Retention is a coordinate.

Every entity that carries signal forward through time against entropy occupies a place on the same map. Eleven axes describe the shape. Position predicts what it holds, what it costs to hold, what survives a power cut, a sleep, a death, a millennium.

c = ⟨ τ, ρ, C, E᳗, E᳠, E᳐, A, F, R, W, V ⟩

The cell coordinate · eleven axes, one tuple

Position predicts behavior.

A periodic structure earns its name when where a thing sits tells you how it behaves. For memory, the dimensions are how long the trace lives, how the substrate is refreshed, how many distinguishable states it holds, what it costs to write, hold, and recall, how the trace is reached, how it evolves while held, what form it takes, how it enters, and what guarantees travel with it on recall.

Read across the coordinate and the system explains itself — what it can retain, what it must rewrite, what survives a partition, what it pays per bit in joules. The same map covers a CPU register, an L1 cache line, a DRAM row, a flash page, a hippocampal engram, a cortical schema, a CRISPR spacer, a strand of DNA, a Vedic verse, an Aboriginal songline, an Inca khipu, and a single trapped ion.

The map is a way of seeing, not a verdict. It classifies what retains, makes the structure of the design space legible, and lets a retention substrate be reasoned about before it is built — the same move the sibling stacks make for computation, synthesis, data, state, and communication.

Eleven axes describe a retention substrate.

Three are shared with the sibling stacks — E inherits the Landauer floor from compute, V and R are shared with synthesis, data, and communication, and τ is shared with data, state, and communication. The other eight are memory-specific.

The addressable map.

The product of the axis cardinalities is the discrete coordinate space. Structural constraints prune it to an admissible remainder on which every retention substrate has a place.

8 · 5 · 6 · 7 · 7 · 7 · 6 · 6 · 6 · 6 · 5 = 533,433,600

Discrete cell count · the addressable map of memory-space

533,433,600

discrete cells

11

orthogonal axes

258

compute primitives below

One method, applied across fields.

The same axes recur. E inherits from the compute stack. V is shared with synthesis, data, and communication. R is shared with synthesis and data. τ is shared with data, state, and communication. A primitive carries consistent coordinates across all of them.