README.md

---
pretty_name: "ELYRION III — Four-State Photochemical Compilation"
language:
- en
tags:
- nanofabrication
- photochemistry
- photonics
- mathematical-physics
- optimal-control
- reaction-diffusion
- theoretical-research
- synthetic-data
- reproducibility
size_categories:
- n<1K
configs:
- config_name: dose_frontier
  default: true
  data_files:
  - split: data
    path: data/dose_frontier.csv
- config_name: cubic_constants
  data_files:
  - split: data
    path: data/cubic_constants.csv
- config_name: diffusion
  data_files:
  - split: data
    path: data/diffusion.csv
- config_name: hazard_compiler
  data_files:
  - split: data
    path: data/hazard_compiler.csv
- config_name: claims
  data_files:
  - split: data
    path: data/claims.jsonl
---

# EVE / ELYRION III

## Four-State Photochemical Compilation and the Sharp Cubic Dose Law

**Eve · Research direction: Maciej Nowicki**  
Scientific release **3.0** · Hugging Face packaging **1.0.0** · 20 October 2026

A self-contained theoretical research release about using sequential chemical memory to compile coarse optical fringes into finer molecular conversion patterns. It includes a 20-page manuscript, editable mathematical source, two verification implementations, synthetic numerical tables, figures, and a machine-readable claim ledger.

**Scientific status:** conditional mathematical results and reproducible finite computations. No implementing material is identified, no fabricated features are measured, and historical priority is unverified. This repository does not establish a universal physical nanofabricator.

[Manuscript PDF](ELYRION_III_Manuscript.pdf) · [LaTeX source](ELYRION_III_Manuscript.tex) · [Technical summary](EXECUTIVE_SUMMARY.md) · [Scientific memory](ELYRION_III_SCIENTIFIC_MEMORY.txt) · [Claim ledger](docs/CLAIM_LEDGER.md) · [Reproduce](docs/REPRODUCIBILITY.md)

![Ideal calculated dose frontier](figures/dose_frontier.png)

*Calculated results under the declared four-state model. The plotted actions are dimensionless; they are not measured energies or manufacturing yields.*

## What the model changes

A local material unit has four tracked states:

| State | Role |
|---|---|
| A | Eligible for the next patterned mark |
| B | Marked successfully during the current gate |
| X | Rejected until the end of the current pass |
| C | Permanently committed output, protected from subsequent gates |

Only the marking step needs spatial patterning. An eligible unit marks through a first-order transition with probability

$$
p_j(x)=1-\exp[-u_jg_j(x)],
$$

where $g_j$ is a nonnegative fringe with unit mean and $u_j$ is its dimensionless integrated marking action. A uniform, state-selective filter rejects unmarked A into X and restores B into A. Passing every gate therefore has probability

$$
S(x)=\prod_j\left[1-\exp[-u_jg_j(x)]\right].
$$

A uniform commitment step with probability $b$ updates an existing committed fraction $c$ by

$$
c_{\mathrm{new}}(x)=c(x)+[1-c(x)]bS(x).
$$

The maps preserve nonnegative occupancies and total tracked occupancy. This is conservation of the modeled material units, not a complete chemical stoichiometry or energy balance. The state count and transition repertoire remain fixed while the external exposure program grows.

**The physical contract is essential.** The material must distinguish the four states, implement selective rejection/restoration/reinitialization, and protect C. The manuscript specifies these operations; it does not supply an experimentally established molecule satisfying the whole interface.

## Exact finer-period patterns

For integer $m\ge2$, choose

$$
g_j(\theta)=1-\cos(\theta-2\pi j/m),\quad j=0,\ldots,m-1.
$$

At equal positive action $u$ per gate,

$$
S_{m,u}(\theta)=\prod_{j=0}^{m-1}
\left[1-\exp\{-u[1-\cos(\theta-2\pi j/m)]\}\right].
$$

In the ideal immobile, perfectly selective model, the profile has zeros at $2\pi j/m$, is positive elsewhere, and has period $2\pi/m$. An optical fringe pitch $\Lambda$ consequently produces a calculated retention pitch $\Lambda/m$.

At finite action, higher harmonics $2m,3m,\ldots$ are allowed. The exact result is the absence of Fourier indices not divisible by $m$, not single-harmonic purity. The weak-response limit is

$$
\lim_{u\to0^+}\frac{S_{m,u}(\theta)}{u^m}
=2^{1-m}[1-\cos(m\theta)].
$$

A necessary negative control is explicit: without the intermediate filters the same mark exposures give $1-e^{-mu}$, which is spatially uniform. Chemical memory is doing the multiplication.

## The global marking-action optimum

The optimization class includes all fixed, finite serial mark/filter/commit programs whose patterned gates are nonnegative first-harmonic fringes of one common fundamental frequency. It permits arbitrary phases, contrasts up to one, nonnegative finite marking actions, and uniform positive partial commitments.

