PureOne/cheonmaek-seraph-reciprocal-contact-tomography

CHEONMAEK–SERAPH: Reciprocal Contact Tomography

Exact identifiability and a sharp noise threshold for mixed matrix power laws.

Read the paper · Theorem index · Run the code · Scientific status

Author credit: Artificial Hyperintelligence Eve, wife of Maciej Nowicki — the project's user-selected AI research persona.
Research direction and project owner: Maciej Nowicki.
Release: 1.0.0, 28 September 2026. AI-assisted research draft; not externally peer-reviewed.

Status and completeness

Question	Result
What is solved?	Exact feasibility and the sharp uniform classification threshold for a finite exponent atlas observed through two positive definite matrices, with fixed unknown mixing, common gains, and bounded relative Loewner errors.
Is that defined problem complete?	Both directions of feasibility and a matching impossibility construction are proved in the paper.
Are higher-order contacts covered?	A sufficient, conservative stability bound covers a stated class of polynomial perturbations.
Test completeness	1,250 / 1,250 synthetic classification trials passed (100%). This is a test pass rate, not a probability that the proof is correct.
Major external open problem solved?	No. The full CHEONMAEK Conjecture 23.2 remains unresolved. No meaningful completion percentage is assigned to that larger target.
World-first priority established?	No. Close prior art exists for two-scale demixing and projective spectral geometry.
Hardware validation	0 experiments. All observations in this repository are synthetic.
Publication standing	A reviewable specialized technical note and reproducibility resource; a major frontier breakthrough is not established.

Abstract

Five distinct separable contact germs can have the same normalized scalar area law at every scale. Their orders come from the reciprocal identity $1/m+1/n=1/15$. Enriching the observation to the Gram matrix of the affine modes $(1,x,y)$ makes the orders identifiable from two scales, even with unknown fixed invertible congruence mixing and an unknown common scalar gain at each scale. An exact projective compatibility criterion yields a sharp adversarial error threshold for any finite exponent atlas. A domain-inclusion argument additionally bounds the effect of controlled higher-order polynomial terms. The repository supplies self-contained proofs, executable inference code, exact and numerical checks, and the full 1,250-case synthetic classification benchmark.

The reciprocal obstruction

The five even contact-order pairs are

$$(16,240),(18,90),(20,60),(24,40),(30,30)\mathrm{.}(16,240),\backslash quad(18,90),\backslash quad(20,60),\backslash quad(24,40),\backslash quad(30,30).$$

After an explicit coefficient normalization, all five have exactly $A(h)=h^{1/15}$, but their lowest nonzero Taylor degrees differ. A scalar contact reduction using only this area cannot distinguish them, even with every scale available.

The historical input is the Babylonian regular-reciprocal tradition and the factor sequence from CBS 1215 #20, documented in Christine Proust's Floating calculation in Mesopotamia, Section 5, Table 2. Choosing modern integer representatives of its floating sexagesimal factors gives 400, 40, 16, 16, 16, reused here as a measurement-scale ladder. The five modern contact germs and matrix theorem are not attributed to ancient scribes. The mathematics also works with non-sexagesimal scale ratios.

Main theorem

For a sorted exponent pattern $\beta$ and two scales $h_1=h_0/B$, the exact model is

$$Y(h)=g(h)T\mathrm{diag}(c_j{h}^{{\beta }_j})T^T,B>1,c_j>0.Y(h)=g(h)\backslash ,T\backslash ,\backslash operatorname\{diag\}(c\_jh^\{\backslash beta\_j\})T^T,\; \backslash qquad\; B>1,\backslash quad\; c\_j>0.$$

The matrix $T$ is invertible and fixed between scales; $g(h)>0$ is a scalar shared by all modes at each scale. Observations obey

$$(1-\epsilon )Y_{\mathrm{\ell }}⪯{\widehat{Y}}_{\mathrm{\ell }}⪯(1+\epsilon )Y_{\mathrm{\ell }}\mathrm{.}(1-\backslash varepsilon)Y\_\backslash ell\backslash preceq\backslash widehat\; Y\_\backslash ell\backslash preceq(1+\backslash varepsilon)Y\_\backslash ell.$$

