# Bounded Holomorphic Completion Results

Date: 2026-10-29. Scoped gate: PASS. Uncommitted and not deployed.

## Implemented boundary

`POST /v1/bundles/{name}/brain/holomorphic`, enabled by `kahler`, implements
bounded scalar holomorphic interpolation on the open unit disk. It returns a
Schur-function representation and marginal admissible-value disks, or a precise
infeasible/unresolved verdict. The represented function has harmonic real and
imaginary parts. No assertion about arbitrary manifolds or raw physical laws is
made. The specification is `docs/BOUNDED_HOLOMORPHIC_SPEC.md`.

The generic mathematical implementation is `src/geometry/holomorphic.rs`.
The transport and measurement boundary is
`src/bin/gigi_stream_handlers/holomorphic.rs`. The route and full schema are
documented in `openapi.json`. No existing inference algorithm was replaced.

## Gate evidence

Logs live in `output/bounded-holomorphic/`.

| Gate | Evidence |
| --- | --- |
| Initial mathematical red | `red-math.log`: 10 behavioral failures against the stub |
| Initial HTTP red | `red-http.log`: 2 behavioral failures against the stub |
| Rounded unit norm red | `red-rounded-unit.log`: wrong uniqueness classification reproduced |
| Integer rounding red | `red-integer.log`: silently rounded measurement reproduced |
| Pick mechanism removed | `mutant-pick.log`: contradiction verdict gate fails |
| Query-radius mechanism removed | `mutant-radius.log`: radius becomes 2 instead of 1; gate fails |
| Restored math and HTTP | 13 mathematical tests and 5 HTTP tests pass in the kahler suite |
| `cargo test --features kahler` | 2,079 passed, 0 failed, 23 ignored including doctests |
| `cargo test` | 1,580 passed, 0 failed, 22 ignored including doctests |
| `cargo test --examples`, with and without kahler | All three available example targets compile/run; no example unit tests defined |
| Fresh live real-data acceptance | PASS: all 17 fields, 408 held-out queries, and mutation/restart controls |

Both intentional mutants were restored. Near-unit ambiguity is not rounded into
uniqueness. Nonrepresentable integers and timestamps are refused rather than
silently converted. Encryption refusal covers all five modes. Transport gates
cover JSON/DHOOM equality, missing/unknown/duplicate fields, nulls, updates,
deletion, and same-name recreation at an identical revision number.

The kahler run's 23 ignored items comprise 19 pre-existing test exclusions and
four pre-existing ignored doctests; default has three ignored doctests (22 total).
They are not counted as passes or repaired here.
Some describe unresolved engine defects outside this read-only feature.
The initial `green-http.log` is an intermediate attempt that exposed the
encrypted fixture's missing durable seed declaration; final restored evidence
is `all-targets-kahler.log`, not that intermediate attempt.

## Real data protocol

`e2e/probes/bounded_holomorphic_real_data.py` uses the same code on every measured
numeric field of public UCI Wine Quality and Combined Cycle Power Plant data.
It imports the original records for traceability, computes 32-bin empirical
probability generating functions from the pinned source files, and stores seven
interior evaluations per field as explicit complex observation bundles.

Nonnegative empirical probabilities summing to one establish the generating
function's unit bound. Binning is lossy. Chemistry and turbine physics are not
being declared holomorphic. The independent oracle evaluates the full empirical
polynomial and derives value disks using a Pick-matrix Schur complement, not a
copy of the production Schur recursion. Withheld values are not expected to equal
the selected representative.

Final measurements and source hashes are recorded in
`output/bounded-holomorphic/real-data-report.json`.

| Measurement | Observed result |
| --- | --- |
| Wine Quality | All 6,497 red/white records, all 12 numeric measured fields |
| Combined Cycle Power Plant | All 9,568 first-sheet records, all 5 measured fields including power output |
| Derived interpolation observations | 7 per field, 119 total, with original records retained for traceability |
| Held-out queries | 24 per field, 408 total; every oracle value contained |
| Median admissible radius | 0.0326711382, versus unconstrained radius 1; 96.73% smaller |
| Worst admissible radius | 0.3615180139; no hard cases dropped |
| Maximum independent disk disagreement | 1.9953e-14, below the predeclared 1e-7 tolerance |
| Maximum normalized interpolation residual | 2.2697e-16, below the predeclared 1e-8 tolerance |
| Maximum representative error against withheld oracle | 0.1792607945; the representative is not asserted to recover the original function |
| Contradictory edit and restoration | Infeasible while contradicted; original query results recover after restoration |
| Same-size coherent change | Query values change; independent oracle still agrees |
| Restart | All 17 fields rechecked successfully |

The median-radius threshold of 0.5 was specified before the oracle preflight.
This proves useful narrowing within the declared analytic class, not calibrated
population uncertainty or accuracy of arbitrary physical predictions. The
largest observed endpoint time was 17.02 ms for this seven-observation workload
in a debug build; this is not a production latency benchmark.

Source attribution and pinned hashes:

- [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`.

The live executable was explicitly rebuilt after the regression suites, copied
to the owned probe location, and checked against the build's SHA-256:
`9719fb3f86349c3046f42f66c3550ead6d1873818c0c2498da914a4c4b17c9ac`.
Its recorded mtime is 2026-10-29 20:40:25 UTC. The harness starts and stops its
own process in a temporary directory, uses 127.0.0.1, and strips production
GIGI/Tigris/AWS environment settings from the child only.

Reproduction from the repository root:

```powershell
cargo test
cargo test --features kahler
cargo test --examples
cargo test --features kahler --examples
cargo build --features kahler --bin gigi-stream
python e2e/probes/bounded_holomorphic_real_data.py --binary target/debug/gigi-stream.exe
```

The first two commands run libraries, binary tests, integration tests, and
doctests; the next two cover the explicit example targets as well. Other optional
feature combinations such as halcyon were not enabled for this scoped change.

## Limitations and deployment

V1 admits 1..64 observations and at most 256 queries, with nodes separated from
the disk boundary. Dense Pick diagnostics cost cubic time in observation count;
the Schur representation is linear in count. No learned chart, noisy-data fit,
annulus extension, probability calibration, or Marcella integration is included.
Results are finite-precision evidence, not formal exact-arithmetic certificates.

All work remains uncommitted. The user's existing release engine has not been
restarted or modified; probe servers use owned executables and scratch data.