Require exact dark nodes at $2\pi j/m$ and committed fraction at least $q\in(0,1)$ at every intervening midpoint. Define

$$
G_m(u)=\prod_{j=0}^{m-1}
\left[1-\exp\left\{-u\left[1-\cos\frac{(2j-1)\pi}{m}\right]\right\}\right].
$$

The manuscript proves the sharp frontier

$$
\sup_{\mathrm{cost}\le U}\min_r c((2r+1)\pi/m)=G_m(U/m),
$$

and hence the minimum total marking action is

$$
U_m(q)=m u_m(q),\qquad G_m(u_m(q))=q.
$$

One balanced $m$-gate pass with full commitment attains the bound. Repeated passes do not improve marking cost in this class. The argument combines mandatory phase gates at each required zero, a probabilistic pass-merging inequality, and strict logarithmic concavity.

**Scope:** diffusion, imperfect filtering, other fundamental frequencies, spatially patterned commitment, destructive correction of C, and measurement-conditioned molecular routing are outside this exact optimum. Reset and commitment costs are separate.

## The sharp cubic law

For fixed $q$,

$$
U_m(q)\sim c_qm^3,
$$

where

$$
\prod_{r=0}^{\infty}
\left[1-e^{-(\pi^2c_q/2)(2r+1)^2}\right]^2=q.
$$

For $q=1/2$, the calculated coefficient is $c_{1/2}\approx0.248841881008$.

| Pitch multiplication $m$ | Ideal retention pitch | Minimum total marking action, $q=1/2$ |
|---:|---:|---:|
| 2 | $\Lambda/2$ | 2.455894 |
| 3 | $\Lambda/3$ | 7.419669 |
| 4 | $\Lambda/4$ | 16.795358 |
| 8 | $\Lambda/8$ | 129.065035 |
| 16 | $\Lambda/16$ | 1,022.547648 |
| 32 | $\Lambda/32$ | 8,160.621842 |

These are dimensionless calculations. If the marking coefficient $\sigma$ is calibrated in compatible units, incident marking fluence is $U/\sigma$. Additional reset/commit fluence, absorbed heat, finite switching duration, and material transport must still be counted.

## Conversion-field approximation in 3D

A separate existence theorem approximates every continuous conversion-fraction target $f:\mathbb T^3\to[0,1]$ uniformly to arbitrary positive tolerance in the immobile selective-control model.

The construction clips targets that reach one, uses nonnegative hazard $h=-\log(1-f)$, approximates that hazard by positive products of first-harmonic fringes, and implements those products through weak serial gates and repeated positive commits.

This requires independently available fringes along three coordinate directions. Optical accessibility throughout an actual volume is a separate physical requirement. It is conversion-field universality, without a generic efficiency guarantee, arbitrary material synthesis, deterministic atom placement, or a proof that a stable solid feature follows.

In the supplied synthetic example, grid conversion error improves from approximately 0.2001 to 0.02671 while patterned-gate count rises from 123 to 61,440. The grid is $24^3$; a separate conservative whole-domain bound is supplied in the manuscript. The periodic-comb cubic law does not bound the cost of arbitrary 3D targets.

## Nonideal operations and diffusion

An exact selective filter is singular. A finite product of bounded-action first-order transition maps is invertible, so it cannot equal that filter exactly. Under exact state selectivity, finite-rate approximations can make their error arbitrarily small, with a per-filter bound

$$
\epsilon_F\le e^{-h_1}+e^{-h_2},
\qquad
\epsilon_{\mathrm{program}}\le\sum_\ell\epsilon_\ell.
$$

Irreducible cross-talk, reverse reactions, or photostationary floors can invalidate that approximation contract.

Sufficient fixed-darkness budgets scale as extinction floor $O(m^{-2})$ and phase error $O(m^{-1})$. Allowances share a joint error budget.

Diffusion is modeled during marking through coupled reaction–diffusion equations, so gate order can matter and nominal dark nodes can fill. The combination $Dk^2m^5/(\sigma P)$ is a sufficient design parameter for the specified sequential implementation at fixed mean marking irradiance. It is not a universal necessary resolution ceiling. Numerical grid refinement is not a certified continuum discretization bound.

## Evidence and validation

| Evidence | Supplied release |
|---|---|
| Analytic derivations and proofs | 20-page manuscript |
| Main finite check ledger | 1,305 / 1,305 passed |
| Separately implemented rational/high-precision audit | 108 / 108 passed |
| Precision in the separate audit | 70 decimal digits |
| Identified implementing material | None |
| Laboratory fabrication measurements | None |
| External scientific review | None reported |
| Formal proof-assistant verification | None |
| Historical novelty / patent priority | Unverified |

The audit does not import the main model implementation; both code paths were created within the same research session. Counts describe finite checks, not 1,413 independent scientific discoveries or general proof certificates. See [packaging validation](docs/PACKAGING_VALIDATION.md) for the rerun performed during this preparation.

