nox explanations
conceptual documentation — why nox works the way it does, the design choices behind it, and the consequences that emerge.
these pages illuminate the architecture. for formal definitions, see reference/. for task-oriented instructions, see docs/guides/ (when available).
pages
| page |
topic |
| why-nox.md |
the frozen foundation — what nox enables and why the patterns never change |
| lineage.md |
from combinatory logic to nox — two lineages meet: minimalism and convergence |
| completeness.md |
why exactly these instruction groups — structural, field, bitwise, hash, hint |
| structural-patterns.md |
the five tree patterns — axis, quote, compose, cons, branch |
| field-patterns.md |
the six field patterns — add, sub, mul, inv, eq, lt over Goldilocks |
| bitwise-patterns.md |
the four binary patterns — xor, and, not, shl and the two-algebra problem |
| nouns.md |
the one data structure — binary trees of field elements, and why nothing else is needed |
| triple.md |
object, formula, focus — the three inputs and why the third changes everything |
| layers.md |
the ontological separation — truth, possibility, speed |
| confluence.md |
why evaluation order is irrelevant — and why that enables a planetary cache |
| hint.md |
the boundary of knowledge — one instruction that provides privacy, search, and oracles |
| content-addressing.md |
every computation has a name — the seed of planetary memoization |
| proof-native.md |
execution IS proof — why there is no circuit compilation step |
| jets.md |
optimization without compromise — from patterns to silicon |
| self-verification.md |
the system that verifies itself — recursive proof composition to arbitrary depth |
| five-algebras.md |
one VM, five algebras — nebu, kuro, jali, trop, genies and why each is irreducible |
| decider.md |
89 constraints — verifying all history from genesis cheaper than one hash call |
| transformer-jets.md |
compiled cybergraph inference — 7 composite jets across 6 languages |
Dimensions
explanation
rs/docs/explanation
explanation
zheng/docs/explanation
zheng explanations zheng is a polynomial proof system. these documents explain the concepts, design decisions, and historical context. for formal definitions, see reference/. for the hash primitive, see hemera. for the VM whose traces we prove, see nox. reading path pages vision | page | topic |…
trop/docs/explanation
tropical semiring arithmetic an encyclopedia of the mathematics behind trop's (min, +) algebra — from first principles to applications. every concept is grounded in the semiring we implement: tropical addition is min, tropical multiplication is ordinary addition, and shortest paths are matrix…
kuro/docs/explanation
binary field arithmetic an encyclopedia of the mathematics behind kuro's F₂ tower — from first principles to applications. every concept is grounded in the tower we implement: F₂ → F₂² → F₂⁴ → F₂⁸ → F₂¹⁶ → F₂³² → F₂⁶⁴ → F₂¹²⁸. foundations binary-fields — field axioms in characteristic 2, GF(2) as…
trident/docs/explanation
💡 Trident Explanation [← Documentation Index](/trident/docs/readme) Understanding-oriented. Deep dives into why Trident works the way it does, for readers who want the full picture. 🏗️ Core Architecture | Document | Description | |----------|-------------| |…
genies/docs/explanation
isogeny group action arithmetic an encyclopedia of the mathematics behind genies — supersingular isogenies, class group actions, and the CSIDH construction. every concept connects back to the central operation: the commutative group action of cl(O) on supersingular elliptic curves over F_q.…
bbg/docs/explanation
explanation
hemera/docs/explanation
why Hemera works the way it does design decisions behind the Hemera hash primitive. philosophy why-hemera — eight design principles: permanence, the tree, endofunction, self-reference, identity, unity, beauty, the name the-name — etymology: Hemera in the Protogenoi, genealogy of hash names…
jali/docs/explanation
polynomial ring arithmetic an encyclopedia of the mathematics behind jali's polynomial ring R_q = F_p[x]/(x^n+1) — from first principles to applications. every concept is grounded in the ring we implement: structured vectors of Goldilocks field elements with negacyclic convolution. foundations…
nebu/docs/explanation
finite field arithmetic an encyclopedia of the mathematics behind the Goldilocks field — from first principles to applications. every concept is grounded in the field we implement: p = 2⁶⁴ − 2³² + 1. foundations finite-fields — field axioms, existence and uniqueness, GF(p), characteristic, the…