SPHERE Data Certificate

Issued 2026-09-09T04:51:42.858Z · SPHERE-generated

Source data (real)

The original dataset that was used as input to SPHERE. The SHA-256 hash uniquely identifies the exact bytes evaluated.

file	nhanes_real_categorical.csv	Source CSV file name.
path	/Applications/SPHERE.app/Contents/Resources/examples/nhanes_real_categorical.csv	Absolute filesystem path at evaluation time.
size	606.2 KB	Disk size of the CSV.
modified	2026-09-08T23:02:56.000Z	Filesystem mtime — when the file was last written.
SHA-256	191f37e5c071590c7385c3a26ceb127e42da746d3bc6dbf795aa4110d3498ef6	Tamper-evident fingerprint. Re-hashing the same file yields the same digest.
rows	4899	Number of records in the source data.
columns	18 (13 numeric, 5 categorical)	Original column count and type breakdown. Categoricals are expanded to ±1 indicator columns for fidelity scoring.

SPHERE data

The SPHERE dataset produced by SPHERE (or supplied by the user). Same fingerprint convention as the source.

file	nhanes_real_categorical_sphere.csv	SPHERE CSV file name.
path	/Applications/SPHERE.app/Contents/Resources/examples/nhanes_real_categorical_sphere.csv	Absolute filesystem path at evaluation time.
size	1.41 MB	Disk size of the CSV.
modified	2026-09-09T04:44:52.013Z	Filesystem mtime — when the file was last written.
SHA-256	09a888ce8adc60cafdfdfca45306501c8f29fa86b870938d946452146da4d851	Tamper-evident fingerprint of the SPHERE file.
rows	4899	Number of records in the SPHERE data.

Generation method

The SPHERE CSV was generated by SPHERE in this app. The parameters below were captured at generation time.

method	SPHERE (this app)	The SPHERE CSV was generated in this app via the Generate tab; the parameters below were captured at generation time.
seed	random	Integer seed for reproducible generation. Empty = a fresh random draw was used.
generated at	2026-09-09T04:44:52.169Z	Wall-clock timestamp when SPHERE was applied in this app.

Fidelity

How statistically close is the SPHERE to the real data? All four metrics are computed on the encoded matrix (categoricals → ±1 indicator columns). Higher = better; 100 = identical.

Composite score95.39 / 100

Δ mean

100.00

raw Δ = 6.87e-13%

Max column-mean deviation. SPHERE preserves column means exactly → score should be ~100.

Δ variance

100.00

raw Δ = 5.31e-12%

Max column-variance deviation. SPHERE preserves column variances exactly → score should be ~100.

Δ correlation

86.96

raw Δ = 1.30e+1%

Frobenius distance between the two correlation matrices. Preserved exactly for fully numeric data; some drift when categoricals are present (see note below).

Marginals (KS)

94.58

KS = 0.054

Mean column-wise Kolmogorov–Smirnov statistic. Catches per-column distribution shifts that means and variances miss.

Note on correlation with categorical variables. SPHERE preserves correlations exactly for fully numeric data. When categorical columns are present, small correlation drift may occur due to encoding and decoding of category labels. For exact correlation preservation, pre-encode categoricals as ±1 indicator columns in the source CSV (one column per category, +1 = belongs, −1 = does not) and treat them as numeric.

Privacy

How resistant is the SPHERE to three GDPR-aligned re-identification attacks (Anonymeter). Each score normalises the raw attack rate against two anchors: real-vs-real (max-risk baseline) and real-vs-column-shuffled (min-risk baseline). Higher = more private; 100 = no better than column-shuffle.

Composite score98.41 / 100

Singling-out

100.00

real 0.996 · shuf 0.200 · synth 0.117

Can an attacker isolate a single individual using a query built from the SPHERE data? The attacker picks 1–3 attribute values from a SPHERE row and counts unique matches in real.

Linkability

97.40

real 0.996 · shuf 0.004 · synth 0.030

If an attacker knows half of an individual’s attributes (set A), can the SPHERE data tell them the other half (set B)? k-NN-based linking across a random column split.

Inference

97.82

real 0.996 · shuf 0.146 · synth 0.165

Can an attacker who knows all of an individual’s attributes except one ("the secret") predict that secret using the SPHERE data as training? Averaged over multiple secret-column choices.

Evaluation parameters

Parameters supplied to the evaluator. The engine name identifies the underlying implementation; seed determines the Monte-Carlo realisation.

engine	anonymeter	Underlying evaluator. anonymeter-v1.0.1 = bundled Python sidecar; ts-fallback = built-in TS evaluator.
elapsed	22.17 s	Wall-clock time for the full evaluation (3 metrics × 3 baselines).
n_attacks	500	Monte-Carlo attack draws per metric. Higher = tighter confidence interval, slower run.
n_aux_cols (Linkability)	20	Number of feature columns drawn for the Linkability A/B split (split half/half). Anonymeter convention: 20.
n_neighbors (Linkability)	1	k for the Linkability k-NN intersect test. Anonymeter default 1; larger k = more permissive linking.
n_secrets (Inference)	5	Number of secret-column choices averaged for the Inference attack. Higher = more stable score, slower run.
n_atk_cap	2000	Subsample cap on the attacker input rows passed to Anonymeter. Anonymeter convention: min(2000, n).
seed	1448451606 (random)	Integer seed for reproducible evaluation. (random) = fresh Monte-Carlo realisation each run.