# Geometric inference: evidence for the interactive companion

This companion uses real public data from UCI Wine Quality and Combined Cycle
Power Plant. It reproduces the October 29, 2026 GIGI experiments from their
saved records; the webpage does not contact a running GIGI engine.

## What the viewer changes

All 6,497 red/white wine records and all 9,568 original first-sheet power-plant
records contributed to the source histograms. The slider reveals **fingerprint
evaluations**, not individual wine or plant records. Each field is split into
32 equal-width bins between its measured minimum and maximum. The bin fractions
are the coefficients of a polynomial F(z) = sum p_k z^k. They are nonnegative
and sum to one, so |F(z)| is at most one for |z| at most one.

Seven evaluations of that polynomial were given to the completion endpoint.
At each requested position, the colored disk is the set of values allowed by
the revealed evaluations and the bounded holomorphic model. The answer shown
by “reveal” is independently evaluated from the full histogram and was not used
in constructing the query disk. It is a fingerprint value, not alcohol content,
wine quality, a predicted plant reading, or a probability of correctness.

The “inner” and “outer” positions are two members of the original 24-query test
grid. Moving toward the edge can leave more ambiguity with the same seven
observations. The two positions were selected for explanation; the full result
summary includes all 408 queries across all 17 fields.

## What is saved here

- [data.json](data.json): four illustrative fields, real histograms, source
  statistics, seven observed complex readings, two held-out positions per field,
  eight prefix disks each, and normalized harmonic-polynomial coefficients.
- [verification.json](verification.json): all 17 fields' saved engine radii and
  error summaries, mutation/restart results, and source-file SHA-256 hashes.
- [Research draft](gigi-geometric-inference.pdf).
- [Completion specification](BOUNDED_HOLOMORPHIC_SPEC.md) and
  [saved completion results](BOUNDED_HOLOMORPHIC_RESULTS.md).
- [Harmonic-conjugate specification](HARMONIC_CONJUGATE_SPEC.md) and
  [saved harmonic-conjugate results](HARMONIC_CONJUGATE_RESULTS.md).

The original experiment saved the final engine radii, histograms and numeric
diagnostics. It did not retain full HTTP responses for every prefix. For the
animation, prefix disks are therefore reconstructed from the source histogram
with independent Pick-matrix linear algebra and checked against a Schur
recursion. **All 408 final reconstructed radii match the recorded GIGI outputs
within 2.0 × 10⁻¹⁴.** The 64 illustrated prefix disks are checked for nesting,
representative containment, held-out-value containment and interpolation.

The browser may animate between two states, but only integer slider stops are
computed observation counts. Each displayed disk is a marginal set: choosing
points independently from several disks need not produce one common function.

## Two distinct experiments

Completion starts with seven complex observations and returns possible missing
complex values. Its representative is one compatible function, not an asserted
recovery of the full source fingerprint. The reported 96.73% is reduction of
the median admissible **radius**, not prediction accuracy or retained data.

Harmonic-conjugate recovery starts with a **complete real polynomial**, not
seven scattered observations. GIGI checks the real polynomial's harmonicity,
recovers its conjugate after fixing the imaginary center constant, checks a
bound on the entire complex polynomial, and returns its derivatives. The
real-data run supplied integer-count real coefficients and a bound scaled by
record count; the website uses the equivalent normalized coefficients. The
816 query values and their derivatives were checked against an independent
full-polynomial oracle. They are consequences of the supplied analytic field,
not newly predicted physical measurements.

Both experiments are finite-precision evidence. Histogram binning is lossy;
the analytic fingerprint model does not make wine chemistry or power-plant
physics holomorphic. The tests do not establish statistical calibration,
general manifold gluing, or arbitrary missing-fact recovery.

## Reproduction

From the website repository, with a sibling local `gigi` repository containing
the pinned original archives and saved experiment reports:

```text
python scripts/build-geometric-inference-data.py
python scripts/check-geometric-inference-data.py
```

The builder accepts `--gigi-root PATH`. It requires NumPy and openpyxl, checks
archive hashes, recomputes every histogram directly from the original records,
cross-checks both saved experiment reports, and reproduces all final radii.
It neither starts nor modifies an engine. The standalone checker requires
mpmath and rechecks the published prefix disks at 70-digit precision, then
independently differentiates the example fields and checks the
Cauchy–Riemann and Laplace identities. This validates the displayed data;
it does not rerun GIGI's complete regression suite.

The GIGI specification/results downloads give the original engine reproduction
commands, scope, ignored pre-existing tests, and refusal controls.

## Source attribution

- [Wine Quality](https://archive.ics.uci.edu/dataset/186/wine+quality),
  Cortez et al. (2009), DOI 10.24432/C56S3T, CC BY 4.0. Archive SHA-256:
  `3ed56667f4b828242bd732d7d1dd7f2861e54432239d7fa63877014cbb0304d4`.
- [Combined Cycle Power Plant](https://archive.ics.uci.edu/dataset/294/combined+cycle+power+plant),
  Tufekci and Kaya (2014), DOI 10.24432/C5002N, CC BY 4.0. Archive SHA-256:
  `cc7b2a4977c0a44e8221c91d9a7e5746b3c68186cff7e5c61c70af6432b98c7a`.

Power-plant workbook sheets other than the first are shuffled copies and are
not counted as additional observations. All 12 wine and all five plant numeric
fields were included in the experiment; identifiers were excluded.