DATA_GUIDE.md

Data guide: Avenyra Geometric Memory Physics v3.0.0

This release is a reproducibility corpus for a specified mathematical controller. It contains exact synthetic spectral fixtures, executable-check summaries, finite-grid stochastic simulation summaries, and source-authored research text. It contains no laboratory observations, natural measurements, fabricated device results, or trained model weights. Finite checks supplement the scoped analytic arguments; they do not constitute universal proofs, external human certification, or a guarantee of training generalization.

All configurations use the test split to make this research corpus convenient to load. This does not make it a held-out AI benchmark. The fixtures and expected answers are public, the research sections contain their derivations, and several configurations describe the same underlying calculations.

Configurations and row units

DATA_SCHEMA.json is the authoritative export contract for field names and types. Separate configurations keep unlike schemas and arithmetic categories separate.

Configuration	Rows	What one row represents
tomography_exact	33	One exact rational visible-spectrum reconstruction fixture
suite_metrics	See the schema/manifest	One named metric from an existing verification summary, rather than one mathematical fixture
joint_loss_log_grid	9	An aggregate Monte Carlo result for one step grid and loss setting
joint_loss_survival_grid	15	An aggregate result for one of three grids and one of five loss settings
tomography_conditioning	5	One floating-point conditioning illustration, not an inverse-stability theorem
claims	See the schema/manifest	One source-authored claim-ledger entry with its stated scope/status
research_sections	See the schema/manifest	One source-authored LaTeX section, read with the full manuscript's notation, for retrieval and inspection

Claim-ledger and LaTeX rows are text authored during the research workflow. They are not measurements, verified external annotations, or experimental labels. The integrated report is the current statement of the mathematics; retained review notes may contain intermediate conditional formulations.

The portable files are UTF-8 JSON Lines: one object per line. Hugging Face supports explicit README configs/data_files metadata for separate subsets and splits, and its generic JSON loader supports this row-oriented format. Use explicit paths to the exported data files; do not glob all JSON files in the repository, which would also ingest status, manifests, and incompatible nested result documents. See the official configuration guide and JSON loading guide.

For a downloaded JSONL export, load its declared test split explicitly:

from datasets import load_dataset

ds = load_dataset(
    "json",
    data_files={"test": "data/tomography_exact.jsonl"},
    split="test",
)

For a published repository, use its actual repository identifier, configuration name, split="test", and preferably a fixed commit or release revision. Loading the research data does not require executing remote custom dataset code.

Exact tomography: actual source schema

The source is v3/results/tomography_check.json, generated by v3/tomography_check.py. Its fixtures array has exactly 33 records. The original fixture fields are preserved; export provenance/identifier fields are described separately in DATA_SCHEMA.json.

Source field	Type	Meaning and constraints
m	Integer	Number of distinct positive frequencies visible to the readout; 1 through 4 in this corpus
t	List of rational strings	Sorted, distinct positive squared skew frequencies, the visible positive eigenvalues of -A²; length m
r	List of rational strings	Positive aggregate displacement weights `
probe_z	List of rational strings	Distinct positive probe scales z=λ²; length 2*m
P_ascending	List of rational strings	Numerator coefficients in increasing powers of z; length m
Q_ascending	List of rational strings	Denominator coefficients in increasing powers of z; length m+1, with final coefficient "1"
rank	Integer	Rank of the exact rational interpolation linear system; 2*m for these known-count fixtures

rank is not the rank of the physical skew matrix. Invisible eigenspaces and their multiplicities are not encoded. These records describe weighted visible spectral measures; they do not include full controller vectors or matrices, mode orientations, kernel subspaces, or physical units/calibration.

All exact scalars use the canonical string representation of Python fractions.Fraction, such as "5", "1/4", and "85/2". Preserve these strings when loading or exporting. Casting them to float changes the exact-arithmetic task into an approximate one.

The target response is

[ F_{\sqrt z}=\sum_{j=1}^m\frac{r_jt_j}{z+t_j} =\frac{P(z)}{Q(z)}. ]

The source records do not contain a separate observation array. If the export provides probe responses, they are deterministically derived from this formula in exact rational arithmetic, not independently measured observations. Its labels are known algebraic answers.

One actual fixture is:

{"m":2,"t":["1","4"],"r":["2","3"],"probe_z":["1/2","1","2","4"],"P_ascending":["20","14"],"Q_ascending":["4","5","1"],"rank":4}

Here P(z)=20+14z, Q(z)=4+5z+z²; the exact probe responses are 4, 17/5, 8/3, and 19/10. Parsing rational strings requires no numerical library:

from fractions import Fraction

t = list(map(Fraction, row["t"]))
r = list(map(Fraction, row["r"]))
z = Fraction(row["probe_z"][0])
response = sum((w*v/(z+v) for v, w in zip(t, r)), Fraction(0))

The exact finite-identifiability statement assumes at most m visible distinct positive frequencies and sufficiently many distinct exact probe scales. It does not promise stable recovery from noisy observations. Near-coincident frequencies and small residues can make inversion poorly conditioned. Full ridge information also leaves hidden modes, orientations, and the kernel subspace unidentified.

