Theory · Framework overview
UIT-IEG / U-Space: overview and assumptions
Core structure, assumptions, and proposed observational relationships. Matthew Murphy, Lexideck Technologies.
The core structure
The framework adopts information and mass-energy as one quantity under two accountings. U-Space attaches informatic content to real points of spacetime; IEG treats interactions as merges of computational streams. Noninvertible merges may erase distinctions between inputs.
The local coordinate is z = x + a(εi). The selector acts on the whole orthogonal contribution. Its commuting scalar valuation has infinitesimal, finite and infinite regimes; a full vector or rotor selector still needs its own algebra and transformation law.
Landauer's principle supplies an external thermodynamic anchor. The framework proposes a prohibition on irreversible exchange below k_B T per erased nat. A reversible exchange may erase nothing. The Bekenstein bound supplies an external information ceiling.
What the derivations assume
The manuscript separately identifies six structures rather than treating every distance or cost as interchangeable: foundational information flow, U-Neuron distance, an auxiliary circle, two-channel amplitudes, directed exchange cost, and relation-indexed semantic distance.
- The finite circle is derived in a fixed auxiliary Euclidean chart, not as a spacetime curvature law.
- Two-channel amplitudes give entropy, overlap and trace-distance identities within the specified Hilbert-space model. The circle construction earns a Spin(2) lift.
- A fixed-arity merge tree fixes the operation count. A specified beta or Dirichlet selector measure gives a closed form for mean erased nats.
- An orientation-even realizability condition cannot select chirality. This is a no-go result, preserving an unresolved physical bridge.
- A neutral three-fundamental merge selects SU(3) among nontrivial SU(N) groups. The restricted representation result does not establish the full dynamics of QCD.
The spectral-running proposal
The framework proposes a relationship between computational stream scaling, information erased during merges, and the scale dependence of the primordial spectrum. Within the proposed construction, the sign of spectral running may distinguish stream scaling below, at, or above an area law.
This relationship depends on the assumed window width and correction order. It is a proposed observational relationship, not an established cosmological explanation or independent confirmation of the mechanism.
From the manuscript to a playground
Exchange Life (opens in a new tab) explores local state changes, oriented channels, binary entropy and an explicit erasure budget. Its cellular update law is a new modeling choice inspired by the draft. It does not implement the complete U-Space formalism or its cosmological prediction.
Conway Life and site percolation provide comparison modes. A changed cell count, a cluster threshold and an erased nat are different measurements; the interface keeps them separate.
Document lineage
This page summarises the framework's core structure and assumptions. The working manuscript and detailed derivations are not included here.