Light up top, dark below.the stage every rule plays out on.

Two things the pressure-test already pinned for the world to honour.

What space is, and how cells sit in it. Everything in §2.2–2.5 is built on this.

Space is a graph — realised as a lattice

• The world's space is a graph — a fixed scaffold of parcels (nodes) at real 2D (x,y), joined by edges. Concretely we realise it as a regular lattice: each edge carries a conductance, each node a medium-type (water / solid / sediment / …) plus its C, N and light.
• Uniform start = water everywhere, equal conductances → behaves exactly like a grid.
• Structure enters through coefficients, not rewiring. Channels, solids, a sea floor are made by varying per-edge conductance and per-node medium on the fixed lattice — a solid is simply an edge with ~zero conductance. No rewrite; it's exactly how real finite-volume solvers represent obstacles and heterogeneous media; and it keeps the fast solver (§2.4). Structure is physics — where matter can be, what connects to what — never a rewarded niche. (Steering guardrail.)
• Arbitrary irregular topology is held in reserve. Genuinely non-lattice wiring isn't needed for anything we've designed (every structure so far is a conductance field on the lattice) and would forfeit the fast solver — so we'd adopt it only if some future structure truly demands it. (External review: mainstream cell frameworks use regular grids, not general graphs — see the review section below.)

Cells float over it — two networks, one space

• Cells are off-lattice — floating dots in the same continuous 2D space, each with its own position and size (per §1 reserve/structure). Cells are not nodes; they drift over the space-graph and sample the parcels near them.
• So one X/Y space holds two distinct networks: the space-graph (static scaffold — only the values on nodes change) and the cells + their bonds (mobile dots, with a dynamic spring-bond network from §1). Cells aren't a graph; bonds are optional springs between dots.

Uniform now, structured later — same model

Resolution is precision, not structure

Node density (the grid spacing) sets a length scale and some directional artifacts — a real physical parameter, not a neutral display choice. But it's precision, not ecological structure: a million identical water parcels is just precise emptiness, not a structured world. Every discretisation (graph or grid) has this; the only thing without a length scale is a pure formula, which can't remember edits. So resolution is a tuned constant (§6): set fine enough to sit below biological scales, use an isotropic diffusion stencil, and convergence-test (halve the spacing — if behaviour shifts, it was too coarse).

Implementation note (→§4): the lattice is stored grid-fast throughout — structure lives in per-edge conductances and per-node medium, not in the data layout — which is exactly what lets the implicit diffusion solver (§2.4) run.

The world's shape and how its edges behave — pinned as invariants so no implementation improvises.

A cylinder — wrap sideways, walls top & bottom

• Finite world (forced: a fixed total of C and N can't live in an unbounded space), a 2D rectangle.
• Vertical axis = no-flux walls. Light runs top→bottom, so the vertical is asymmetric — it can't wrap (surface would meet floor, bright meeting dark). A surface on top, a floor on the bottom; nothing crosses either. The photic gradient lives along this axis (§2.3).
• Horizontal axis = periodic (wraps). Side-to-side is symmetric, so it wraps: a cell drifting off the right reappears on the left. This deletes the side edges entirely — no edge artifacts, every horizontal position equivalent. A faithful water column.

Boundary invariants — pinned

Past builds saw edges behave differently every time — the signature of edges hand-coded ad hoc. So the rules are fixed here as invariants, derived from one principle (nothing crosses; wrap = same place), not improvised per build:

• Horizontal — periodic. Position x and x+W are one place. The wrap is applied to every operation — movement, neighbour search, diffusion, bond distances, rendering — so there is no seam to misbehave.
• Vertical — no-flux walls. Zero matter crosses the surface or floor (a mirror boundary for diffusion; cells cannot pass). Surface is the light entry; the floor is where sediment will live if structure is added.
• The canary. Total C and N stay flat every tick (§4). Any edge leak shows up instantly — so "edges drifted and I didn't notice" can't happen again.

The world's width and height (and so how much depth the photic gradient spans) are constants → §6; qualitatively, tall enough that light runs from saturating at the surface to darkness at the floor.

