A property-matched search for cosmic topology: validated framework and first constraints from 1.45 million DESI DR1 quasars

If the Universe is multiply connected, light from a single galaxy or quasar reaches us along several paths, so the same object appears at multiple sky positions, each seen at a different cosmic age. Searches for such "clone" images in three-dimensional catalogues were attempted two decades ago using positions alone and were abandoned in the face of object evolution, viewing-angle differences and distance uncertainties. We revisit the problem with a five-stage verification cascade that combines evolution-corrected intrinsic-property matching with the geometric constraints of holonomy: (i) property matching after rewinding objects along empirical evolution tracks; (ii) a property-weighted pair-separation histogram that suppresses the combinatorial background of classical cosmic crystallography by three orders of magnitude; (iii) a holonomy-consistency test exploiting the fact that all clone pairs share the same small set of translation vectors, extended by an axis-projection statistic that detects screw and glide holonomies directly; (iv) a held-out fingerprint test in which pairs matched on one feature subset must agree in features never used for matching; and (v) a chirality tag: in a non-orientable universe, clone images have mirrored spiral handedness. The cascade is validated end to end by injection on a flat-\(\Lambda\)CDM lightcone for all ten compact flat 3-manifolds (\(E_1\)–\(E_{10}\), generator conventions of the COMPACT collaboration), under published galaxy-evolution tracks, stochastic track divergence, flux-limited selection, survey masks and lensing magnification, and against a control class of injected strong-lensing duplicates, which the geometry separates from topological clones by more than five orders of magnitude in pair separation. We then apply the framework to 1,452,003 spectroscopically confirmed DESI DR1 quasars (\(0.8 < z < 3.5\)), using amplitude-normalized redrock template coefficients as a magnification-invariant spectral identity. After identifying and removing three classes of spurious excess with a redshift-shell-restricted permutation null, the search returns a null result: the largest set of property-matched pairs sharing a common translation vector is 22, consistent with the null expectation of \(19.6 \pm 2.3\) (empirical \(p = 0.20\) over 25 permutation realizations). Injection-recovery on the real footprint, with clone identity noise drawn from the distribution measured on 42,355 DESI repeat-observation pairs of the same quasars, converts this into constraints from large-scale structure. Marginalizing over tested manifold orientations and quasar duty-cycle assumptions down to \(10^{7}\) yr, compact flat topologies are excluded for side lengths \(L \lesssim 9\) Gpc (comoving; \(\simeq 64\%\) of the horizon radius), extending to \(L \simeq 12\) Gpc (\(\simeq 86\%\)) for favourable orientations at the central quasar-lifetime value. For the cubic 3-torus this is an independent cross-check of the stronger CMB matched-circle bound; for the Klein-type non-orientable manifolds \(E_7\)–\(E_{10}\), which published circle searches do not cover, it is a bound on topology-parameter space with no previous observational constraint. Quasar spectral evolution over Myr–Gyr baselines beyond the measured repeat-visit noise is the remaining stated caveat. The duplicate channel additionally recovers 102 same-object repeat observations hidden in the catalogue under distinct targeting identifiers, at sub-arcsecond separations and \(|\Delta z| \sim 10^{-4}\): an end-to-end positive control demonstrating on real data that the pipeline identifies true duplicates when they exist.