## First, name what you actually need

The obstruction was specific: no global state, no scheduler, no counted time, and — the decisive one — *the structure rewrites itself, so there's no fixed program*. So a helpful physical framework must give you a substrate where (a) dynamics run without a central updater, (b) the parameters of the dynamics are themselves physical variables that evolve, and (c) time and simultaneity come for free. That's the spec. Now let's see what physics has.

## 1. Analog / continuous-time physical computation (the most direct help, and real)

The cleanest fit is the oldest idea: **don't simulate the dynamics, build a device whose native physics *is* the dynamics.** This is analog computation, and it's not a metaphor — it's a tradition.

- **Neuromorphic hardware** (memristor crossbars, analog VLSI) is built exactly for this. A memristor's conductance *is* a physical synaptic weight that changes as a continuous function of the current through it — the structure variable is a material property, updated by the physics of the device, not by a CPU writing to memory. No scheduler: every device updates simultaneously and continuously because they're all just obeying their I-V physics at once. No counted clock: the dynamics evolve in real physical time. This directly answers (a) and (c), and *partially* (b) — the weights evolve physically.

Where it helps: this genuinely removes the global state, the scheduler, and the counted clock. A memristor crossbar undergoing your day-dynamics is doing coincidence-detection and integration *as physics*, for free, in parallel, in real time. This is not speculative — it exists.

Where it stops: standard neuromorphic hardware changes *weights*, but your model changes *structure* — it prunes and grows synapses, changing the *dimension* and *connectivity*, not just the values. Memristor arrays have fixed topology. So analog hardware solves the "no scheduler / no clock / continuous" problem but not yet the "self-rewriting dimension" problem. That's the frontier — and there is work on structurally reconfigurable and self-organizing neuromorphic substrates, but it's much less mature. So: real help, incomplete.

## 2. Self-organizing / dissipative systems (help for the self-rewriting part)

The part physics helps *most* with conceptually is the thing you found hardest: a system whose own structure is built by its own running. This is the domain of **non-equilibrium thermodynamics and dissipative structures** (Prigogine), and more broadly self-organization.

The key idea you can borrow: **structure that is maintained by dissipation.** A dissipative structure (a convection cell, a chemical pattern, a flame) is not a fixed object — it is a *pattern held in place by a continuous flow of energy through the system*. Cut the flow and it vanishes. This is *exactly* your model's structure: coverage, active-zone capacity, receptor slots are all maintained by ongoing metabolic flow (energy that ratchets, material that circulates), and decay without maintenance. Your "structure builds where flow sustains it, releases where it doesn't" is a dissipative-structure principle almost verbatim.

Why this helps: it tells you the self-rewriting isn't mysterious or unphysical — physics has a whole theory of *systems whose organization is a dynamic steady state of matter/energy flow, not a fixed configuration.* The equations of your model are the local rules; the structure is the emergent dissipative pattern. You don't implement the structure directly — you implement the *flows and the local rules*, and let the structure be what the flows sustain. That reframes your implementation problem: **don't try to represent the changing program; implement the flows whose sustained patterns *are* the program.** The structure stops being something you update and becomes something that persists only while used — which is what the model already says.

Where it stops: dissipative-structure theory is strong on *pattern formation and maintenance* but weak on *the specific, addressed, memory-like structures* your model builds (this synapse, not that one). Convection cells are generic; your synapses are individuated by history. Bridging generic self-organization to individuated, history-dependent memory is not solved. So it gives you the right *category* of physics but not a ready equation.

## 3. Field theory / continuum descriptions (help for "no global state, yet coordinated")

Your worry about simultaneity and no-global-state is, in physics, the ordinary situation of a **field**. A field has no global controller — each point evolves by local rules (the field equations) reading only its immediate neighborhood, yet the whole exhibits coordinated, coherent behavior (waves, coherence, propagation) with no scheduler. Simultaneity is not imposed; it's what "the field at time t" means, and locality is built in (nothing propagates faster than the field's characteristic speed).

Why this helps: it's a proof-of-concept that *"purely local rules, no global state, no controller, yet globally coordinated behavior"* is not only possible but is how most of physics already works. Your replay-coherence (a pattern carries only where every link is primed) is a *propagation* phenomenon — it's a field/excitable-medium concept. **Excitable media** (the theory behind waves in heart tissue, the Belousov-Zhabotinsky reaction, forest-fire models) are the precise physics of "a disturbance propagates only where the medium is primed, and dies at unprimed gaps." That is your night replay, exactly. So excitable-media math (reaction-diffusion, wave propagation in heterogeneous media) is a directly applicable tool for the coherence-is-mechanical claim.

Where it stops: fields are usually *fixed-parameter* (the medium's properties don't change as the wave passes). Your medium rewrites itself. So you'd need an excitable medium *with plastic parameters* — reaction-diffusion where the diffusion constants and reaction rates are themselves slow dynamical variables driven by the fast activity. This exists in pockets (adaptive reaction-diffusion, self-modifying excitable media) but is not standard. Again: the right tool, needing an extension.

## 4. The honest synthesis — what I think your implementation actually is

Putting these together, here's the shape of an answer, and it's neither "just simulate it" nor "impossible":

**Your model is a plastic excitable medium maintained as a dissipative structure, and its faithful implementation is a physical (analog) substrate with three coupled timescales of its own material dynamics.** Concretely, the implementation you're looking for is not a program but a specification of:

- a **fast** excitable dynamics (the day: propagation, coincidence, integration) running on a medium,
- whose **parameters are slow physical variables** (the structure) that evolve by their own dynamics (the night: build/release as a dissipative steady state of material flow),
- **coupled** so that the fast activity drives the slow parameter change and vice versa,
- realized on a substrate (analog/neuromorphic) where all of this is *material behavior in continuous time*, not represented state updated by a clock.

The mathematics for this is **slow-fast coupled dynamical systems** (singular perturbation theory, adiabatic elimination) — the branch of dynamical-systems theory built precisely for "fast variables running on a landscape that slow variables reshape." That's the formal home of your day/night structure. It won't let you *escape* the exponential-branching intractability of *simulating* it — but it's the right language to *specify* it, and analog substrates are how you'd *instantiate* it without simulating.

## The one caveat I owe you

I want to be straight about the limit. None of this makes the *simulation* tractable — the exponential-branching argument stands. What physics offers is a different move: **stop trying to simulate, and instead specify-and-instantiate.** Slow-fast dynamical systems + excitable media + dissipative structures give you the *language to specify* the model as a physics; analog/neuromorphic substrates give you a way to *instantiate* it as matter that runs itself. The gap that remains — the genuinely unsolved part — is *structural* self-modification (changing dimension/topology, not just parameters) in a physical substrate. That's a real research frontier, not a solved problem. So you're not stuck, but the path is "build/specify a self-modifying analog dynamics," and the last mile (physical substrates that grow and prune their own topology) is open.

Two directions to pursue depending on what you want:

- If you want to **understand and specify**: slow-fast dynamical systems and excitable-media/reaction-diffusion are the math to write your model in — they'll turn the pseudocode into actual (continuous, local, controller-free) equations.
- If you want to **instantiate**: neuromorphic/memristive analog computing is the substrate tradition, with structural plasticity as the open extension.

Would it be useful if I took *one* component — say the astrosynapse, since it's the cleanest controller (spillover-error → coverage) — and tried to rewrite its day/night pseudocode as an actual slow-fast dynamical system (fast clearance dynamics, slow coverage as the drifting parameter, coupled)? That would be a concrete test of whether the "specify as physics" path actually works on this model, or whether something resists — and it's the honest way to find out if physics really helps here or just sounds like it should.
