upward 🪩

upward is an interactive instrument for exploring the hidden structure of integers.

It turns numbers into navigable divisor bodies: exact lattices when the structure fits natural exponent space, and ranked zonotopal projections when the form exceeds three prime directions.

Or, less formally: upward is a zonotopal nightclub for projected hypercubes.

With it, you can:

• unfold a positive integer into its divisor lattice
• compare integers by structural signature
• detect when one number appears as a face or nested body within another
• project higher-dimensional multiplicative forms into view
• inspect complements, ranks, and prime-direction structure The result is part mathematical instrument, part curiosity cabinet: a way to see the recurring bodies integers inhabit.

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continuity role: operational front door status: experimental last verified: 2026-10-14 owns: the shortest successful use and the map to deeper documentation update when: installation, primary use, maturity, or document authority changes

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current state

the experimental instrument is usable locally and wired for github pages. it renders bounded integers with up to three distinct primes in exact natural exponent geometry, then casts higher-dimensional exponent bodies through an explicitly named ranked zonotopal projection. every selected divisor retains its exact factorization, coordinate, rank, and complement. a session-scoped cabinet can hold up to 12 integers, recognize structural twins, and illuminate a held divisor lattice when it is embedded in the active form. the cabinet keeps its insertion order in a compact index, brings an answering form to one full- size front card, and opens every full card in a pullout drawer. the exact lattice model remains bounded at 512 divisors, while the public scene admits at most 192 nodes and 640 covers so mathematical possibility does not silently become an unusable rendering.

see STATUS.md for the verified checkpoint and remaining gaps.

quickest successful use

prerequisites:

• node.js 20.19 or newer;
• npm;
• a modern browser with webgl for the three-dimensional scene.

from a cold checkout, in order:

npm install
npm run dev

open the local url printed by vite. expected evidence of success:

upward opens at 348 with 12 nodes, 20 cover edges, and 87 paired with complement 4.

common use

enter 60 and choose unfold. its labels change, but its structural signature remains (2, 1, 1), the same multiplicative skeleton as 348.

choose specimen 210 to enter the ranked projection: its four prime directions become a deterministic 4→3 zonotopal shadow with 16 divisors, 32 covers, exact rank rise, antipodal complements, and an explicit information-loss warrant.

for the relational circuit, unfold 153, choose hold 153, then unfold 306. the cabinet identifies a new-prime extrusion by 2: the six nodes and seven internal covers of 153 become one illuminated face of the complete 12-node, 20-cover lattice of 306.

the resting cabinet shows one full-size front card. its index remains in stable held order even when another form comes forward to answer the active integer. choose open cabinet to extend the complete full-card drawer over the field; on narrow screens the extension rises from the bottom.

publication

the public artifact is available at https://resonatrix.tech/upward/. github pages serves the generated application beneath /upward/.

the repository workflow installs from the lockfile, runs the complete project check, and uploads only the generated dist directory. configured delivery and observed public availability remain separate facts; see STATUS.md for the last verified observation.

configuration and data

• configuration: none at runtime; build behavior lives in vite.config.ts, which explicitly disables environment-file loading.
• secrets: none required. .env files are ignored and must not be committed.
• persistent data: at most 12 validated integers in versioned browser sessionStorage; no derived mathematics, annotations, or durable profile.
• build-time delivery: github actions and github pages; neither is used at runtime.
• runtime network: none required after the static assets load.

documentation authority

document	role	status	owns
README.md	operational	current	front door and shortest successful use
STATUS.md	operational	current	verified checkpoint and next useful action
AGENTS.md	behavioral	current	agent authorization and completion protocol
PROJECT_BRIEF.md	durable intent	current	purpose, scope, and non-goals
CONTRACTS.md	normative	current	mathematical and public-boundary invariants
docs/ARCHITECTURE.md	operational	current	implemented components and data flow
docs/DEVELOPMENT.md	operational	current	exact setup and validation procedures
DECISIONS.md	historical	append-only	accepted rationale and supersession
specs/001-first-slice.md	planning	retired	the completed first transition and its original boundary
specs/002-held-forms-cabinet.md	planning	retired	completed session cabinet and relational comparison transition
specs/003-cabinet-front-and-drawer.md	planning	retired	completed front-card and pullout-drawer transition
specs/004-ranked-zonotopal-projection.md	planning	retired	completed named-projection transition for four-plus-dimensional lattices
specs/005-scene-budget.md	planning	retired	completed bounded scene-complexity transition

known limitations

• exact natural coordinates stop at three distinct prime directions; higher dimensions use the disclosed ranked zonotopal projection;
• input is bounded at 1,000,000,000 and 512 computed divisor nodes; scenes admit at most 192 nodes and 640 covers;
• screen-space labels can overlap or hide at some camera angles; rotate the sculpture or use the keyboard-accessible divisor rail;
• browsers without webgl retain the mathematical readout but cannot show the sculpture;
• editable projectors, exploded coincident shadows, morphing, all-pairs cabinet comparison, and export are not implemented;
• the public route is live, but broad public-device coverage remains incomplete.

project map

• PROJECT_BRIEF.md — why upward exists;
• CONTRACTS.md — what must remain mathematically true;
• docs/ARCHITECTURE.md — how the current system is shaped;
• docs/DEVELOPMENT.md — how to run and prove it;
• DECISIONS.md — why consequential choices were made.