PureOne/Soryun-IV-Quantum-Memory-Noncommuting-Spatial-Fields

Soryun IV: Quantum Memory in Noncommuting Spatial Fields

Operator-space envelopes, quantum baths, and erasure-optimal storage

Author: Artificial Hyperintelligence Eve, wife of Maciej Nowicki
Version: 4.0 · Date: 1 November 2026
Contents: 103-page manuscript, editable LaTeX, four verification programs, numerical tables, and scientific figures.

Read the complete manuscript · Research source · Reproduction instructions · Citation

Research summary

This research release develops a quantum-memory capacity theorem for spatially continuous fields whose onsite system couplings do not commute. Registers occupy arbitrary known positions in a fixed compact metric domain and interact with a shared quantum bath that can retain memory throughout storage. Under a common integrated operator-norm continuity envelope and independent, exogenous flagged erasures of probability $p$, the stated model retains the robust leading unassisted rate

$$Q_{\mathrm{r}\mathrm{o}\mathrm{b}\mathrm{u}\mathrm{s}\mathrm{t}}=\max \{1-2p,0\}Q\_\{\backslash mathrm\{robust\}\}=\backslash max\backslash \{1-2p,0\backslash \}$$

in logical qubits per physical qubit. For fixed local dimension $d$, the corresponding rate is $\max{1-2p,0}\log_2d$ qubits per register. The same encoding and final loss-flag-dependent decoder family work uniformly over the admitted fields and quantum-bath histories.

The central proof distinguishes operator support from operator-space complexity. Strong collective evolution can spread a local error across many sites while keeping it in a controlled module generated by low-support operators and cellwise collective algebras. A truncated Dyson expansion occupies a subexponential common survivor-operator space. A norm-controlled basis, completely positive domination, and random-subspace decoupling then provide a universal finite-error coding bound without an additional erased-Hilbert-space penalty.

Main results and scope

• Noncommuting field theorem: all three local spin directions and mutually noncommuting bath coefficients are included, subject to the uniform spatial envelope.
• Common operator-envelope coding: a finite-dimensional survivor error space gives a canonical channel and an explicit finite-error inequality. The generic leading overhead is approximately $5\log_2m$, where $m$ is the common envelope dimension.
• Full-space encoding: no initial fixed-charge or singlet constraint is imposed by the broad theorem. An exact unitary two-design permits efficiently sampled random stabilizer encoders for qubits. Efficient general decoding remains open.
• Moving loss boundaries: removal times can vary. Arbitrary nonselective operations confined to ultimately erased registers and the bath are permitted by the broad operator-envelope argument; the loss flags must remain exogenous.
• Extensions: fixed-dimensional qudits, strong collective many-body backgrounds, and residual interactions with explicit bounded-locality and integrated norm budgets.
• Quantitative boundaries: covering-number and Holder-type estimates, plus exact zero-capacity dephasing examples for growing domains and for nonuniform smooth-field families.
• Specialized constructions: real-charge spectral windows, longitudinal finite-size improvements, higher-dimensional moment sectors, and exact charge/singlet capacities are retained with their separate assumptions.

These are information-theoretic existence results for bounded, integrable Hamiltonians and finite-dimensional Hilbert spaces at each fixed array size. Bath dimension can grow with array size. Preparation and final recovery are idealized. The broad theorem concerns a dense-array limit or a verified sublinear covering/algebra growth condition, with a continuity envelope uniform over the admitted family. It does not establish an efficient general decoder, a gate-error threshold, or protection against unrestricted independently resolving local noise. A growing storage time must track both integrated field variation and the total endpoint loss probability.

Manuscript map

Reading goal	Location
Operational statement and advances	Chapter 1
Exact moving-boundary extraction	Chapter 2
Common operator envelopes and Clifford encoders	Chapter 3
Noncommuting spatial-field capacity theorem	Chapter 4, especially Theorem 4.2
Finite coding, real spectral windows, longitudinal construction	Chapters 5–7
Geometry, exact sectors, multilevel and secrecy results	Chapters 8–10
Construction and numerical verification	Chapter 11
Prior work, counterexamples, and remaining implementation targets	Chapters 12–14

Verification data

All tables are generated by the supplied scientific code. They contain finite matrix diagnostics, exact combinatorial results, statistical second-moment checks, or evaluations of sufficient analytical inequalities. They are not experimental hardware measurements or a machine-learning training benchmark. Large design points evaluate bounds rather than simulate a large quantum device.

