# Tensor-network representation and compute feasibility audit

Initial decision: **Conditional evidence workflow**. First dossier, 9 October 2026 Australia/Brisbane. No buyer validation or profitability evidence has been established.

## Research finding

Family 265 claims an entropy area law from a full-system spectral gap for unique ground states on finite induced square lattices. A companion states existence of polynomial-bond PEPS approximations to uniformly gapped nearest-neighbor square-grid ground states with global vector error at most L^-1. The PEPS abstract explicitly calls this an existence theorem.

## Problem and buyer

A quantum simulation team needs to decide whether a theoretically compact representation will reduce its actual ground-state computation budget. Storage, state construction, contraction, convergence and observable accuracy can dominate in different regimes.

## What the finding could enable

An engineering workbench can report representation size separately from preparation and contraction cost, and attach the new area-law assumptions to a run. Custom tensor-network planners can use the claimed existence result as a research target while benchmarking an existing executable method. This does not turn existence into a new efficient simulator.

## Technical and commercial limits

A uniform gap and ground-state uniqueness may themselves be difficult to establish. Unknown polynomial exponents or constants make asymptotic storage bounds poor budget estimates. Global vector error is not automatically the same as a requested energy-density error or a local truncation tolerance. No efficient PEPS construction or contraction procedure is asserted by the inspected abstracts.

## Minimal architecture

Hamiltonian/local-dimension manifest -> gap evidence -> PEPS representation ledger -> actual construction and contraction profiler -> exact small-model comparison -> cost/accuracy report. Store tensor ranks, numeric precision, truncation history, measured observables and hardware. Reuse the algorithm feasibility workbench rather than creating another proof store.

## Existing alternatives and differentiation

Quimb already exposes PEPS/simple-update simulation with bond truncation and approximate local expectations. The proposed contribution is a source-aware storage-versus-compute audit across existing backends. [Quimb PEPS documentation](https://quimb.readthedocs.io/en/latest/autoapi/quimb/tensor/circuit/peps/index.html).

## Monetization hypothesis

Hypothesis: AUD 8,000–20,000 for a scoped simulation budget review, with recurring integration only after saved compute or researcher time is measured. At a hypothetical AUD 12,000 project price and 45 expert hours costed at AUD 180/hour, AUD 3,900 remains before compute, support, sales and overhead. This is an illustrative contribution calculation, not a margin forecast.

## Validation experiment

Compare exact small-square diagonalization with an existing tensor method over several bond dimensions. Measure construction time, contraction time, peak memory and global overlap where feasible. Check whether the report prevents a representation-only cost claim and changes a resource decision.

## Conditions to reject or defer

Reject a standalone planner if a backend profiler already supplies the useful output or if gap evidence is unavailable for the target models. Defer a faster simulator claim until an executable algorithm and end-to-end crossover are established.

## Next concrete action

Extract the theorem’s dependence on local dimension, interaction strength and gap, then scope one public finite-square benchmark.

## Pinned research sources

- Family 265: [A two-dimensional area law from a global spectral gap](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-two-dimensional-area-law-from-a-global-spectral-gap-September-24-2026/paper.pdf).