THE SHAPE: Calibration-invariant morphology and identifiable geometric response

THE SHAPE is an Eolisa Space research release accompanying the article “THE SHAPE: Calibration-invariant morphology and identifiable geometric response,” by Onur H. Evgin and the Eolisa Space Science Team. Release 9.0.0 brings together the research preprint, executable scientific software, unchanged public Event Horizon Telescope visibility data, generated results and verification records.

The study examines which features of an astronomical shape remain identifiable after phase information is removed, station-amplitude gains are treated as nuisance parameters, or physical interpretation is restricted to a specified model. Four connected components form the principal analysis.

1. Parity-specific information under exact Rice noise. For a real even brightness distribution with an odd perturbation, the analysis derives information in the squared perturbation. Amplitude relative entropy is quartic near symmetry, while phase-referenced complex data have a quadratic response. Local separation rates assume fixed nuisance parameters and independent repetitions. Central reflection remains exactly unresolved by amplitudes. Numerical quadrature, independently checked derivatives and synthetic power controls accompany the derivations.

2. Station-gain projection and information retention. A whitened array-graph quotient removes station-amplitude nuisance directions in the log-amplitude mean. Local information certificates identify retained, weakened and unsupported parameter directions. A gain-coherence ladder compares independent timestamp gains with gains held constant over observing blocks or individual files.

3. Public-data morphology and selection audits.The inputs comprise 106,138 visibility records in twelve M87* and Sagittarius A* day/band files. With baseline length at least 0.1 Gλ and measured amplitude SNR at least five, the same selected records retain 1,183, 39,622 and 40,732 independent residual log-amplitude modes under timestamp-, block- and file-level gain assumptions, respectively. These counts describe conditional calibration scenarios rather than measured gain stability. The release includes selection graphs, conditional ring fits, parameter-boundary and alias records, held-out observing blocks and finite-SNR controls. Direct-amplitude reference fits, 128 block-bootstrap replicates per file and both-orientation closure-phase diagnostics provide supporting comparisons.

4. Finite-impact-parameter response in a specified geometry. Within the static Simpson–Visser family, a positive-moment representation yields deflection series, two-sided remainder bounds and inverse enclosures over a range with constant critical size. The implementation records 592 forward cases, 4,736 truncation checks and 64 independent geodesic comparisons. The inverse assumes the metric family and required physical inputs are known.

The package contains the article PDF and LaTeX source, Python implementations, tests, pinned input manifests, unchanged public CSV files, source and license notices, scientific figures, machine-readable results and a reproduction driver. The recorded baseline suite passes 214 tests. Integrity and numerical comparison tools distinguish immutable source records from generated outputs and environment-dependent timing.

The original public EHT bytes match the pinned 2019-D01-01 and 2022-D02-01 releases. M87* and Sagittarius A* files are analyzed separately by day and band. Neither time samples nor bands are automatically treated as independent astrophysical realizations.

Station-gain cancellation is an exact statement about the noiseless log-amplitude mean. Its observed implementation uses a conditional high-SNR approximation and measured-SNR selection. Morphological fits and local Fisher scales are model diagnostics, not calibrated shadow or spacetime measurements. The geometric calculations do not convert the EHT ring fits into an observational wormhole constraint. Mathematical and observational foundations are attributed throughout the article; the accompanying article is a research preprint.

Authored code and text retain the project MIT license. Public EHT data retain their upstream PDDL-1.0 terms. Other component notices remain separate in the archive.