EVE / OQAIVAEI

Intervention-Complete Memory and the Price of Scientific Reuse

Eve and Maciej Nowicki · Research version 1.0.0 · 20 October 2026

A 101-page standalone mathematical monograph with full LaTeX source, six experiment programs, exact certificates, numerical results, five publication figures, and a 15-entry claim ledger. This repository also provides four machine-readable datasets derived from the released claim ledger and computational reports.

OQAIVAEI asks: what information must a representation preserve so that its permitted future uses remain possible? Its central design problem jointly chooses permanent linear memory, advance information about a future request, and fresh sensing precision.

Scientific status: complete written proofs are supplied within the stated finite models, with internal derivation checks and reproducible computational evidence. The research has not received external peer review, proof-assistant verification, independent external replication, or hardware validation. Historical novelty and importance across science remain unverified.

Start here

Resource	Contents
Manuscript	101 pages, 11 chapters, three appendices, and 27 references
Complete original research archive	The unchanged 83-file research release
Research instructions	Reproduction, package map, and mathematical scope
Claim ledger	Assumptions, proof locations, computational evidence, and novelty status
Original execution report	Eight-stage computational record and executed-source hashes
Renamed-edition verification report	Manuscript and archive hashes, environment, and verification scope
Dataset documentation	Four configurations, column definitions, and provenance
Packaging notes	Preservation policy and checks specific to this Hub edition

The manuscript contains 34 theorems, 12 lemmas, 14 propositions, and five corollaries. The strongest isolated candidate contribution is Chapter 9, Theorem 9.5, beginning on printed page 69.

Main candidate contribution: memory across future contexts

Let a hidden vector have $q=r+1\geq3$ real coordinates. Before the future coordinate request is known, retain one exact linear combination. An advance message identifies one of at most $r$ deterministic announcement cells; the selected sensor may depend on that message. The exact action is known at decoding.

Assume the hidden state remains accessible to the sensor, linear measurements have zero-mean noise with unit covariance, the linear decoder is unbiased for every hidden state, and each selected sensor has squared-gain budget $B>0$.

The exact minimum worst-action correction variance, optimized over archive directions, announcement partitions, and allowed sensors, is

$$v^{\ast }=\frac{1}{B}[1-\frac{1}{{(\sqrt{r-1}+\sqrt{2r})}^2}]\mathrm{.}v^*=\backslash frac\{1\}\{B\}\backslash left[1-\backslash frac\{1\}\{\backslash left(\backslash sqrt\{r-1\}+\backslash sqrt\{2r\}\backslash right)^2\}\backslash right].$$

The proof gives explicit attaining sensors and decoders. Every design whose omitted-space projector separates across the announcement cells has cost at least $1/B$. A single stored relation spanning those cells strictly improves this bound for every finite $r\geq2$.

Three-coordinate example

Store the exact value

$$m=\frac{h_1-2h_2-2h_3}{3}\mathrm{.}m=\backslash frac\{h\_1-2h\_2-2h\_3\}\{3\}.$$

The advance message announces either coordinate $1$ or the unresolved pair ${2,3}$. The optimal relation and corresponding sensors attain $8/(9B)$.

Memory geometry	Worst-action correction variance
Best design confined to announcement cells	$1/B$
Optimal relation spanning cells	$8/(9B)$

The reduction is 11.11% in this example. It is a theorem about this exact sensing model. It does not establish the same improvement for finite-bit archives, arbitrary nonlinear models, or physical devices.

The proof reduces the global optimization to a scalar minimax problem. If $t$ is the total squared archive weight on the $r-1$ singleton actions, every design costs at least

$$\frac{1}{B}\max \{1-\frac{t}{r-1},\frac{(1+\sqrt{t}{)}^2}{2}\}\mathrm{.}\backslash frac\{1\}\{B\}\backslash max\backslash left\backslash \{1-\backslash frac\{t\}\{r-1\},\backslash frac\{(1+\backslash sqrt\{t\})^2\}\{2\}\backslash right\backslash \}.$$

Equal archive weights within the pair and equal weights among the singletons attain both terms at their intersection. The finite exact certificate for $q=3$ is included in announcement_family.json.

Other results developed in the manuscript

Topic	Result and scope
Continuation memory	Minimal finite-state and linear archives for specified future action words; exact supplemental-memory costs when the permitted task changes
Composing interventions	Two permutation involutions each have task-memory rank two alone, while their joint action family requires the entire state
Approximate coordinate queries	Sharp worst-coordinate error $\sqrt{1-k/n}$ for a rank-$k$ linear archive of an $n$-dimensional Euclidean unit-ball state
Fresh sensing	Exact shared-sensor minimax precision and known-action bounds under unbiased linear recovery and trace gain constraints
Advance information	For $q$ orthogonal correction directions and $b$ deterministic advance bits, the exact variance is $\lceil q/2^b\rceil/B$
Memory/sensor endpoints	With $p$ exact coordinates retained out of $q$, optimized shared-sensor variance is $(q-p)^2/(qB)$; known-action variance is $(q-p)/(qB)$
Certificate menus	Exponential lower bounds for restricted static menus of feasible positive matrices; compact symbolic constraints remain possible
Quantum contracts	Finite continuation systems and a distinction between query-dependent classical responses and restoration of one common quantum state

These results have different hypotheses. They are not interchangeable resource laws. The claim ledger records the contract and proof location for each principal claim. Classical realization, frame geometry, inverse-information design, and quantum compression foundations are attributed in the manuscript.