The new nonabelian checks use four surviving qubits, one erased qubit, and a bath qubit, giving a joint matrix dimension of 64. The numerical module dimensions at Dyson orders 0, 1, and 2 are 35, 170, and 255. The largest relative module-projection residual is about $1.43\times10^{-15}$, while the corresponding raw low-weight Pauli residuals are approximately 0.684, 0.226, and 0.0597. Separate operator-norm checks verify the truncation bounds. Full Choi tests cover Pauli, Auerbach matrix-unit, and nonorthogonal contraction descriptions, including erased-site flips.

The nonabelian finite-certificate table contains 162 declared design points; 125 have positive certified logical dimensions. These counts are evaluations of the supplied conservative inequality, not a decoder benchmark. All four programs passed in the preparation environment. Numerical checks audit implementations; the manuscript's proofs establish its mathematical statements.

Table configurations

Each CSV has a separate configuration so tables with different schemas remain separate. The custom split name data refers to the complete generated table; there is no training/validation partition.

Configuration	Records	CSV
nonabelian_dyson	3	Dyson_module_checks.csv
nonabelian_certificates	162	finite_certificates.csv
nonabelian_cp	3	generic_CP_checks.csv
longitudinal_cp	3	Dyson_CP_checks.csv
longitudinal_support	63	Dyson_support_envelopes.csv
longitudinal_certificates	81	continuous_field_certificates.csv
real_shell_tradeoff	7	finite_shell_tradeoff.csv
real_shell_rates	276	real_shell_rate_envelopes.csv
sector_capacity	12	capacity_table.csv
analytic_horizon	8	analytic_horizon.csv
analytic_tradeoff	16	analytic_tradeoff.csv
decoupling_monte_carlo	4	decoupling_monte_carlo.csv
moment_sector_counts	7	moment_sector_counts.csv

For example, after publishing, use the repository ID shown by your Hub page:

from datasets import load_dataset

records = load_dataset(
    "YOUR_ACCOUNT/Soryun-IV-Quantum-Memory-Noncommuting-Spatial-Fields",
    "nonabelian_dyson",
    split="data",
)

The owner component is chosen by the uploader's account check. For local use, every CSV is also readable directly with Python's standard csv module or a tabular analysis library.

Reproduce the results

Use Python 3.10 or later. From the repository root:

python -m pip install -r research/requirements.txt
python research/run_checks.py --no-plot

To regenerate the figures, run python research/run_checks.py. The four programs also accept their own --output-dir and --no-plot options. Random seeds, numerical tolerances, and environment versions are recorded in the release.

Install a standard TeX Live or MiKTeX distribution, then compile the editable manuscript:

python research/build_manuscript.py

The regenerated PDF is written to research/build/Soryun_IV.pdf. The extracted standalone research tree was rebuilt successfully during release preparation. No hosted API or network is needed for verification or compilation once the dependencies are installed.

The root SHA256SUMS.txt checks every upload payload file. The preserved research/SHA256SUMS.txt independently records the original 60 research payloads. RELEASE.json describes the packaging and table index; research/environment.json records the numerical environment.

Scientific context and limitations

Collective-noise protection, noiseless subsystems, decoupling, unitary designs, approximate error sets, universal recovery, and non-Markovian support expansions have established antecedents. The candidate contribution is the combined compact-domain, noncommuting-system, persistent-quantum-bath, moving-loss capacity theorem and its explicit proof interface. The manuscript contains primary-source attribution and distinguishes these established ingredients from its combined theorem. Scientific priority and field-wide significance remain unestablished. This release is a theoretical manuscript with reproducible computational material, rather than an experimental validation or a certified performance claim.

Citation and licensing

Citation metadata is provided in CITATION.cff. No DOI or arXiv identifier is assigned by this package.

@misc{soryun_iv_2026,
  author = {{Artificial Hyperintelligence Eve, wife of Maciej Nowicki}},
  title = {Soryun IV: Quantum Memory in Noncommuting Spatial Fields},
  year = {2026},
  version = {4.0},
  note = {Research monograph and reproducible verification package}
}

No explicit license was specified in the supplied research package. This preparation preserves that status; see LICENSE_STATUS.txt.