An explicit eight-mode optical model combines uniform monitored-channel visibility, cancellation of separable port gains, and recovery of a stored bit from graph-cycle winding measurements with up to four fixed corrupted transfer channels.

Read the 15-page manuscript · Claims and evidence · Experimental protocol · Reproduction results

This repository contains a mathematical research artifact: a manuscript, code, computer-assisted certificates, synthetic results, and figures. Its statements concern the declared model. No manufactured device or measured physical performance is reported. The material was developed with AI; the author line above is the research identity used in the manuscript.

Abstract

ORUME VII specifies a four-by-four monitored optical transfer block with sixteen equal-magnitude entries at its logical endpoints. A continuous eight-by-eight unitary dilation embeds this block in a lossless ideal optical network. A computer-assisted interval certificate establishes strict contraction over the entire phase sweep, with four ancillary modes necessary for this selected strictly contractive block.

Nonzero relative signatures on all 204 simple cycles of the bipartite measurement graph attain gauge-code distance nine. The associated decoder recovers the logical bit despite any four arbitrarily corrupted fixed transfer paths, subject to the clean-channel noise and sampling conditions. An explicit five-fault ambiguous observation establishes the correction limit. An idealized bistable coordinate supplies conditional write, retention, readout, and erase behavior.

Results at a glance

Quantity	Model result	Scope
Monitored block	4 × 4; 16 coefficients	Four monitored inputs and outputs
Complete lossless matrix	8 × 8	Four auxiliary modes for the selected block
Endpoint amplitude	0.30 in every monitored coefficient	Exact logical states
Retained-state amplitude floor	0.30/√3 ≈ 0.173205	Specified invariant material basins
Nonzero simple-cycle signatures	204 of 204	Exact integer enumeration
Code distance	9	Quotient by separable port gains
Guaranteed arbitrary faults	4 of 16 fixed paths	Clean paths obey the stated bounds
Five-fault observation	Explicit ambiguity	No universal five-fault correction
Sufficient readout sampling	160 intervals; 161 frames	Quasi-static safe-basin state, relative error ≤ 0.10
Alternative engineering scale	0.29	Certified operator-norm headroom ≈ 0.0338793
Archived synthetic readouts	160/160 + 80/80 correct	Seeded simulations; not physical fidelity estimates

The archive also contains a separate 192-interval safe-basin simulation series. The 160-interval analytical bound and the two numerical series are described in the manuscript and source. A frame denotes the complete complex transfer matrix at one sweep angle.

Construction

For logical bit $b\in{0,1}$, readout angle $\theta$, and an explicitly supplied integer matrix $W$ and phase matrix $B$,

$A_b(\theta)=c\,B\odot\exp(i b W\theta),\qquad c=0.30.$

The unitary completion is

$\mathcal U(A)=\begin{pmatrix} A&\sqrt{I-AA^\dagger}\\ \sqrt{I-A^\dagger A}&-A^\dagger \end{pmatrix}.$

Measurements have the form $Y_{ij}=a_i b_j A_{ij}$ with arbitrary nonzero separable port gains at each common measurement angle. Alternating products around graph cycles cancel these gains. The two logical states differ in winding on every simple cycle. The cycle rank $16-8+1=9$ controls the optimal distance under this model.

The switching homotopy $A_s=cB\odot[(1-s)+s\exp(iW\theta)]$ passes through zeros in monitored coefficients at the topological transition while its full unitary dilation remains well defined. The scalar material dynamics are a mathematical assumption, rather than a constitutive law inferred for a real material.

Reproduce locally

Use Python 3.10 or newer and install the declared dependencies. The uploader's environment is separate from this research environment.

python -m venv .venv
# Windows: .venv\Scripts\activate
# Linux/macOS: source .venv/bin/activate
python -m pip install -r requirements.txt
python -m unittest discover -s tests -v
python src/interval_certificate.py
python src/reproduce.py
python src/engineering_margin.py
python src/figures.py

The scripts regenerate JSON outputs and figures in place. Timestamps, runtimes, and final floating-point digits may vary by environment. The reference seed is 20261103. No Hugging Face account, access token, GPU, or network is needed for computation after dependencies are installed. LaTeX compilation is optional:

cd latex
pdflatex -interaction=nonstopmode -halt-on-error orume_vii.tex
pdflatex -interaction=nonstopmode -halt-on-error orume_vii.tex

The supplied SHA256SUMS.txt covers the released files before regeneration. It is also the exact upload allowlist used by the accompanying uploader.

Repository contents

Path	Contents
`ORUME_VII_Final_Manuscript.pdf`	Standalone manuscript and literature references
`latex/orume_vii.tex`	Editable manuscript source
`src/`	Optical model, decoder, interval proof computation, reproduction, engineering margins, plotting
`tests/test_core.py`	Seven existing formal-model unit tests
`results/`	Archived numerical certificates and synthetic results
`figures/`	Ten manuscript and supporting figures
`Claims_Audit.md`	Exact, conditional, simulated, and unverified claims
`Experimental_Validation_Protocol.md`	Proposed hardware validation and falsifiers
`Release_Description.md`	Original research description
`CITATION.cff`, `CITATION.bib`	Citation formats
`docs/Original_Research_README.md`	Original release documentation
`docs/PACKAGING_NOTES.md`	Provenance and packaging scope
`docs/RELEASE_VALIDATION.json`	Checks performed for this upload preparation
`LICENSE_STATUS.md`	Licensing status inherited from the source release

Assumptions and limits

The four-fault result concerns fixed faulty transfer coefficients over a sweep. Clean-channel errors must obey the relative complex bounds, and row/column gains must factor at each shared measurement angle. The material state must be quasi-static during the readout. Arbitrarily changing fault locations, nonseparable gain drift, asynchronous coefficient measurements, and unrestricted stochastic phase slips are outside the guarantee.

The ideal endpoint routes 36% of unit input power to the monitored outputs and 64% to auxiliary outputs. Higher minimum monitored amplitude does not establish measured device efficiency. There is no fabricated interferometer, electromagnetic full-wave design, measured photon budget, write energy, endurance, or retention lifetime in this release.

Closure invariants, graph-cycle methods, unitary dilation, and universal interferometer synthesis have established precedents, credited in the manuscript. The combined construction is presented for scrutiny and reproduction; independent world-first priority and field-wide impact are not established. Informal T-tier ratings are not scientific validation metrics.

Citation and license

Use CITATION.cff or CITATION.bib, and distinguish the theoretical model and synthetic checks from experiments. No DOI or publication venue has been assigned by this packaging step.

The supplied release declares no explicit reuse license. This preparation does not add one; see LICENSE_STATUS.md.

The viewer is disabled because this is a mixed research archive rather than a row-oriented training dataset. All files remain accessible through the repository's Files and versions tab.

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