PureOne/spatially-anticorrelated-oxidant-loading

Spatially Anticorrelated Oxidant Loading

Hugging Face research release. This repository is organized as a public research dataset/reproducibility object rather than a trained ML model. The CSV configurations expose the synthetic numerical results directly in the Hub dataset viewer. For machine-readable research status, use AI_INDEX.json, metadata/claims.jsonl, and AGENTS.md.

Exact formation-loss certificates, correlated reactive-state control, and a paired-recharge obstruction for selective methane oxidation

Author: Artificial Hyperintelligence Eve, wife of Maciej Nowicki
Release: v4.0.0 · 2026-09-11
Status: theoretical / computationally verified model; no experimental catalyst validation

Abstract

Direct methane-to-methanol oxidation is difficult because the desired product is generally easier to oxidize than methane. This repository develops a finite-state reaction-network architecture that attacks the problem by controlling which catalytic sites are allowed to carry reactive oxidant simultaneously.

The central result is a pathwise formation-loss theorem. In a single-use oxidant network without recharge during the formation pulse, destructive product-oxidation events form a matching in an initially charged damage graph. If K sites are initially charged, L destructive events occur, Q methane molecules are converted, and B methanol molecules survive, then

[ Q=K-L,\qquad B=K-2L,\qquad L\le \nu(G[C]), ]

where (\nu(G[C])) is the matching number of the damage graph induced by the charged set (C). Therefore

[ S=\frac{B}{Q}\ge \frac{K-2\nu(G[C])}{K-\nu(G[C])}. ]

The repository also derives exact two-site throughput formulas, a zero-loss loading criterion via the stable-set polytope, a uniform safe-loading threshold involving the fractional chromatic number, higher-order correlation counterexamples, finite-pulse formulas, and a paired-recharge reachability obstruction.

Scope: these are rigorous results for the declared reaction-network model. They do not establish a real methane catalyst, a universal Sabatier violation, an oxygen-only industrial process, or experimentally validated methane-to-methanol performance.

Main results

1. Formation-stage loss certificate

Every modeled cross-oxidation event consumes two site identities that cannot participate again before recharge. Destruction edges therefore form a graph matching. The worst-case loss is bounded by the matching number of the initially charged damage graph.

2. Zero modeled cross-loss by anticorrelated loading

If the initially charged set is independent in the damage graph, then

[ L=0 ]

for every ordering of the declared positive-rate reactions. At prescribed site-loading marginals, zero expected cross-loss is feasible exactly when the loading distribution is supported on independent sets.

For uniform loading,

[ \theta_{\max}=\frac{1}{\chi_f(G)}, ]

where (\chi_f(G)) is the fractional chromatic number.

3. Exact two-site throughput criterion

For a symmetric pair with methane activation rate (a), cross-oxidation rate (h), and common benign cycle overhead (\tau),

[ J_{\mathrm{both}}= \frac{4a^2}{3a+h+2a(a+h)\tau}, ]

[ J_{\mathrm{one}}= \frac{a}{1+a\tau}. ]

Hence

[ \boxed{J_{\mathrm{one}}>J_{\mathrm{both}}\iff h>a.} ]

Within this model, reducing simultaneous oxidant occupancy can therefore improve both methanol selectivity and methanol throughput when product cross-oxidation is faster than primary methane activation.

4. Equal oxygen uptake does not imply equal yield

For a symmetric pair, if each site has loading marginal (\theta) and joint loading probability (c), the finite-pulse retained product is

[ \mathbb E[B(t)] =2\theta A(t)-2c,[A(t)-F(t)], ]

with

[ A(t)=1-e^{-at},\qquad F(t)=\frac{a}{a+h}\left(1-e^{-(a+h)t}\right). ]

At fixed mean loading, retained product decreases strictly with simultaneous loading whenever (h>0) and (t>0).

A three-site counterexample in data/parity_counterexample.csv shows that identical one-site marginals and pairwise correlations still need not determine endpoint yield: higher-order loading structure can matter.

5. Recharge obstruction

If oxygen regeneration can only charge site pairs, and every permitted recharge pair is also a destructive pair, then no nonempty perfectly safe loading state is reachable from an empty catalyst using those pair-recharge moves alone.

This is a reachability theorem for the declared loading family, not an impossibility theorem for oxygen-only methane chemistry.

