Datasets:

PureOne
/

OQAIVAEI

---
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).

	---
	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).