Light enters at the surface and descends the space graph, dimming as it goes. This resolves O3 — light becomes a competed, depletable resource.

Three things dim the light

As light descends from the surface, attenuation accumulates from three sources (Beer–Lambert — exponential, the physical law; linear would be unphysical):

• Water — the baseline decay with depth (water's own coefficient).
• Biomass — cells in the path absorb light, so upper cells shade those below (the canopy / self-shading).
• Medium on the space graph — solids and sediment are opaque, so the light pass reads each node's medium-type as it goes.

Light descends the space graph from the surface, accumulating all three per node. Uniform start → a simple top-down sweep per column. Once structure exists, light follows the graph and respects opaque nodes — so a region tucked under a solid, or with no open path up, goes dark on its own: emergent shadow pockets / refugia, no special-casing.

Day & night

Surface intensity is a periodic function of the tick clock — bright by day, ~dark at night. Nothing downstream changes: only the value at the top of the column rises and falls, then the same descend-the-graph attenuation runs.

• It activates the §1 carbon reserve: every autotroph now banks carbon by day and respires it through the dark — real phytoplankton physiology, and a constant selective pressure on storage instead of a reserve that mostly sits idle.
• It creates a temporal niche (photosynthesise by day / survive by night) and the pressure behind diel vertical migration — rise toward light, sink at night.
• Pure environmental physics, so temporal niches emerge, not coded. Day-length is a §6 constant — and it pins part of §2.5 (it defines what "a day" is in ticks).

Direction stays vertical. Underwater, almost all light is downwelling regardless of the sun's angle (refraction funnels it toward vertical), so straight-down light is the faithful choice. A moving / angled sun (sweeping shadows) is logged as an optional embellishment for when solid structure exists — not built now.

Light has no memory

Light stays a per-tick derived field: recomputed every tick from the current biomass and the (mostly static) medium — never stored across ticks. So self-shading adds no persistent state; it just lets the recompute read the current biomass. (This is the "computed, not remembered" field from the §2.1 discussion — unlike the nutrient ledger, which persists.)

Constants → §6: surface intensity, water attenuation, biomass attenuation, per-medium opacity.

The store was settled in §2.1 (the graph); this fixes how nutrients spread across it, and hands the numbers to §6.

• What diffuses: inorganic C and N. Light doesn't (recomputed top-down each tick); detritus dynamics → §3.
• Conservative graph diffusion: along each edge, flux = conductance × concentration difference, and what leaves one node enters its neighbour — so total C/N is conserved by construction (the flat-total canary watches it). No-flux at the surface/floor walls (§2.2); no currents/advection (§1 guardrail).
• Isotropic stencil: on the uniform grid, diagonals are weighted in, so a plume spreads as a round blob, not a diamond — no grid-direction artifacts to steer outcomes.
• Per-edge conductance ties matter to the medium: solids get ~zero conductance (matter can't diffuse through a wall — mirroring how solids block light), sediment gets low conductance (slow). Both light and matter respect the same graph.
• Per-element rates: C and N diffuse at their own rates (cheap, marginally more faithful).
• Implicit, operator-split solver: diffusion is solved implicitly, split from the cell exchange step, so it's unconditionally stable — no CFL sub-stepping to babysit. On the regular lattice this is a row/column (LOD / Thomas) solve; the periodic horizontal axis is a cyclic-tridiagonal solve, the walled vertical axis a plain one. (This is what BioFVM-class solvers do — see the review below.)
• Cells exchange conservatively (off-lattice ↔ field): a floating cell reads and writes the field through the same spatial kernel, over the node(s) its footprint covers — removing exactly the mass it gains. The seam between mobile cells and the node field can't leak (the standard agent↔field bookkeeping). Node spacing vs max cell size → §6.

Handed to §6: per-element diffusion rates, per-medium conductance, and the initial inventory (total C & N and how they're distributed at the start). The implicit solver removes the old sub-stepping/stability worry.

