The Periodic Stack of Communication
Every channel is a coordinate.
A communication system commits to eleven independent quantities. Each is bounded by a named theorem. Position predicts what the system can carry, what it can guarantee, what survives a partition, and what it costs in joules per bit delivered.
c = ⟨ C, E, L, B, R, D, O, V, A, N, τ ⟩
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 communication, the dimensions are rate, energy, time, in-flight volume, fidelity, delivery, order, trust, addressing, topology, and lifetime — each a physical quantity bounded by a named theorem.
Read across the coordinate and the system explains itself — what it can carry, what it can guarantee, what it can prove, what it costs per delivered bit in joules. The same map covers TCP, QUIC, WebRTC, MoQT, MLS, SIP, Tor, Kademlia, BGP, Bluetooth LE, LoRa, and a deep-space DTN bundle.
The map is a way of seeing, not a verdict. It classifies what carries, makes the structure of the design space legible, and lets a channel be reasoned about before it is built — the same move the sibling stacks make for computation, synthesis, data, and state.
The design space
Eleven axes describe a communication system.
Four are shared with the sibling stacks — E inherits the Landauer floor from compute, R and V are shared with synthesis and data, and τ is shared with data and state. The other seven are communication-specific.
Capacity
01 · MAX RELIABLE RATEthe ceiling on rate.
Energy per bit
02 · ENERGY FLOORjoules per delivered bit.
Latency
03 · PROPAGATION FLOORspeed of light + Cramér–Rao.
Bandwidth–delay product
04 · BITS IN FLIGHThow much is in transit at saturation.
Rate–distortion
05 · COMPRESSION FLOORminimum bits per symbol at fidelity D.
Delivery semantics
06 · TERMINATION + AGREEMENTwhat holds under failure.
Ordering
07 · OBSERVABLE ORDERpartial order across nodes.
Verifiability
08 · TRUST THAT TRAVELSclaim strength bound to the message.
Addressing
09 · LOOKUP + PRIVACYhops to find + cost to hide.
Network topology
10 · CONNECTIVITYcut, paths, mixing.
Persistence
11 · LIFETIME AT RESTthermodynamic budget against time.
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 communication system has a place.
7 · 6 · 7 · 6 · 5 · 7 · 5 · 6 · 6 · 7 · 6 = 466,754,400
Discrete cell count · the addressable map of communication-space
discrete cells
orthogonal axes
compute primitives below
Companion stacks
One method, applied across fields.
The same axes recur. E inherits the Landauer floor from compute. R and V are shared with synthesis and data. τ is shared with data and state. 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.
Memory
The eleven-axis retention 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.