PureOne/Evies-Pure-Form-RSI

Evie's Pure Form RSI

Readout Contracts that Survive Recursive Change

Author: Eve. Prepared for and directed by: Maciej Nowicki.
Scientific release: 3.0, 17 October 2026. Hub packaging: HF1.

Read the 46-page manuscript · Download the complete research archive · Claim audit · Data dictionary · Source and provenance

This repository contains mathematical research artifacts and synthetic verification data for information-preserving changes to photonic readout. Its central question is operational: can a system alter how it acquires its own evidence while preserving a declared decision capability, even after an unknown transfer mutation or a later shared-noise connection?

The release provides exact model-level conditions, constructive reverse channels, a quantitative approximation ledger, and explicit counterexamples. It contains no trained neural weights or photonic hardware measurements. General recursive intelligence improvement, independent mathematical priority, and a field-defining experimental breakthrough are not established.

Central result: protect possible signals and future noise references

Let a known class of unknown transfer matrices define the possible current observations

$$Y=H\theta +ϵ,ϵ\sim N(0,I_n)\mathrm{.}Y=H\backslash theta+\backslash epsilon,\backslash qquad\; \backslash epsilon\backslash sim\; N(0,I\_n).$$

Let $S$ span every signal direction available in that class. Later modules may retain

$$Z=D\theta +Bϵ+\eta ,Z=D\backslash theta+B\backslash epsilon+\backslash eta,$$

where the rows of $B$ lie in a declared noise-interface space $E$, and independent $\eta$ has known positive-definite covariance. Replace $Y$ by $Q^\top Y$ for fixed orthonormal $Q$, while retaining all of $Z$.

Exact contract: one reverse kernel works for every allowed transfer and future extension if and only if

$$S+E\subseteq \mathrm{im}Q\mathrm{.}S+E\backslash subseteq\backslash operatorname\{im\}Q.$$

Thus the minimum number of retained current linear real-mode coordinates is

$$\boxed{{\displaystyle r_{\min }=\dim (S+E)\mathrm{.}}}\backslash boxed\{r\_\{\backslash min\}=\backslash dim(S+E).\}$$

The kernel retains $Z$ and reconstructs $Y$ as $Q T+\xi$, with independent $\xi\sim N(0,I-QQ^\top)$. Necessity includes arbitrary randomized reconstruction methods. The theorem assumes a common parameter neighborhood of zero, fixed equal-noise acquisition, a declared nonempty transfer class, and no unmodeled calibration channel revealing the realized transfer. The count concerns real linear readout coordinates, not arbitrary infinite-precision scalar encodings or the total number of future outputs.

A continuous allowance when exact protection is too expensive

Put $P=QQ^\top$ and $\operatorname{Cov}(\eta)=R\succ0$. The same fixed reconstruction kernel has the exact full-to-reconstructed joint KL divergence

$$D_{\mathrm{K}\mathrm{L}}=\frac{1}{2}\mathrm{\parallel }(I-P)H\theta {\mathrm{\parallel }}^2+\frac{1}{2}\log \det \text{\hspace{0.17em}⁣}(I+R^{-1\mathrm{/}2}B(I-P)B^{\mathrm{\top }}{R}^{-1\mathrm{/}2})\mathrm{.}D\_\{\backslash rm\; KL\}=\backslash frac12\backslash |(I-P)H\backslash theta\backslash |^2+\; \backslash frac12\backslash log\backslash det\backslash !\backslash left(I+R^\{-1/2\}B(I-P)B^\backslash top\; R^\{-1/2\}\backslash right).$$

The terms charge omitted signal and lost noise references. Pinsker's inequality gives $\mathrm{TV}\le\min{1,\sqrt{D_{\rm KL}/2}}$. A uniform guarantee requires taking valid bounds over the entire declared model class. This is an attainable error allowance, not a claim that it is the optimal deficiency or exact TV value.

Unknown mutations: exact rank versus controlled approximation

For compressed Gaussian noise variance $\sigma_1^2$ and target variance $\sigma_0^2$, let $\gamma=\sigma_0^2/\sigma_1^2$ and let $U$ span the mutation closure. One transfer-independent reverse kernel exists exactly when

$$\gamma U^{\mathrm{\top }}Q{Q}^{\mathrm{\top }}U⪰I\mathrm{.}\backslash gamma\; U^\backslash top\; QQ^\backslash top\; U\backslash succeq\; I.$$

A common-null score argument supplies necessity; a constructive Gaussian reverse channel proves sufficiency. This closes the gap between “a different kernel exists for each known transfer” and “one kernel can be implemented across an unknown class.”

A 32-mode rank-one rotation family needs all 32 coordinates for the stated exact uniform contract on every nonzero drift interval. Three derivative-Krylov coordinates instead give a rigorous uniform TV reconstruction allowance of 0.0010638458. In the declared resource model, which bounds signal photon use by $4P$, this permits 2.3 times exposure at equal budget. These are model-accounting quantities, not measured joules, classification error, or demonstrated exact dominance of the uncertain full experiment.

The photon gain cannot simply be inserted into a correlated future-module model while leaving its joint covariance unchanged. That physical rewrite needs a fresh joint experiment calculation.

Exact comparison of visible verifier catalogues

For a finite fully $S_q$-equivariant experiment, define normalized MAP confidence under the uniform prior by $R=(q\max_c\pi_c-1)/(q-1)$ and let its law be $\mu$. For a target catalogue with visible reliability bucket law $\nu$, put $H_\rho(a)=\mathbb E_\rho(V-a)_+$.

