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upward project brief

continuity role: durable intent status: current last verified: 2026-10-14 owns: purpose, users, scope, non-goals, constraints, and success update when: project direction changes, not when implementation merely advances

purpose

upward is a small public web instrument for encountering the multiplicative architecture of a positive integer as an interactive three-dimensional divisor lattice.

intended users and consumers

  • people exploring number theory through direct spatial manipulation;
  • researchers who may eventually carry neutral lattice data into separate local investigations;
  • public visitors who should need no account, backend, or prior mathematical vocabulary.

goals

  • make correct divisor-lattice structure visible and enjoyable to manipulate;
  • derive geometry from prime-exponent structure rather than an arbitrary graph layout;
  • keep the mathematical model independent of the renderer;
  • preserve a clean public boundary for future, explicitly requested export.

non-goals

  • a generic number-theory course or worksheet system;
  • gematria, qabbala, cipher, corpus, or glossololary integration;
  • accounts, telemetry, server persistence, or a durable user profile;
  • pretending a three-dimensional projection preserves every property of a higher-dimensional exponent lattice.

repository boundary

this repository owns a client-only mathematical model, its interactive web projection, and public documentation. private phrase data and downstream local analysis remain outside the repository. any future integration must cross an explicit, mathematically neutral export boundary.

current phase

the current artifact proves three complete circuits: unfold and inspect one bounded positive integer in exact natural exponent geometry; cast a four-plus- dimensional exponent body through a named ranked zonotopal projection; then hold several integers within a tab session and expose structural kinship or exact divisor-lattice containment against the active form. the cabinet separates collection from reading: stable-order held forms remain indexed while one answering form comes forward, and the complete full-card collection opens as an extension of the instrument.

success

  • 348 renders as a usable 12-node, 20-edge lattice;
  • 60 renders with the same structural signature and geometry;
  • 210 renders all 16 divisors and 32 covers through an explicitly named 4→3 projection that preserves rank and complement symmetry;
  • held 153 becomes one complete illuminated face of 306, with quotient 2;
  • session storage retains only bounded integer values and never becomes mathematical or private-research authority;
  • a cold checkout reaches the instrument and passes its documented validation;
  • deferred integrations do not determine the first implementation.

constraints

  • static browser application with no required backend or runtime network calls;
  • deterministic equal-step geometry for the exact one-, two-, and three-dimensional cases;
  • deterministic ranked zonotopal projection with visible information-loss and coincidence disclosure for higher-dimensional cases;
  • separate computation and scene-complexity limits protect the browser while keeping admitted forms visually inhabitable;
  • public source contains no private corpus material, secret, or environment value.