Extended by §3: the diffusing set grows to four matter species — inorganic C/N and dissolved-organic C/N (DOM) — all conservation-checked together, plus three massless signal channels (markers) that diffuse and decay but sit outside the matter canary. Same solver, more fields (a performance note for §4).

How time advances, and in what order things happen inside one step.

The tick

• Time is discrete ticks — the atomic step. Every rate in the model is expressed per tick, and a day = N ticks (the constant pinned by 2.3).
• Diffusion is solved implicitly each tick (operator-split, unconditionally stable, §2.4) — no sub-stepping needed.

Asynchronous, reshuffled, seeded

• Each tick, cells act one at a time, each on the live state — so a draw can never take more than is currently present. Conservation is natural, no rationing needed.
• The acting order is reshuffled every tick, which removes systematic first-mover bias (fair on average).
• Seeded RNG → every run with the same seed and start replays bit-for-bit. Reproducible every time.
• The shuffle uses a separate RNG stream from mutation, so changing biology logic doesn't desync the order — A/B comparisons stay clean.

The trade we accepted: update order is an extra (seeded) source of noise. We chose it over synchronous-with-arbitration because it's simpler, conserves for free, and stays fully reproducible — the arbitration logic sync needs wasn't worth its cost here.

Order within a tick

The types of process run in a fixed, conservation-safe sequence, identical every tick — only the per-cell order inside the "act" stage is shuffled. The exact loop is §4's job; 2.5 pins that it's fixed and ends on the canary.

Edge cases pinned

• Newborns wait a tick: a cell created this tick doesn't act until the next, and a cell that dies mid-tick is pulled from the remaining order — so there are no order-dependent within-tick cascades.
• The canary has teeth: it checks C/N totals against a tolerance (floating-point sums drift), with a no-negative-concentration guard on uptake and diffusion, and it monitors — never silently renormalises. Drift past tolerance is a bug to surface, not to paper over.

Checked against the established coupled agent–field models, then the seams hardened.

Checked against real models

• The architecture is the standard one. PhysiCell (off-lattice cell agents) coupled to BioFVM (a finite-volume reaction–diffusion field) is essentially what we designed — floating cells over a node field, each cell secreting/uptaking substrates and tracking the material it adds and removes. Off-lattice was their deliberate choice too, to avoid lattice artifacts.
• The field is a regular grid, not a general graph. These frameworks use Cartesian voxel meshes. Our "graph" earns its keep only as a regular lattice + per-edge conductance + per-node medium — which is the finite-volume standard for obstacles and heterogeneous media. Arbitrary irregular topology is unused there and unneeded here, so it's held in reserve (§2.1).
• Self-shading is textbook. Ocean and photobioreactor models build the attenuation coefficient as a sum of each constituent's concentration × its specific coefficient — exactly our water + biomass + medium. §2.3 is faithful.
• The one upgrade — implicit diffusion. BioFVM solves diffusion by operator splitting + implicit (LOD/Thomas) steps for absolute stability; explicit schemes carry strict step limits. Adopted in §2.4/§2.5 (cyclic-tridiagonal on the periodic axis).
• The rejected alternative — a cell as many lattice squares — is Cellular Potts (CompuCell3D/Morpheus), which doesn't scale to large cell counts. Good that we passed.

Fixes folded in

• G1 — conservative cell↔field exchange: same kernel both ways; remove exactly the mass you gain. §2.4
• G2 — footprint vs node spacing: act and shade over the nodes a cell covers; spacing ↔ max size → §6. §2.4
• G3 — implicit, operator-split solver: unconditionally stable; replaces sub-stepping. §2.4 / §2.5
• G4 — newborns wait a tick; the dead leave the order: no within-tick cascades. §2.5
• G5 — canary with teeth: tolerance, no-negative guard, monitor not renormalise. §2.5

Logged & caveats

Calibration couplings (→§6): day-length vs reserve capacity vs maintenance must balance so autotrophs survive the night (the intended pressure, but miscalibration = nightly die-off); node spacing must sit below biological scales (convergence-test).

Reproducibility scope: "bit-for-bit" holds within a build / device; across platforms, floating-point and Math differences can diverge.