The Periodic Stack of Memory
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
The thesis
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.
The design space
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.
Retention
01 · HOW LONG IT LIVEShalf-life of the trace, in seconds
Refresh ratio
02 · INFO LIFE OVER SUBSTRATE LIFEτ_information / τ_substrate · dimensionless
Capacity
03 · STATES BEFORE INTERFERENCEdistinguishable retained states · bits
Write energy
04 · COST TO WRITEjoules per bit · log₁₀(E / Landauer) above floor
Hold energy
05 · COST TO HOLDjoules per bit per second of retention
Recall energy
06 · COST TO RECALLjoules per bit returned on read
Access regime
07 · HOW IT IS REACHEDthe mechanism that returns a trace
Fidelity dynamics
08 · HOW IT EVOLVES WHILE HELDhow the trace changes between write and recall
Representational form
09 · THE FORM OF THE TRACEhow the trace is etched into the substrate
Write regime
10 · HOW IT IS WRITTENhow a trace enters memory
Verifiability
11 · TRUST ON RECALLwhat guarantee travels with a recalled trace
The coordinate space
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
discrete cells
orthogonal axes
compute primitives below
Companion stacks
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.
Compute
258 primitives, 33 families.
Synthesis
The seven-axis synthesizer stack.
Data
The ten-axis data-system stack.
State
The nine-axis state stack.
Communication
The eleven-axis channel stack.
Knowledge
Seven axes · the object the others handle.
Agent
Four axes · the actor and selection.
Stack
The overview · three names, one substrate.
Verify
Seven axes · joules per verified output.
OpenIE
The parent thesis.