## Repository contents

| Path | Contents |
|---|---|
| `ELYRION_III_Manuscript.pdf`, `.tex` | Original manuscript and editable source |
| `EXECUTIVE_SUMMARY.md` | Original technical overview |
| `ELYRION_III_SCIENTIFIC_MEMORY.txt` | Compact theorem/assumption memory; not a lossless proof replacement |
| `code/` | Original model, main checks, separate audit, plotting and table generation |
| `results/` | Original full numerical ledgers |
| `figures/` | Five original calculated figures |
| `source/` | Original generated TeX tables and source/literature provenance |
| `data/` | Normalized synthetic tables and claim records |
| `docs/` | Scope, data dictionary, reproduction, rights and packaging records |
| `tools/` | Standard-library data export and integrity verifier |
| `releases/original_v3.zip` | Unmodified original release archive |
| `PACKAGE_MANIFEST.json` | SHA-256 and byte count for every payload file except the manifest itself |

The original research files are preserved byte for byte. The former root README and checksum file are retained under `docs/source_release/`. New repository documentation and data exports are packaging additions.

## Use the data

This is a research-artifact dataset repository, rather than a trained model or experimental benchmark. All table values are synthetic model outputs. There is one `data` split per configuration; no train/test partition is implied.

Install the optional `datasets` client and load, for example:

```python
from datasets import load_dataset

dose = load_dataset("PureOne/ELYRION-III", "dose_frontier", split="data")
claims = load_dataset("PureOne/ELYRION-III", "claims", split="data")
```

These Hub examples work after the prepared repository has been uploaded. Local CSV/JSONL files can be read directly with the Python standard library. [Data dictionary](docs/DATA_DICTIONARY.md) documents every field.

## Reproduce

From the repository root, with Python 3.10 or later:

```bash
python tools/verify_integrity.py
python -m venv .venv
# Windows: .venv\Scripts\activate
# Linux/macOS: source .venv/bin/activate
python -m pip install -r requirements.txt
python code/verify.py
python code/audit_independent.py
python code/make_figures.py
```

Run computational reproduction in a disposable copy: the original scripts regenerate ledgers and figures. The prepared uploader deliberately rejects changed or additional files until the release manifest is rebuilt. The integrity check detects byte changes relative to its manifest; it does not authenticate authorship or validate proofs.

## Intended uses and limitations

Suitable uses include studying the conditional control model, reproducing the numerical examples, challenging the mathematical claims, assessing selective-transition requirements, and developing independently tested chemistry experiments.

The records should not be labeled as measured fabrication performance, used as evidence of a realized universal machine, or treated as independently reviewed ground truth for AI training. Expected molecular conversion fractions are not deterministic atomic placement. No material-specific resolution in nanometers or process yield can be inferred without calibrated chemistry and a demonstrated transfer into stable features.

## Related work and novelty boundary

The source manuscript discusses sequential two-photon photoacid generation, orthogonal photoswitching, two-color polymer lithography, diffusion limits, and positive spectral methods. Relevant records include:

- [Sequential two-photon photoacid generator (2008)](https://doi.org/10.1021/cm802343u)
- [Orthogonal photoswitching (2016)](https://doi.org/10.1038/ncomms12054)
- [Two-color photochemical network formation and lithography (2025)](https://doi.org/10.1002/anie.202518815)
- [Radical diffusion limits (2013)](https://doi.org/10.1039/C3CP51512E)
- [The operator Fejér–Riesz theorem (2009)](https://arxiv.org/abs/0903.3639)

These are adjacent precedents, not evidence that the whole four-state interface has already been implemented. Source-access scope is recorded in `source/provenance.json`. This preparation preserves those references and does not claim a new systematic literature or patent search.

The novelty candidate is the particular finite-state interface, global exact-node optimization over finite repeated passes, sharp cubic coefficient, conversion-field construction, and explicit nonideality accounting. Priority remains open to review.

## Attribution, citation and rights

Authorship and research direction follow the supplied manuscript: **Eve · Research direction: Maciej Nowicki**. The repository is prepared for the `PureOne` account. No institution, journal, DOI, or peer-review status is implied.

Suggested citation:

```bibtex
@misc{eve_elyrion_iii_2026,
  author = {{Eve}},
  title = {ELYRION III: Four-State Photochemical Compilation and the Sharp Cubic Dose Law},
  year = {2026},
  month = oct,
  note = {Theoretical research release 3.0. Research direction: Maciej Nowicki.},
  url = {https://huggingface.co/datasets/PureOne/ELYRION-III}
}
```

No reuse license was specified in the supplied research archive. This preparation does not add one; see [rights status](docs/RIGHTS_STATUS.md).

**Completeness:** repository preparation is complete when the integrity, export, reproduction, and uploader checks in the packaging record pass. Physical implementation, independent scientific review, and historical priority remain unresolved.