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
parameters
parameters — rationale for every parameter (field, S-box, width, rounds, computational elegance)
chunk-size — why 4 KB chunks (10-point analysis)
architecture
sponge-only — why no compression mode (practical, economic, mathematical)
capacity — structured capacity: one function, unlimited contexts, cost analysis
content-ids — why raw 64-byte CIDs, no headers, endofunction closure
self-bootstrap — why self-bootstrapping, non-circularity argument
analysis
security — security margins, quantum resistance, ecosystem comparison
performance — hash rate, proving cost, steady-state adequacy
operations
migration — emergency protocols, no algorithm agility, storage proofs
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.…
nox/docs/explanation
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…
bbg/docs/explanation
explanation
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…