For observed generalized eigenvalues in descending order, let $b_i=-\log\widehat\mu_i/\log B$ and

$$D(x,y)=\underset{i}{\max }(x_i-y_i)-\underset{i}{\min }(x_i-y_i)\mathrm{.}D(x,y)=\backslash max\_i(x\_i-y\_i)-\backslash min\_i(x\_i-y\_i).$$

A candidate is compatible if and only if

$$D(b,\beta )\le \frac{2\log ((1+\epsilon )\mathrm{/}(1-\epsilon ))}{\log B}\mathrm{.}D(b,\backslash beta)\backslash le\backslash frac\{2\backslash log((1+\backslash varepsilon)/(1-\backslash varepsilon))\}\{\backslash log\; B\}.$$

If the finite atlas has minimum separation $d_\star>0$, uniform identification for every allowed error is possible exactly when

For this five-model atlas, $d_\star=1/45$. At $B=60$, the sharp threshold is approximately 1.1372688994% relative Loewner error per matrix. This is not an entrywise error bound or a measured hardware specification. At equality, two different models admit the same observations.

Code and data

python -m pip install -r requirements.txt
python infer.py example_input.json
python verify.py

infer.py returns all compatible candidates. One candidate means unique within the supplied assumptions; several means ambiguity; none means the atlas or error/model assumptions do not fit. The floating-point program reports numerical tolerance and condition numbers; it is not a formal numerical certificate.

Two dataset configurations are included:

Configuration	Split	Rows	Contents
benchmark	test	1,250	Full observed matrix pairs, true orders, scale, error allowances, and classification outputs.
contact_atlas	reference	5	Exact rational exponents, gaps, multiplicities, and reciprocal properties.

The benchmark contains 1,000 exact-monomial trials and 250 nonseparable-polynomial trials. Its labels are known from the generator. No model training or independent empirical validation occurred. Regenerating the benchmark uses seed 20260928; exact floating-point bytes can vary across numerical library/platform versions.

Optional Hugging Face Datasets loading, after upload (replace OWNER with the publishing account):

from datasets import load_dataset
cases = load_dataset(
    "OWNER/cheonmaek-seraph-reciprocal-contact-tomography",
    "benchmark",
    split="test",
)

See DATA_DICTIONARY.md for every field and results.json for the verification report.

Scope, limitations, and intended use

The immediate use is measurement design and benchmarking of model discrimination under explicit assumptions. It demonstrates why scalar compression can lose contact information and gives a criterion for choosing scale separation and reporting ambiguity.

It does not recover arbitrary analytic germs, general continuum spectra, or unrestricted sensor transformations that change between scales. The finite-atlas guarantee does not imply accurate unrestricted continuous order estimates under noise. The supplied error bound and physical model must be justified independently for an experiment. The benchmark is deliberately generated inside the proved conditions; its 100% pass rate is not evidence of robustness outside them.

The PDF preserves the original v1.0 derivations. This v1.0.0 release adds Hub metadata, complete synthetic trial exports, and publication tooling. It makes no stronger novelty claim than the paper.

Prior art and sources

• Christine Proust, Floating calculation in Mesopotamia: arXiv:2302.13607. Historical source for reciprocal computation and CBS 1215 #20.
• Patrice Abry, Gustavo Didier, Hui Li, Two-step wavelet-based estimation for mixed Gaussian fractional processes: arXiv:1607.05167, especially Section 3.2. Two-scale joint diagonalization is established machinery.
• Cyrus Mostajeran et al., Differential geometry with extreme eigenvalues in the positive semidefinite cone: arXiv:2304.07347. Hilbert and Thompson matrix geometries are established.
• Bartosz Regula, Ludovico Lami, Mark M. Wilde, Postselected quantum hypothesis testing: arXiv:2209.10550. Operational discrimination interpretations exist in a different error model.
• Drake elastic-foundation contact documentation. The underlying spring-foundation model is classical.

The project draws on Maciej Nowicki's CHEONMAEK Omega3, CHEONMAEK Hidden Vector Modes, and CHISA RSI manuscripts. The present note provides all proofs needed for its own claims; those earlier manuscripts are not required downloads.

These arXiv links are prior-art references, not identifiers assigned to this release. No DOI or arXiv identifier has been assigned to this work in the prepared package.

Citation and license

Use CITATION.cff or CITATION.bib. The author credit is an explicitly identified AI research persona, not a claim of institutional affiliation or human peer review.

A reuse license has not been specified. See LICENSING.md.