PureOne/controlled-spectral-reconstruction

Controlled Spectral Reconstruction

Version 2.0 · 5 October 2026 · A research note prepared for Maciej Nowicki

This repository contains a mathematical manuscript, proof audits, reproducible Python checks and a structured dataset of validation examples. It studies reconstruction from magnetic graph data, interacting spectra, analytic calibration scans and finite threshold queries.

Read the manuscript · Editable LaTeX · Original release notes · Validation data

The written derivations are complete under the stated assumptions. Supplied computational checks pass. Originality, scientific priority and a 10/10 breakthrough rating are unverified. This release does not solve the original one-channel Lapidus–Maier problem or the Riemann hypothesis. Development and cross-audits used six AI agents and a primary agent; external human peer review and formal proof-assistant verification have not occurred.

Results and the data they require

Domain	Statement in the manuscript	Essential scope
Adaptive count queries	For H(u) ≤ B u⁻ᴰ, 0 < D < 1, adaptive minimax sorted-length loss is Θ_D(B^(1/D) (Q+1)^(-1/D)); nonadaptive loss is Θ_D(B^(1/D) (Q+1)^(-1)).	Exact real thresholds, integer counts and unit query cost; positive summable length sequences. The matching fixed-mass corollary is for L = B^(1/D)/2.
Connected metric graphs	The magnetic ground-band Hessian and integral flux lattice determine the metric graph within the promised class, including nonplanar examples.	Compact Kirchhoff graphs, no electric potential, simple 3-vertex-connected topology, marked integral flux lattice and exact Hessian. The topology step applies established metric Torelli and Whitney rigidity.
Finite-rank interactions	Complete unordered spectra of T − u_i C at r+1 distinct known nonzero settings recover the spectrum of T, including multiplicities.	T > 0, trace-class inverse, bounded positive additive C of rank at most r, and positive observed operators. Eigenvectors and commutation are not required. Minimality is established only for ranks 1 and 2.
Blind analytic calibration	Two complete clean-energy scans identify a common analytic branch and an infinite summable length sequence up to a scalar gauge; one absolute calibration fixes that gauge.	Distinct known clean energies, complete crossing coverage and a common real-analytic branch with positive derivative. Smoothness alone is insufficient.
Noise limits	Count-amplitude errors below 1/2 round away; errors at least 1/2 allow a positive minimax floor. Bounded-band cosine data admit no uniform Hölder inverse bound on the stated fixed-prior class.	Adversarial amplitude noise, not threshold-position noise. The harmonic instability construction preserves common total length and a tail envelope; exact analytic uniqueness is not contradicted.

The models have different hypotheses. These statements do not establish a universal reconstruction method for arbitrary physical systems. The noisy harmonic upper and lower stability exponents in the supplementary audit do not match and are not claimed to be sharp.

Verification

Supplied suite	Exact integer/rational checks	Numerical checks
Threshold-query reconstruction	10,622	10
Constructive graph/operator checks	891	126
Moment-cancellation certificates	592	0
Total	12,105	136

The ten numerical threshold-query examples use high-precision Decimal arithmetic. The 126 magnetic finite-element assertions use floating-point computations; the supplied run's worst relative quadratic-coefficient error is approximately 3.982e-5. These are consistency checks, not certified eigenvalue enclosures.

The graph checks recover lengths on supplied labeled topologies with marked cycle coordinates. They do not compute topology recovery from an unmarked lattice. Finite exact checks do not formally verify the infinite-dimensional theorems or establish novelty.

Reproduce

Use Python 3.10 or later. From this repository's root:

python -m pip install -r requirements-validation.txt
python scripts/reproduce.py

The runner works in a temporary copy and preserves the published results. It checks suite exit statuses, assertion counts and exact result records. Floating-point values may vary across platforms; the original finite-element acceptance checks still apply.

To run without NumPy or SciPy:

python scripts/reproduce.py --exact-only

This runs all 12,105 exact checks plus 10 Decimal examples, skipping the 126 finite-element checks. Add --output PATH.json to save a run report. For direct suite commands and XeLaTeX compilation, see the original release notes.

Validation dataset

data/validation.jsonl contains 145 selected result records in one validation split. These rows index the supplied suite reports; they are not the 12,241 individual assertions, independent samples, or an ML benchmark. Three determinant rows are representative examples from a larger test run.

Category	Rows
Threshold-query examples	14
Exact graph metric reports	5
Magnetic finite-element reports	54
Representative determinant examples	3
Critical-cutoff inertia examples	15
Moment certificates	48
Hölder-divergence examples	5
Compact counterexample	1

Every row has the same seven string columns:

Field	Meaning
case_id	Stable identifier within this release.
suite	Original verification suite.
category	Type of example.
arithmetic	Exact rational, high-precision Decimal, floating point, or exact values with logarithmic displays.
source_file	Path of the original JSON report.
source_pointer	JSON Pointer locating the original record.
record_json	Canonical JSON encoding of that record; rational numbers retain their exact strings.

Regenerate the index with:

python scripts/build_validation_dataset.py

Use the examples to inspect calculations, reproduce demonstrations or test implementations under the manuscript's hypotheses. They were deliberately constructed for these proofs, including negative controls, and are not representative observations of general physical systems. There is no train/test independence or leaderboard score.

Repository contents

• research/: the unchanged 21-file v2.0 source release, including the PDF, LaTeX, eleven audit notes, three verification scripts, their outputs and the original checksum manifest.
• data/validation.jsonl: the structured index described above.
• scripts/: deterministic dataset extraction and temporary-copy reproduction.
• requirements-validation.txt: dependencies for the optional numerical checks.
• release.json, CITATION.cff, CITATION.bib: release and citation metadata.
• SHA256SUMS: integrity checksums for this repository's payload, excluding the checksum file itself.

Provenance, attribution and licensing

The manuscript credits Eve / AI-assisted mathematical development and is a standalone research note for Maciej Nowicki. This card preserves that credit. The graph topology argument explicitly relies on Lucia Caporaso and Filippo Viviani's metric Torelli theorem; related prior work and limitations are discussed in the manuscript and audit notes.

The source release specifies no license. This packaging adds no license grant. No DOI or arXiv identifier has been assigned to this release in this package. Links and identifiers in the manuscript's bibliography refer to prior literature.

Citation

@misc{eve2026controlledspectral,
  author = {{Eve}},
  title = {Controlled Spectral Reconstruction},
  year = {2026},
  month = oct,
  howpublished = {Standalone research note, version 2.0},
  note = {AI-assisted mathematical development; prepared for Maciej Nowicki.
          Manuscript, proof audits, reproducible checks and validation artifacts.
          Priority and external peer review remain unverified.}
}

When citing a hosted copy, add its actual repository URL and access date. The accompanying citation files contain no invented persistent identifier.