One place for the whole research surface — including the dead ones. A catalogue that lists only survivors is a sales sheet; the kill reasons are the reusable part, and two of them have already prevented a second mistake. Nothing here is routed or exported.
Verdicts are this repo's own judgement, and the occupancy half is separate from the feasibility half. A direction can be perfectly good mathematics and still be infeasible here — this tree does validated numerics and ships zero-dependency verifiers; it cannot train models. Two entries below died on that alone. Three turned out to be things already delivered in this programme under another name, which is the most common outcome so far and the most useful one.
A pattern over three artifacts that already pass their gates: multiplicity PROVED in disjoint balls, a Wardrop face DEMONSTRATED, a refusal wall MEASURED. Cannot be killed by a literature search — it claims no empty ground.
PATH 13, opened 2026-07-31 after requisite 0 survived: the polynomial kernel clusters and bifurcates in cluster count, so substituting a rational attention for softmax does not kill the phenomenon. Continuous-β form named. Locator / Newton / (2.5,2.7) under-iteration defects demoted. Existence, 1-cluster spectrum, bistability at β=5/3, and reduced 2-cluster angle law (one-sided semi-stable, exact rationals) decided. Tight ω-limit not claimed. Never about Transformers.
Finite-dimensional dynamics; certifying a bifurcation = enclosing an eigenvalue crossing. Reuses the stack unchanged. Softmax put it behind interval-transcendentals; PATH 13 takes the rational substitute out from behind that blocker. Occupancy check pending — validated continuation may already cover it generically.
The only survivor of the first five. Discrete enclosure DISCHARGED 2026-07-31 (exact-rational signedGap≡0 + interval wrap contains 0 with explicit r); open is the continuum with the discretization clause.
test-transpose-sin.js: 'adjoint-matched pair FP = HJBᵀ certified (operator level)', two mutants caught. The core is delivered; only the Transformer framing is new. The 'eliminates vanishing gradients' claim is almost certainly false — adjointness is structural, explosion is spectral.
min-max representation IS the tropical form (ICML 2018), and certified robustness over min-max representations is published (arXiv:2310.04916). A search for 'tropical' never surfaces it.
Died on its own premise: an interval rotor is a SET, and a set cannot satisfy R R† = 1 exactly unless it is a point. The word carrying the proposal cannot survive interval arithmetic. This constraint recurs whenever someone proposes exactness inside an enclosure.
The deliverable is a trained world model. No GPU, no torch, no datasets here. An idea whose proof is an experiment cannot be certified in this tree.
Two independent kills: heavily occupied since the WGAN lineage and Sinkhorn divergences, AND the deliverable is again a trained model.
Empty by keyword, occupied in substance: a sheaf Laplacian is a finite symmetric PSD matrix and verified Hermitian eigensolvers are mature. The empty search measured the absence of a paper nobody needs.
Two of three tiers die — the truncation bound is folklore, exact Chen is degenerate (exact arithmetic on exact data). The third is unlocated but blocked: for H < ½ the true value needs a definition before it can be enclosed.
the flagship forward item — a map of where behaviour changes across a parameter box, rather than one equilibrium. Directly instantiates the thesis above.
a parameter-bracketing candidate; survived triage on the same 'certifiable by bracketing' pattern.
the python-vs-js agreement raised from a check to a claim.
UNBACKED DRAFTS, owner ruling 2026-07-30: notes, not reports. Each is the sole file in its unit — no kernel, no battery, no gate, no ledger record.
an interval-arithmetic certificate of a parametric monotonicity law; carries its own PARTIAL_RULING. Unshipped.
unshipped draft, but its tests/probe-tierb.js is CITED BY a certificate record — the directory is load-bearing even though the page is not.
NOT unbacked: exact rationals + Sturm, with a battery wired into make check. Listed here for completeness, not as a draft.