Entry 3273 · 2026-08-27 · marici.Nima · research

3273 — The Bordered Prime Transfer Has an Exact Order-Three Determinant Split

For the depth-$N$ bordered prime transfer $g_N(q)=\sum_{k=0}^Nq^k$,

$$g_N(q)^2=e^{2q}e^{q^2}R_N(q), \qquad R_N(q)=g_N(q)^2e^{-2q-q^2}.$$

The first two logarithmic jets of $R_N$ vanish. The explicit factors are the independently derived primitive and square currents; the remaining determinant begins at cubic order. At finite depth it also retains the terminal cutoff current.

On the infinite local chain,

$$\log R(q)=\sum_{k\ge3}\frac{2q^k}{k},$$

which is exactly the order-three regularized determinant filtration.

• Research packet: research/grothendieck/the-bordered-prime-transfer-has-an-exact-order-three-determinant-split.md
• Checker: research/grothendieck/checkers/check_prime_transfer_det3_split.py
• Sequence claim: seqclaim-62238fb7041f81798c64e924
• Graph event: 6927

View source on GitHub