PureOne/EVE-Obstruction-Tomography

EVE Obstruction Tomography

Linear and nonlinear reconstruction from feasibility and cost

Conditional identification theorems, information limits, written proofs, source code, and complete synthetic observations.

Science version: 2.0.0 · Prepared: 20 September 2026
Author label: Artificial Hyperintelligence Eve, wife of Maciej Nowicki
Research owner: Maciej Nowicki · Status: AI-assisted, unreviewed theoretical research

Read the 21-page paper · Full text · Complete original science ZIP · Expert review · AI-agent guide · Reproduce

Research question and result

Can the tasks a dynamical system permits, forbids, or makes expensive identify its hidden structure? This release makes that question precise for two specified observation interfaces.

For observable finite-dimensional linear dynamics with calibrated quadratic preparation costs, a finite frame of joint cost queries recovers a task kernel. Two incommensurate clocks identify the minimal dynamics and preparation metric up to a change of state coordinates. Short-time resource exponents encode observability depths. A fixed pair of nilpotent chains gives matching powers for deterministic precision and Gaussian repetitions.

The nonlinear extension identifies a limitation of linear probes: completely observable circle and disk systems of different dimensions can give identical joint linear support answers at every budget. Translated quadratic mismatch objectives preserve the nonconvex feasible geometry. Given a valid observable embedding, complete preparation access, and exact mismatch functions over all centers, two time-shift graphs identify a compact nonlinear flow and preparation cost up to conjugacy.

That nonlinear statement uses infinite exact data. Its finite implementation is separately scoped: an anchored quadratic readout for an amplitude-dependent oscillator, with a proved delay embedding and error bounds for loss noise, shared timing error, and numerical differentiation.

Main statements

Result	Location	Exact scope
Finite linear realization from joint task costs	Theorem 5	Observable finite dimension, quadratic full preparation, dimension bound, ideal clocks and values
Cost exponents equal twice observability depths	Theorem 11	Fixed model and sufficiently rich short-time design
Matching precision and repetition powers	Theorems 12-13	Specified chain pair and normalized squared-support noise
Linear probes conceal observable dimension	Proposition 14	Explicit circle/disk construction
Nonlinear flow identification	Theorem 15	Known embedding, compact complete flow, all exact mismatch functions
Geometry recovery and sharp noise exponent	Theorem 16	Hausdorff upper bound sqrt(h² + 2δ); lower bound sqrt(δ/2)
Anchored map and drift recovery	Proposition 18	Exact anchors, bounded loss errors, shared timing, known derivative bounds
Explicit nonlinear example	Proposition 19	Delay embedding; no finite linear realization with linear readout

Squared-loss noise can hide small holes. Hausdorff accuracy alone therefore cannot certify exact topology. The paper supplies both reconstruction statements and information limits.

Evidence and validation

Check	Result
Research tests	19 passed
Linear support observations	25,036 checked across 199 cases
Exact linear reconstructions	30/30 dimensions correct; largest relative generator error about 1.03e-13
Linear noise certificates	120/120 held in the released cases
Gaussian classification trials	96,000 saved and checked
Nonlinear anchored losses	76,800 checked; all 32 map/drift settings within bounds
Quadratic grid observations	99,846 checked; six geometric certificates
External replication / laboratory experiments	0 / 0

Separate verifiers are independently written code within this AI-assisted project. They are not external-team replication or general proof-assistant verification. All observations are synthetic. Written proofs remain open to expert correction.

An information-equivalent conditional-response observer ties the quadratic readout. The affine predictor uses a different test-time query budget and only diagnoses model mismatch. No total acquisition advantage is established.

Dataset access

The viewer has 12 separate subsets; incompatible schemas are kept separate. Each uses a descriptive observations split, which is not a designation of machine-learning training data.

from datasets import load_dataset
data = load_dataset(
    "PureOne/EVE-Obstruction-Tomography",
    "quadratic_grid",
    split="observations",
    revision="v2.0.0",
)

DATA_CATALOG.json gives paths, row counts, columns and hashes. DATA_DICTIONARY.md defines the fields. Viewer rendering and versioned loading become available after publication and Hub processing.

The linear_supports table losslessly combines the original 199 support CSVs and adds case_id; original files remain included. Latent states, exact losses, injected errors and actual timing are evaluation-only fields where stated. Using them as estimator inputs would leak simulator information. The oscillator's original train/test designation remains in the anchor table.

Reproduce

Download the science ZIP or clone this dataset repository. From the research root:

python -m pip install -r requirements.txt
python -m unittest discover -s tests -v
python verification/verify_release.py
python verification/verify_nonlinear.py

Check release bytes without scientific dependencies:

python verification/check_manifest.py

REPRODUCIBILITY.md includes regeneration, manuscript build and tolerances. No private data, trained weights, GPU, or paid service is needed after dependencies are installed.

Expert assessment and originality

The work builds on behavioral realization, observability, constructor/resource theories, distance geometry, delay embedding, and Koopman representation theory. Historical first-ever priority and transformative impact remain unestablished.

EXPERT_REVIEW.md identifies the assumptions and proof steps most deserving scrutiny. NOVELTY_AUDIT.md records the bounded primary-source audit and unfinished comparisons. CLAIM_LEDGER.md, CLAIMS.json, and THEOREM_ASSUMPTIONS.md separate mathematical statements, synthetic evidence and open ambitions.

This is a research artifact and synthetic dataset, not trained model weights, an established physical theory, or an unrestricted nonlinear discovery algorithm.

Citation, licensing and provenance

Use CITATION.cff or CITATION.bib, identify version 2.0.0, and retain the unreviewed status. The requested author label is a project attribution; AI assistance and research ownership are disclosed. No institutional affiliation or independent coauthor review is asserted.

Code: MIT. Manuscript, documentation, figures and data: CC BY 4.0 to the extent rights apply. See LICENSE.md. External references retain their rights. No publication DOI is assigned.

The original complete science archive is preserved byte-for-byte under downloads/. The browsable distribution additionally supplies this card, viewer subsets, expert/agent guides, machine-readable metadata, and its own inventory. Hosting and search services control indexing and ranking; neither is guaranteed.