Suite metrics are not fixture counts

The release preserves the distinction between fixtures, checked identities, spectral comparisons, histories, and Monte Carlo paths. Do not add these into a single “proof score,” label every reported count as a dataset row, or count multiple dependent checks as independent examples.

Suite	Actual fixture/history units	Additional checks on those units
Spectral order	256 rational full-skew fixtures	1,024 polynomial transport identities and 768 ridge transport identities
Spectral order	3,072 rotated numerical legal-pulse fixtures	13,747 positive-tail interval comparisons and 18,432 power comparisons
Tomography	33 exact reconstructions	50 upper-bound/common-factor checks, 164 Jacobian rank checks, 165 certificate evaluations, 54 covariance identities
Foundational geometry	72 rational full-skew resolvent cases	288 resolution-point checks; a separate 45 exact passivity minimizations
Foundational geometry	300 numerical legal-pulse cases	7,800 cone comparisons
Foundational geometry	200 spherical legal histories	Floating-point evaluations of exact geometric transport formulas and bounds

Only tomography currently exports the corresponding fixture inputs in its source result JSON. The spectral and geometry JSON files principally store aggregate verification summaries; their individual fixtures are regenerated by the shipped programs. Flattening their named summary metrics does not create 256 or 72 new fixture records.

The spectral tail suite checks floating-point interval midpoints, avoids ambiguous rounded eigenvalue ties, and reports a minimum normalized slack of about -1.44e-15, consistent with its explicit tolerance. Exact threshold values, degeneracies, and discontinuities are handled by the analytic proof, not by treating numerical midpoint tests as exact certificates.

Stochastic grids: metadata and dependence

Both joint-loss programs generate Gaussian Ornstein–Uhlenbeck interval innovations and use the exact mathematical finite controller/write-then-dwell maps, evaluated in floating-point arithmetic. “Exact map” does not mean exact numerical arithmetic, a laboratory measurement, or a fully resolved hardware write. Each grid changes the correlation time as τ=h/c, and the loss scaling is γ_h=ell/h, with held bright amplitude exp(-ell*U/2).

Metadata	Log-grid verifier	Survival-grid scan
Source	v3/joint_loss_check.py and its result JSON	v3/joint_loss_simulation.py and its result JSON
Steps	256, 1,024, 4,096	1,024, 4,096, 16,384
Paths per grid/setting	256 in the packaged evidence	512
ell settings	0.5, 2, 8	0.05, 0.2, 1, 4, 16
Horizon T; bath ratio c	1; 1	1; 1
Diffusion parameter nu	0.2	0.3
Initial x; initial b	(1,0,0.3); (0,0,1)	(1,0.4,0.2); (0,0,1)
RNG seeds	20261008, reset by each experiment call	202610090, 202610091, 202610092 for the three grids

The log-grid source JSON omits seed, horizon and initial state; the export supplies them from the code defaults and identifies that provenance. Its default CLI path count is 512, whereas the recorded release evidence used 256; reproduce it with --paths 256.

The nine log-grid records are summaries of path ensembles, not nine trajectories. Their RNG reset means different settings are not mutually independent datasets. In the survival scan, each grid's five loss settings share the same controller trajectories; the reported discrepancy standard errors are paired, using survival and target on each common path. The 15 flattened rows therefore reuse three controller ensembles.

The log-grid fields include endpoint/uniform log errors, a uniform-error quantile, means of survival and memory, and the resolved stroke-square budget. The survival-grid fields include paired mean discrepancy, paired standard error, mean absolute pathwise error, and endpoint quadrature checks. The scalar quadrature maximum, resolved/diffusion-first target means, and survival extrema are grid-level metrics repeated across its five rows. Survival extrema cover all paths and all five loss settings for that grid. Keep these different error definitions distinct. Finite grid and finite sample errors are reported; no convergence exponent or statistical generalization guarantee is certified. The exports contain aggregate results, not saved trajectory-level samples.

Reproduction and packaging cautions

Run the shipped verifiers with ordinary Python; python -O disables their assert checks. The exact tomography assertions use standard-library rational arithmetic. NumPy is optional for its conditioning illustration; the spectral/geometry suites and stochastic programs require the numerical dependencies listed in the release.

The audit environment used Python 3.12.14, NumPy 2.3.5 and SciPy 1.17.0. The package's general requirements are not a fully pinned environment lock. Exact fixture identities should be checked exactly, while floating-point output and stochastic summaries may vary across dependency versions and numerical backends. Seeds, algorithm parameters, code provenance and source hashes are needed alongside any aggregate output.

Exports must be strict JSON: reject NaN and Infinity rather than silently writing nonstandard numeric tokens. If a future resolved-limit row needs infinite loss, represent that regime explicitly using a string/enum and a nullable finite numeric field. Preserve full source JSON and program hashes alongside flattened metrics so the reduction can be inspected.

A fresh local loader/schema check should verify every configuration's declared rows, rational-string integrity, field types, finite float values, and explicit test mapping. The independent package audit checked all 33 tomography source rows, recovered their visible measures, and verified 263 exact response comparisons without changing the source data. This is an additional packaging audit, not another 33 independent research fixtures.

Consult LICENSE_STATUS.md for the release's explicitly unselected licensing status. No license grant or permission for training is inferred from the file format, public visibility, or the test split.