+++ title = “Architecture Overview” section = “technical” +++

Architecture Overview

htpy is organized as a Rust workspace with 14 crates. The core computation is pure Rust with no external dependencies beyond the standard library; the web interface uses Axum and Askama.

Crate dependency graph

                    htpy-fp
                      |
                  htpy-algebra
                      |
               +------+------+
               |      |      |
          htpy-sseq   |   htpy-resolution
               |      |      |
               +------+------+
                      |
              htpy-deduction
                      |
          +-----------+-----------+
          |           |           |
     htpy-web    htpy-wasm    htpy-tools
     (local)     (browser)    (CLI)

Supporting crates: htpy-fp, htpy-once, htpy-bivec, htpy-maybe-rayon, htpy-archive, htpy-groebner.

Core crates

htpy-fp

Field arithmetic and linear algebra over $\mathbb{F}_p$.

Bit-packed vector representation (FpVector, FqVector)
Matrix operations with M4RI (Method of Four Russians)
NEON SIMD on ARM, optimized odd-prime row reduction
Subspace computation, affine subspaces

htpy-algebra

The Steenrod algebra and module categories.

AdemAlgebra, MilnorAlgebra: both bases of the Steenrod algebra
MotivicAdemAlgebra: the motivic Steenrod algebra over $\mathbb{F}_2$
PStarAlgebra: the polynomial subalgebra $P^*$ (for CESS)
Module types: finite-dimensional, free, $C\tau$, truncated-$\tau$, $P^$-polynomial, $P^$-exterior
Generic grading framework: Grading trait with i32 (classical) and MotivicDegree (trigraded) instances

htpy-sseq

Spectral sequence data structures and deduction algorithms.

Sseq<P>: bigraded spectral sequence with differential tracking
Staircase data structure: per-bidegree echelon form with level encoding for page-by-page survival
Deduction algorithms: degree argument, Leibniz propagation, Moss’ theorem, $E_r$ Massey products, elimination by contradiction
Profile-specific implementations: StaircaseSseq<Adams>, StaircaseSseq<Cess> with motivic and CESS deduction passes

htpy-resolution

Minimal free resolution engine.

Resolution: classical resolution of $A$-modules
MotivicResolution<T>: motivic resolution, generic over target module
Chain map computation and connecting homomorphism
Yoneda products and Massey products (3-fold, 4-fold, matric)
$\tau$-torsion via iterated LES (motivic_chain_map.rs)
resolution_core.rs: shared two-phase resolution step (extend_resolution_matrix + finalize_resolution_step)

htpy-deduction

Standalone deduction engine (extracted from htpy-web).

run_deduction(): 11-pass fixed-point loop
Types: UserDifferential, DiffKnowledge, VanishingLine, NaturalityInput, DeductionResult
Can be used by htpy-web, htpy-wasm, and future CLI tools

htpy-web

Axum web server with embedded viewer.

Routes for archive browsing, computation, deduction, export
Askama HTML templates with Canvas-based chart renderer
Module library with persistence to ~/.htpy/
Build binaries for generating archive data (build_motivic, build_ctau, build_cess, build_novikov)

Data flow

Module definition (JSON)
        |
        v
htpy-resolution: minimal free resolution
        |
        v
htpy-archive: ComputationRecord (Ext dims, products, diffs)
        |
        v
htpy-web: ChartData (pre-computed pages, products, annotations)
        |
        v
Browser: Canvas renderer (pan/zoom, selection, detail panel)

Parallelism

htpy uses optional parallelism via the concurrent Cargo feature, which enables rayon through htpy-maybe-rayon. Without it, all computation is sequential (useful for WASM targets).

Parallel workloads:

Classical resolution wavefront scheduler (diagonal parallelism)
Motivic resolution weight batching within each $(s, t)$ step
LES chain map and homotopy inner loops
Cofiber/fiber resolution via rayon::join

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