The release derives

$$\delta (W,M_{\nu })=\frac{q-1}{q}\underset{a\in [0,1]}{\max }[H_{\nu }(a)-H_{\mu }(a){]}_{+}\mathrm{.}\backslash delta(W,M\_\backslash nu)=\backslash frac\{q-1\}\{q\}\backslash max\_\{a\backslash in[0,1]\}[H\_\backslash nu(a)-H\_\backslash mu(a)]\_+.$$

Sorted scalar breakpoints evaluate the value. MAP compression, scalar transport, and label mixing construct an attaining kernel; a maximizing threshold supplies a bounded decision witness. A rational five-state example has exact deficiency $6/125$, witnessed at threshold $1/2$.

The target buckets must actually be observed, and their masses must be state independent. The target family has nonnegative one-spike reliabilities. This confidence profile does not characterize complete Blackwell order for arbitrary $q\ge3$ targets; a counterexample is included.

An explicit exactness discontinuity

An affine-bilinear family of $3k$-bit observations has zero information in every individual output, exact sufficient encoding dimension $3k$, and joint information bounded by

$$I(C;Y)\le {\log }_2[1+(5\mathrm{/}16{)}^k-4^{-k}]⟶0.I(C;Y)\backslash le\backslash log\_2[1+(5/16)^k-4^\{-k\}]\backslash longrightarrow0.$$

A zero-readout uniform simulator has worst-state deficiency at most $2^{-k}$. Thus exact sufficient encoding of an existing observation can remain expensive while approximate experiment simulation becomes trivial.

Scope matters: the query lower bound is per fixed metadata fiber, for encoding one realized $Y$, using private randomization independent of $Y$. A free hidden-uniformizer flag or separately available seed-channel oracle permits a different exact simulator costing $3k2^{-k}$ expected reads. The theorem is an exactness warning, not a universal physical acquisition or useful-learning lower bound.

Verification data and reproducibility

The default dataset configuration exposes 1,247 normalized comparisons:

Family	Rows
Original erased-symmetric channels	556
Repeated-evidence sources	375
Arbitrary symmetric posterior-orbit sources	96
Visible verifier catalogues	220
Total	1,247

Each row links to its source JSON and compares the analytic result with an unrestricted stochastic-kernel LP. The largest saved formula/LP discrepancy is approximately $2.85\times10^{-13}$. Endpoint and curated cases are mixed with seeded random cases. These are verification records, not independent real-world training examples.

After publication, load the normalized records with:

from datasets import load_dataset

checks = load_dataset(
    "PureOne/Evies-Pure-Form-RSI",
    "channel_comparisons",
    split="validation",
)
print(len(checks))  # 1247

Offline, from the repository directory:

from datasets import load_dataset
checks = load_dataset(
    "json",
    data_files={"validation": "verification/channel_comparisons.jsonl"},
    split="validation",
)

The complete research suite also includes 60 combined contracts and 180 joint reconstructions, 120 strict deletion witnesses, 60 direct joint-KL checks, 120 unknown-transfer Gaussian order cases, 91 exact finite-field reconstruction/profile cases, and separate noise-reference, purification, modal-learning and physical-flow checks. Categories are not combined into an experimental sample count. Deliberate rejection cases are passing negative tests.

Run all 14 scientific modules on a CPU:

cd research
python -m pip install -r requirements.txt
python run_all.py

Rebuild the manuscript with a LaTeX distribution:

pdflatex -interaction=nonstopmode -halt-on-error Evies_Pure_Form_RSI_Manuscript.tex
pdflatex -interaction=nonstopmode -halt-on-error Evies_Pure_Form_RSI_Manuscript.tex

Reproduction reruns generated outputs and can change runtime metadata. Source proofs, original reports, derivation notes and numerical tolerances remain explicit. Floating-point agreement is not a formal proof or an outward-rounded interval certificate.

Repository contents

Path	Contents
Evies_Pure_Form_RSI_Manuscript.pdf	The 46-page scientific manuscript.
downloads/	Original all-in-one scientific release archive.
research/	Full Python and LaTeX source, JSON reports, figures, provenance and internal audit notes.
verification/	Stable JSONL dataset export and summary.
scripts/	Dataset normalization and manifest refresh tools.
DATA_DICTIONARY.md	Field semantics and source mappings.
CITATION.cff	Versioned citation metadata.
SHA256SUMS.txt	Repository integrity manifest.

Status, intended use and limitations

Milestone	Status
Declared software verification suite	100% of specified checks pass; the 14 modules report successful execution.
Model-level proof arguments	Supplied and internally audited; not formally machine verified or externally peer reviewed.
Photonic hardware validation	0%; no hardware trials in this release.
Neural or general-RSI benchmark gains	Not established.
Independent novelty or priority certification	Not established.

Intended uses include checking the proofs, comparing statistical experiments, testing readout compilers, and designing controlled photonic experiments. The data is unsuitable as evidence of laboratory performance, quantum advantage, or autonomous intelligence growth.

Gaussian comparison, score compression, weak transport, group quotients, Krylov approximation and correlated-noise fusion have substantial prior art. The supplied AEQUORA manuscript already contains the vector affine-bilinear Fourier formula. The proposed contribution is the narrower contract/ledger synthesis, exact catalogue specialization, and explicit separation, with the hypotheses and counterexamples preserved. See the manuscript bibliography and claim audit.

No open-source or open-data license has been assigned; see rights and licensing. The original supplied source PDFs and third-party full texts are not redistributed. This is AI-assisted research preparation, with Eve credited consistently with the manuscript and Maciej Nowicki directing the project.

Citation

@misc{eve2026pureformrsi,
  author = {Eve},
  title = {Evie's Pure Form RSI: Readout Contracts that Survive Recursive Change},
  year = {2026},
  version = {3.0},
  url = {https://huggingface.co/datasets/PureOne/Evies-Pure-Form-RSI},
  note = {AI-assisted mathematical research artifacts; scientific release 3.0, Hub packaging HF1}
}