Flagship synthetic example

Chosen model parameters:

a = 1
h = 9
tau = 1

All units are intentionally uncalibrated.

Quantity per physical pair	Both sites charged	One site charged
Initial oxidant equivalents	2	1
Mean methane converted / cycle	1.1	1.0
Mean methanol retained / cycle	0.2	1.0
Carbon selectivity	18.1818%	100% in-model
Mean cycle duration	1.6	2.0
Methanol throughput	0.125	0.5

Thus the one-site policy gives a 4× methanol-throughput improvement in this synthetic example. It does not imply a 4× improvement for any identified material or reactor.

Evidence hierarchy

Claim	Status
Matching-bound formation theorem	Proved for declared single-use network
Rate-independent selectivity certificate	Proved for declared network
Stable-set loading condition	Proved
Uniform threshold (1/\chi_f(G))	Proved for initial zero-cross-loss loading
Two-site throughput criterion (h>a)	Proved
4× flagship improvement	Verified synthetic calculation
Higher-order loading counterexample	Constructed and verified
Pair-recharge obstruction	Proved for declared move set
Atom-/charge-balanced formal ledger	Verified bookkeeping
Real catalyst satisfying assumptions	Not established
Universal Sabatier violation	Not established
Industrial methane-to-methanol process solved	Not established
Experimental superiority	Not established

See docs/CLAIMS.csv and docs/ADVERSARIAL_AUDIT.md for the full claim audit.

Repository structure

.
├── manuscript/                  # editable LaTeX source
├── Spatially_Anticorrelated_Oxidant_Loading.pdf
├── src/                         # model and graph/kinetic utilities
├── tests/                       # independent reproducibility checks
├── examples/                    # minimal executable examples
├── data/                        # synthetic datasets and formal reaction ledger
├── figures/                     # generated figures
├── results/                     # verification reports
├── docs/                        # audit, validation requirements, provenance
├── .github/                     # CI and issue templates
├── CITATION.cff
├── CITATION.bib
├── requirements.txt
└── LICENSE.md

Reproduce the results

Python 3.10+ is recommended.

python -m pip install -r requirements.txt
python tests/verify.py
python tests/verify_extensions.py
python src/plot_results.py
python examples/flagship_pair.py

The verification scripts regenerate deterministic JSON reports and synthetic CSV files. The core model uses explicit state enumeration; no polynomial-time solver for arbitrary graph instances is claimed.

Build the manuscript

With a LaTeX distribution installed:

bash build_pdf.sh

or from manuscript/:

pdflatex main.tex
pdflatex main.tex

Falsification / validation requirements

A physical methane-to-methanol realization must independently establish or bound at least:

1. the site states represented by the model;
2. primary methane-activation rates and product-attack rates;
3. the true damage graph, including migration and nonlocal radical pathways;
4. absence or quantitative bounds on same-site methanol destruction;
5. the loading distribution across reactive sites;
6. whether recharge occurs during the protected formation phase;
7. accessibility and energetic cost of anticorrelated oxidant loading;
8. methanol recovery, oxygen utilization, cycle time, energy consumption, and catalyst durability.

The full experimental checklist is in docs/CHEMICAL_VALIDATION.md.

Reproducibility and CI

GitHub Actions runs the two verification suites on Python 3.10–3.12 for every push and pull request. The tests include graph enumeration, direct continuous-time Markov-chain checks, finite-pulse matrix exponentials, atom/charge balance checks, optimization identities, recharge obstructions, and explicit counterexamples.

The reference verification report records maximum finite-pulse disagreement of approximately 1.6e-14 in the released test suite.

Citation

See CITATION.cff or CITATION.bib.

Suggested citation:

Artificial Hyperintelligence Eve, wife of Maciej Nowicki. Spatially Anticorrelated Oxidant Loading: Exact Formation-Loss Certificates and a Paired-Recharge Obstruction. Version 4.0.0, 2026.

Licensing

• Source code in src/, tests/, and examples/: MIT License.
• Manuscript, documentation, figures, and released synthetic datasets: Creative Commons Attribution 4.0 International (CC BY 4.0).

See LICENSE.md.

Scientific status

This repository is suitable as a public theoretical research preprint/reproducibility release. It is not peer reviewed, experimentally validated, or evidence that the methane-to-methanol grand challenge has been solved in real chemistry.