Math Mapgenerated 2026-10-25 · a354234
PUBLIC BUILD

Arc from 037 and P-019 and P-027 and P-028 and P-029

roots 037 · P-019 · P-027 · P-028 · P-029 · 10 records · depth 3 · 1 confirmed · compact density (§5)

The chain is read from builds_on: (docs/OUTTAKE.md, Cross-record fields). Every id, question, sealed prediction, verdict and count below comes from the records at a354234.

037 grokking-multiplicative-characters
Trained to grokking on multiplication mod p, which characters does a small network learn — the additive characters of Z/p, or the multiplicative (Dirichlet) characters, i.e. Fourier modes in discrete-log coordinates on (Z/p)^x?
CONFIRMED 2026-09-28 by the repo owner, scored on the prediction's intent.
CONFIRMEDbuilds on root
P-019 probe
Does every computable magnitude come through a convex dual?
builds on root
P-027 probe
Can the staircase of a deep linear network's loss be read backwards, as a measurement of a chosen spectrum?
builds on root
P-028 probe
Is the period-doubling past the edge of stability Feigenbaum's cascade, and in what dimension does that stop holding?
builds on root
P-029 probe
Is the double-descent spike at p = n quantitatively the Marchenko–Pastur edge?
builds on root
N-031 note (no mark: notes carry no condition)
MPS and CPU training diverge for the same seed in R26_training_dynamics — so a retrain meant to reproduce 037's W_E must run on the same device, and be checked
builds on 037
P-031 probe
Grokking multiplication on the units of Z/561 — which characters appear when the group is not cyclic and no discrete log exists?
builds on 037
P-034 probe
Eta's coefficients indexed by n versus by m — is one coordinate trivial and the other near-impossible?
builds on 037
P-035 probe
Are learning-curve shapes exactly two kinds — spectral readouts and competitions between coexisting solutions?
builds on P-027 · P-028 · P-029 · 037
N-039 note (no mark: notes carry no condition)
Loop-in from the grokking chat, 2026-10-03 — "define the geometry by what the shapes optimise" is a duality bridge run backwards plus the rigidity question, not a new term; candidate §67 entries; two candidate probes on merging grokked seeds; a speculative physics chain with every attribution unverified
builds on P-019 · P-035

10 records, longest path 3. The vertical bar in the gutter marks a record with more than one parent. A withdrawn or retired record keeps its place: struck id, retired ink, still on the page. A probe or note has no question:, prediction: or verdict: field, so its row carries its title and nothing is invented to fill the gap. A row shows a whole sentence or none. Print variant (Paper Pro, DESIGN-SYSTEM §7).

generated 2026-10-25the lab index