserving rotation R on the basin manifold.
Grounding, meaning as coordinate
Basins carry meaning as a geometric coordinate, so the same relation is the same shift. Without that, basins are structureless and relations are inconsistent.
Honest determination, commit or abstain
Commit only on real field movement, otherwise abstain. Leftover pressure opens a nested reasoning frame instead of a bluff.
How evidence should be measured.
- Match the task. Measure the requested capability through its actual output. Distinguish learning and retention from generalisation.
- Report the conditions. State what the system saw, what changed, and which inputs were held out.
- Use causal controls. Compare the relevant mechanism with an ablation under otherwise comparable conditions.
- Preserve the record. Record correct outputs, incorrect commits and abstentions with the code, configuration and inputs needed to interpret them.