Scheduling
Arbitration, retry delay, fractional rates and ordered initialization.
DETERMINISTIC PRIMITIVES · 3 PRODUCTS
Small state.
Explicit transformations.
Axiom One and its neighboring mathematical systems address different embedded and deterministic problems. The family page shows their shape; each repository defines its own contract.
01 / ONE LIBRARY
Axiom One: a toolbox of bounded operations
One C99 static library; independent modules remain opt-in through normal static linking.
22 MODULESAxiom Onecaller-owned state · no heap · no I/O
Signal & numeric
Filtering, input checks, thresholding, slew, quantization and range conversion.
Sequence & protocol
Freshness, voting, replay windows and cyclic sequence arithmetic.
State containers
Buffers, packed fields, lookup, sets, records and bounded traces.
Integration model. The public API uses plain C99 headers. Stateful modules keep their objects with the caller; the library supplies no hidden clock, random source, timer service, callback loop or global mutable state. Synchronization and API-specific numeric domains remain caller responsibilities.
02 / MATHEMATICAL PRIMITIVE
GrayGyre: a self-inverse placement transform
A compact index mapping for spreading nearby logical values across configured cells.
- Input: logical index
- Apply configured Gray-code shear
- Output: physical placement index
- Apply the same mapping again to recover the original
ALLOCATION-FREE · TABLE-FREE
Placement, not traversal
GrayGyre documents deterministic index placement for logical pages, banks and similar layouts. Its repository explicitly says the transform is not encryption, a hash, wear leveling, error correction or a full-cycle scheduler.
The repository reports physical ESP32-S3 performance measurements and separate compile/static validation for listed Cortex-M and RISC-V targets. Those records apply to GrayGyre’s documented configurations and do not establish hardware validation for the whole Axiom One family.
Read GrayGyre’s mapping, evidence and limits03 / IMPLICIT SEARCH
SkipSpace: navigate without storing the tree
A traversal primitive whose key design condition is whether compact state preserves future-relevant behavior.
Prefix→Sufficient state→Bounded subtree count→Visit or skip
SkipSpace keeps caller-owned navigation state and a fixed workspace. It updates a sufficient-state model, counts valid continuations with saturating arithmetic, and can skip a subtree without materializing every node.
Model boundary. Prefixes may share a state only when their future-relevant behavior is equivalent for the modeled problem. If the model needs more history, the state space can grow and the compression advantage can disappear. Counting and skip checks cost more than push/pop; the README recommends sparse skip checks for the described use.
04 / FAMILY DIRECTORY
Three separate repositories
Only Axiom One’s 22 modules share a library and API umbrella. GrayGyre and SkipSpace are separate projects with their own sources, tests, evidence and limits.