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Prepare fixed value intervals once, replace a few weight intervals, and ask whether every permitted weighted average satisfies a threshold. DynamicBank also returns exact sharp coordinate bounds. Its default runtime has no third-party dependencies, training, GPU, or account requirement.

The method combines established support-function, fractional-optimization and Fenwick-tree mathematics. Mathematical priority, a major general-purpose breakthrough and superiority across all algorithms are not established.

Download and use

Download and extract the complete release ZIP, then run from its extracted folder:

python examples/dynamic_policy.py

For offline installation from that folder:

python -m pip install --no-index --no-deps wheels/qyxo_zhaenivoth_guard-1.0.0-py3-none-any.whl

If you downloaded/cloned this entire Hugging Face repository instead, run python source/examples/dynamic_policy.py, or install the same wheel from the repository's wheels/ directory. Keep the original source manifest unchanged.

After installation:

from fractions import Fraction
from qzguard import DynamicBank

bank = DynamicBank([0, 100], [1, 1], [10, 10])
assert not bank.query(60).all_guaranteed
assert bank.query(60, total_mass=19).all_guaranteed
bounds = bank.enclose(total_mass=19)
assert bounds.lower == (Fraction(900, 19),)
assert bounds.upper == (Fraction(1000, 19),)

old = bank.enclose()
bank.update([0], [2], [9])
assert bank.enclose().lower == (Fraction(10),)
assert old.revision == 0 and bank.revision == 1

With independent weights, a violating mean above 60 exists. Specifying total weight 19 rules it out. False means at least one permitted configuration violates the threshold; it does not mean that every configuration violates it.

Mathematical contract and cost

For each coordinate, the model is

$Y=\frac{N_0+\sum_i w_i v_i}{D_0+\sum_i w_i},\qquad L_i\le w_i\le U_i,\quad l_i\le v_i\le h_i.$

Weights and D0 are nonnegative; D0 + sum(L) > 0 is required. Guarantees refer to the finite binary64 values produced by input conversion, not arbitrary original real numbers. Values and base terms stay fixed. Exact known-total mode adds sum(w)=W, with W inside the current feasible weight range.

Sorted static values and two Fenwick moments per ordering avoid a full row rescan. Exact threshold supports decide universal inequalities. One binary-lifting traversal finds each sharp support root; known-total mode fills width capacity in value order, including a partial boundary weight.

Operation	Arithmetic-operation or comparison cost
Preparation, `M` rows and `P` coordinates	`O(P M log M)` comparisons; `O(P M)` state
Replace `K` weight intervals	`O(K P log M)` integer operations
Threshold query or sharp coordinate enclosure	`O(P log M)` integer operations
Public mass getters or immutable snapshot	Full copy; outside the logarithmic query claim

Wide exact integers and rational reduction have additional bit costs. Coordinate extrema can require different weight configurations. Rebuild when value intervals or base terms change. Concurrent mutation needs external synchronization.

Measured evidence and its boundary

The final paired benchmark on one Linux host used 65,536 rows, ten independent seed groups per primary cell and 24 timed update/query requests plus one warmup per group. The table models preparation divided by 10,000 plus measured median request cost. It does not claim that 10,000 requests were executed. Interpreter startup, imports, input generation, transport and serialization are excluded.

Coordinates `P`	Patched rows `K`	Modeled speed ratio vs fastest rescan	Corrected one-sided rescan lower bound	Modeled ratio vs fastest exact indexed peer
1	1	5.46×	5.30×	0.96×
1	8	2.67×	2.62×	1.03×
4	1	16.10×	15.61×	1.08×
4	8	7.27×	7.05×	1.17×

Ratios above one favor the default dynamic implementation. The joint all-four-cell fivefold target failed; three individual rescan cells passed. Rescan gains do not establish superiority over a well-engineered moment index. GMP-backed indexed queries, dense updates, small banks, fixed thresholds and cached unchanged-box endpoints can favor existing methods. Timing uncertainty and all negative controls remain in the full measured report and raw data.

All 13,282 decision coordinates, 5,252 exact support coordinates and 72 sharp endpoint coordinates checked in the main report agreed with the comparison methods. This is finite numerical verification, not a proof of production reliability or exhaustive testing of all possible inputs.

CompactDynamicBank is an opt-in memory alternative. In a two-seed development ablation with 4,096 rows, its approximate retained Python payload was 2.16–2.53× smaller than the default. One-row patch latency was similar; eight-row patch latency was about 24–30% higher. These are descriptive payload/time results, not process-RSS measurements or held-out superiority findings. Compact raw report.

A conditional replay on Beijing air-quality records also checks sparse updates and known-total bounds. The tighter constrained bounds produced zero additional threshold certifications at the selected cutoffs. It does not establish sensor accuracy, calibrated uncertainty or a matching-primitive runtime ratio. Replay assumptions and results.

Verification and reproduction

Qualification	Executed result
Source suite with optional dependencies	171 passed
Dependency-free source suite	152 passed; 19 declared optional NumPy skips
Fresh installed exact wheel	142 passed; 19 declared optional NumPy skips
Fresh installed wheel with optional dependencies	161 passed
Original sealed release	238 manifested files verified after extraction
Manuscript	150 pages rendered and reviewed; no observed layout defects

The source suite includes ten qualification-tool tests excluded from the installed-runtime suite; counts are not independent oracle designs. Final local qualification, installation evidence, tests, theory, API, prior-art boundary, and hostile review are included.

From the frozen source/ directory, reproduce with the following commands. Before starting either benchmark, set OPENBLAS_NUM_THREADS=1, OMP_NUM_THREADS=1 and MKL_NUM_THREADS=1. On Linux/macOS, use export OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 MKL_NUM_THREADS=1. In Windows PowerShell, use $env:OPENBLAS_NUM_THREADS="1"; $env:OMP_NUM_THREADS="1"; $env:MKL_NUM_THREADS="1". These are the recorded numerical-library thread controls; the runner records them rather than silently changing them.

python -m unittest discover -s tests -v
python -m pip install '.[dynamic-benchmarks]'
python benchmarks/run_dynamic.py --mode pilot --output benchmarks/results_new_pilot.json
python benchmarks/run_dynamic.py --mode final --output benchmarks/results_new_final.json

The benchmark dependency installation needs network access unless dependencies are already present. Reports preserve existing output files; choose a fresh filename. Declared protocol.

Limitations and research status

Exact arithmetic cannot repair invalid uncertainty bounds or an incorrect declared total. The model does not handle arbitrary correlations, signed weights, changing values, or discrete coupled constraints. These tests do not certify learned-model accuracy or an application policy's correctness.

Local narrow release preparation: 100% (12/12 declared criteria). Research completeness: 80%. Primary-evidence ledger: 65% verified, 30% derived, 5% conjectural. These are documented checklist and evidence classes, not probabilities or a breakthrough score. Independent second-machine performance replication and audited production integration remain open. Status ledger.

The uploader bundle was prepared for PureOne/Qyxo-Zhaenivoth-Guard; preparation itself performs no public Hub upload. The original runtime, original ZIP, wheel, citation and scientific evidence are preserved byte-for-byte.

License and citation

MIT license. Please retain attribution to established methods as well as the software citation in CITATION.cff. The author name is a research pseudonym; it does not imply human authorship or independent peer review.

Original release ZIP SHA-256:

65adfb097b4f2e13112fa8181d780e150103c0e757d77b86a741f17f8d4dae2b

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Total file size:

31.7 MB