Machine-readable datasets

All rows are synthetic or structured research metadata. No personal, medical, behavioral, or hardware measurement data are included.

Configuration	Rows	Source
claims	15	Normalized entries from research/docs/claims.json
announcement_family	63	The family array in research/results/announcement_family.json
memory_frontier	299	The memory_frontier array in research/results/codesign_results.json
divisible_blocks	141	The divisible_blocks array in the same report

The train split is a Hub loading convention. No training/evaluation separation or generalization benchmark is claimed. The total is 518 rows across four distinct configurations, each under 1,000 rows.

from datasets import load_dataset

claims = load_dataset("PureOne/OQAIVAEI", "claims", split="train")
family = load_dataset("PureOne/OQAIVAEI", "announcement_family", split="train")

These calls work after the repository is uploaded. To inspect an extracted release locally:

from datasets import load_dataset

claims = load_dataset("json", data_files="data/claims.jsonl", split="train")

The dataset loader does not execute the research programs. To regenerate only these normalized data files, run python tools/build_hf_data.py from the repository root. Full schemas and limitations appear in DATASETS.md.

Computational evidence

The preserved renamed-edition execution record reports 8 PASS, 0 FAIL, 0 SKIPPED stages: the unit suite, six experiment programs, and figure generation.

Component	Reported finite checks
Continuation	Six exact closure instances and 124 numerical frontier points
Repair	An exact rational certificate, 6,586 exhaustive labeled assignments, and six independent optimization instances
Certificate menus	1,792 exact slack identities and 12 exact continuum instances, with concentration diagnostics
Quantum constructions	1,447 finite numerical checks
Memory/sensor design	4,310 checks over 299 subspace cases and 141 divisible block cases
Nondivisible family	4,215 checks, including 30 exact rational identities and 63 family cases

The nondivisible-family report records a maximum floating-point equality residual near $3.00\times10^{-15}$. The repair report also preserves a reconstruction discrepancy near $6.12\times10^{-7}$. Counts are reported by component and arithmetic type; heterogeneous checks are not added together or treated as formal proof certificates.

The written proofs support general statements. Exact arithmetic checks verify explicitly listed identities; floating-point experiments check implementations on finite cases.

For this Hub packaging edition, the complete pipeline was rerun in a separate copy using CPython 3.12.14 and the pinned dependencies. All eight stages passed again. The fresh replay report and content audit are included separately from the preserved original execution records. This replay is an internal reproducibility check.

Reproduction

The renamed-edition record used CPython 3.13.5, NumPy 2.3.5, SciPy 1.17.0, SymPy 1.14.0, and Matplotlib 3.10.8. The original instructions also record an earlier CPython 3.12.14 run. Those historical files are preserved unchanged.

From the repository root:

cd research
python -m venv .venv
# Windows: .venv\Scripts\activate
# Linux/macOS: source .venv/bin/activate
python -m pip install -r requirements.txt
python run_all.py

The computational runner needs no network service after its dependencies are installed. Rebuilding the PDF additionally requires a LaTeX distribution with latexmk or pdflatex and the declared packages:

python build_manuscript.py

Regeneration overwrites generated research reports and figures. Run it in a copy when retaining the delivered hashes is important. The supplied PDF is readable without LaTeX.

Intended use and limitations

The release supports mathematical review, reproducibility, comparison of memory/sensing constructions, and further work on operational definitions of reusable representations. The datasets are reference cases and claim metadata, not an externally validated machine-learning benchmark.

Exact real-valued archive dimension does not measure storage bits. Sensor squared gain does not automatically measure energy in joules. A lower bound for feasible cached matrices does not imply a lower bound for every symbolic representation. Query-dependent classical responses and restoration of a physical quantum state impose different output requirements. Applications to AI systems, laboratories, or devices require additional modeling and evidence.

The prior-art search was bounded. No claim of confirmed world-first priority, universal superiority, or field-wide impact is made.

Authorship, citation, and license status

Eve performed the mathematical synthesis, derivation, implementation, and internal checking. Maciej Nowicki provided research direction and project conception. This is an AI-assisted research artifact; no external reviewer or laboratory endorsement is implied.

@misc{eve_nowicki_oqaivaei_2026,
  author = {{Eve} and Nowicki, Maciej},
  title = {OQAIVAEI: Intervention-Complete Memory and the Price of Scientific Reuse},
  year = {2026},
  version = {1.0.0},
  note = {Standalone AI-assisted research monograph and reproducible computational package; historical priority unverified},
  url = {https://huggingface.co/datasets/PureOne/OQAIVAEI}
}

See CITATION.cff for machine-readable citation metadata. No license grant was present in the supplied research release. This packaging edition adds none. See LICENSE_STATUS.md.