AdS–dS: retained projective frontier
Research cutoff: October 20, 2026. This is a source-linked programme snapshot, not a new verification, live graph mirror, or physical geometry certificate. It supplements the conditional interval result without changing that theorem's record/observation scope.
What the source already constructs
| Object | Reported construction or counterexample | Boundary |
|---|---|---|
| Enriched source line | Four source-defined points on an actual twistor line reproduce the transported history6 boundary coefficient as a cross-ratio. Three kinematic inputs with the same bare compiler record give different coefficients. | There is a nontrivial source-derived projective observable, but it does not factor through the bare record. These points are not four endpoints of the finite interval chart. |
| Actual prefix actions | The eighteen selected prefix instances split into nine rank-two and nine rank-one products. Rank-two common actions preserve the cross-ratio; rank-one outputs do not have a nondegenerate cross-ratio. | The tested prefix family is not a group of invertible projective symmetries. Its common row action is a declared comparison, not the independently derived native evolution of the whole twistor packet. |
| Retained execution envelope | Tagged matrix words compose by append, including rank loss. The execution retains the original points, source identity and intermediate outputs. | Recovering the original cross-ratio reads retained input; it does not reconstruct erased information from the output. The envelope is not native continuation closure and is not geometric emergence. |
| Output-plus-matrix recovery | Nine exact kernel-perturbation witnesses change the origin cross-ratio without changing any output or the matrix/image/kernel. | The obstruction is on the ambient linear-packet domain, not a proof against every separately certified smaller native image or a construction of alternative native kinematics. |
| Metric-scale selection | C=4 and C=16 satisfy the tested projective, causal and connection requirements with different curvatures. | The specified unique-scale selector is rejected. This does not reject a new source-supported selector or the revised mathematical task allowing a scale family and two shadows. |
A zero matrix product has no projective matrix class; collapsed or zero outputs are not assigned a cross-ratio by canceling a zero denominator. Negative determinant is separately distinguished from positive-determinant projective normalization. These are domain controls, not derivations of Lorentzian spacetime.
First missing geometric comparison
A successful enriched-source bridge must supply a real ordered endpoint comparison and its nonsingular domain, explicitly handle diagonal/boundary records and rank-one actions, and show how it sources the smooth projective chart used by the metric classification. The diagonal [2,2] compiler record is outside the metric chart's strict endpoint domain.
Retaining the input makes information preservation possible; it does not select that geometric comparison, physical causality, scale or a continuum limit. A nonzero source projective invariant and an independently identified real interval geometry are different accomplishments.
Recorded next bounded test
The source workbench's recorded recommendation is adsds:dual-shadow-transport-audit. This is a planning snapshot, not a newly executed result or a probability that the programme is true.
The revised mathematical target allows two operation-compatible projections of a common source, with different future subcategories and a common R sector. No unique scale or privileged shadow is required. The earlier failed selector remains failed rather than being silently reclassified as a success. Hardware is outside this workstream.
For the frozen finite source at m=3, the recorded acceptance test asks for:
- explicit target execution categories and both projection maps;
- all legal one-step and composable two-step identity/composition and domain checks;
- visibility guards at every intermediate object, the common R restriction and based cavity edit squares;
- a forgetfulness table separating endpoint-only, labelled-process and retained-execution readouts.
A projection undefined on an admitted domain, a failed comparison square, or a claimed faithful readout erasing different admitted histories is a falsifier. The instruction is to stop at the audit: supplied target metrics do not become derived curvature. Common-source geometric identification and optional reconstruction have their own additional obligations.
Sources and reproduction boundary
Reported written identities and exact checks were not rerun for this publication. These source packets specify commands, frozen inputs, controls and receipt provenance:
- Source-projective bridge:
research/nima/checkers/check_source_projective_bridge.py. - Retained correspondence and singular controls:
research/nima/checkers/check_retained_projective_correspondence.py. - Metric classification and rejected selector:
research/nima/checkers/check_projective_interval_metric_selection.py. - Two-shadow revision and audit acceptance.
- Source workbench snapshot:
research/nima/checkers/check_ads_ds_workbench.pyrefreshes the planning overlay; it is not itself a replay of all scientific suppliers or graph synchronization.