The library.

The sixth paper of the series opens a new program in which the earlier papers' trained populations are reference truth rather than the object, and walks the first mechanism for producing weights without training: a closed-form tangent-kernel solve. On Qwen3-0.6B, BoolQ and rank-8 LoRA, one Jacobian pass over 1,024 examples and a CPU ridge solve lift the base from 64.9% to 75.0% (+6.7 SE) at the population's own row space and to 74.8% at a fresh initialization, on held-out examples, replicated on an untouched evaluation slice — pre-registered and confirmed. The same solve has a composed cosine of at most .10 to every compared member of the AdamW-trained population, because only about 3% of a trained adapter's lazy part lies in the span of the initialization's gradient rows and a member is outside that span five optimizer steps into training; lineages retrained with plain SGD from the same initializations and minibatch streams stay inside it (.63–.65 versus .14–.17; confirmed 4/4). At a shared initialization two solves add, to the gap the first-order cross-kernel term predicts. The registered cell for the SGD end-state, falsified as written, measured a difference between example draws; its settling experiment, run after the leg was reopened, found the margin rows to be the wrong tangent space, and in the loss's own tangent rows an SGD lineage stays entirely inside the span through step 32 (the curve is lab notes) and 89–93% inside at step 500 ("partly" against a .95 bar; four lineages; the registered aggregate reads mixed) while its AdamW twin from the same initialization and minibatches is 27% inside at step 5 and 7% at the end.

The fifth paper of the series prices the other factor of a weight population's description — the training per member — with four pre-registered campaigns along an 11-snapshot trajectory of a 1,024-lineage LoRA population. The per-block variance law is render-relevant from 6% of training; the mean's direction is fixed by 40% and, forecast from the 40% snapshots and given the final norm, renders at anchor grade; the mean's norm is the late arrival — it doubles in the last 37% of training, defeats every 1,024-member early description, and is not supplied by the registered early law — but it is nearly a constant of the base model across tasks and ranks and transfers from any other population of the base model and recipe. With the sign gauge discovered from the same snapshots, the description needs zero finals of the population it describes; the cheapest form is eight lineages at 40% of training plus a same-rank population's two constants. Seen through the description, training's late phase is a one-scalar coherence event.

The fourth paper of the series names what the first three converged on — the two-moment description of a gauge-quotiented weight population — and tests it through a four-rung pre-registered ladder. The estimation floor is eight members, sign-gauge self-discovery included; at two, the honest fit renders geometric-novel functional clones that only a functional filter catches. Full-network basins end inside the population's own variance, bounding deep describability to adapter space; off seed-purity, describability survives with structure — rank is coverage, basin depth is an absolute task-conditioned budget, co-centered pools still fail by geometry, and one mis-anchored sign convention silently erases everything. Learning, in its third straight regime, buys steering and not reach.

The third paper of the series: fitted parametric families — an aligned mean plus per-block variances, no training, no learned generator — saturate a memorization-guarded audit at 2–3× the corpus spread and reach 0.781 at 4×, inverting the registered prediction: fresh draws from the described law beat the population's own rescaled residuals, which produce zero passers at depth. Beneath the result, the canonical chart's sign convention had split the population into coin-flip classes and hidden ~95% of the mean's energy, and the residual's realization is the initialization — training learns the law. The render-relevant description of this weight population is its aligned mean and one variance per matrix block.

The adapter-space sequel to Canonicalize, Then Generate. On a 1,024-adapter LoRA population, fixed recombination beats weight-space flows under a joint novelty-and-performance criterion; a 16-dimensional learned merge operator ties the incumbent while adding steering; and calibrated recombine-then-push operators populate the deep novelty frontier to 4x the corpus spread, falsifying a pre-registered thin-manifold prediction.

We put a seven-level reasoning-effort knob on a local AI gateway, made graded thinking budgets enforceable on llama.cpp-served models, and swept the curve on two models plus a judge-selection leg. A named level turns out to be a bet about a question's natural deliberation length: it only pays below that length, its meaning shifts between models, and small budgets are riskier than none at all.

Months of production serving, training, and tooling on a DGX Spark, distilled into the traps that caused real incidents: a unified memory pool where standard tools misreport, page cache that can kill model loads, and bandwidth — not capacity — as the true ceiling. Written for the code agents operating the box, with measured numbers over spec-sheet claims and a symptom→cause→fix table for when something is already on fire.

An audit of the canonicalize-then-generate recipe for neural-network weight generation: what quotienting permutation and scale symmetries actually buys under a memorization-guarded, novel-and-performant criterion — measured on three model-zoo rigs, with a division of labor between learned flows and canonicalized soups, and velocity extinction, a collapse law for small-zoo flow matching.

The Orb's open foundations, the coordination of a hive of agents, and the correlated-failure trap that undermines naive fleets.