---
pretty_name: "OQAIVAEI: Intervention-Complete Memory and the Price of Scientific Reuse"
language:
- en
size_categories:
- n<1K
tags:
- mathematics
- information-theory
- experimental-design
- memory-compression
- linear-algebra
- quantum-information
- synthetic
- reproducible-research
configs:
- config_name: claims
  default: true
  data_files:
  - split: train
    path: data/claims.jsonl
- config_name: announcement_family
  data_files:
  - split: train
    path: data/announcement_family.jsonl
- config_name: memory_frontier
  data_files:
  - split: train
    path: data/memory_frontier.jsonl
- config_name: divisible_blocks
  data_files:
  - split: train
    path: data/divisible_blocks.jsonl
---

# 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](research/manuscript/EVE_OQAIVAEI_Manuscript.pdf) | 101 pages, 11 chapters, three appendices, and 27 references |
| [Complete original research archive](releases/EVE_OQAIVAEI_Complete_Research_Package_v1.zip) | The unchanged 83-file research release |
| [Research instructions](research/README.md) | Reproduction, package map, and mathematical scope |
| [Claim ledger](research/docs/claims.json) | Assumptions, proof locations, computational evidence, and novelty status |
| [Original execution report](research/results/reproducibility_report.json) | Eight-stage computational record and executed-source hashes |
| [Renamed-edition verification report](verification/EVE_OQAIVAEI_Verification_Report.json) | Manuscript and archive hashes, environment, and verification scope |
| [Dataset documentation](docs/DATASETS.md) | Four configurations, column definitions, and provenance |
| [Packaging notes](docs/RELEASE_NOTES.md) | 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

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

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

$$m=\frac{h_1-2h_2-2h_3}{3}.$$

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

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

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](research/results/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](research/docs/claims.json) 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.

```python
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:

```python
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](docs/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](verification/packaging_replay.json) and [content audit](verification/content_audit.json) 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:

```bash
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:

```bash
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.

```bibtex
@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](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](LICENSE_STATUS.md).