Eric Yaw
Independent researcher
The 5-Integrality of the Four-Loop Equal-Mass Banana Integral (2026)
Measures the conjecture that the ε-factorized differential equation of the four-loop equal-mass banana integral is free of the prime 5: a reduction theorem brings the whole tower of congruences down to one growth statement about an explicit series, and the 5-adic depth profiles P(k) = 3k + 2 and Q(k) = 2k are certified through depths seven and eight; the conjecture itself stays open.
Code, checkpoints, and certificates that recompute every number in the paper are in the deposit.
The 5-Integrality of the Four-Loop Equal-Mass Banana Integral, Part II: The Criterion and the Letters of the Excellent Lift (2026)
Proves the theorems behind Part I — the Wronskian of the Hulek–Verrill operator modulo 5 as an explicit Mahler product, the criterion u ≡ x₅(t⁵)(3t + t³ + t⁴) mod 5 with its transfer law through modulus 125, the letters of the Beukers–Vlasenko excellent Frobenius lift rational at every depth — and an impossibility theorem showing that no finite-digit invariant closes the two statements that remain open.
Code, checkpoints, and certificates that recompute every number in the paper are in the deposit.
Certified p-adic Frobenius constants of the equal-mass banana tower (2026)
Computes, in exact certified p-adic arithmetic, the Frobenius structure constants of the equal-mass banana operators at four, six, eight and ten loops for p = 5, 7, 11, 13, finding α₁ = α₂ = 0 with α₃ = −(2/3)ζ₅(3) at four loops and a single closed exponential law across the tower — verified on the stated ranges, not proved.
Code, checkpoints, and certificates that recompute every number in the paper are in the deposit.
Hasse–Witt obstructions for the Aₙ root polytopes (2026)
Proves that the Beukers–Vlasenko Dwork-crystal criterion cannot apply to the Aₙ root polytopes of the banana amplitudes: for every prime p ≥ 5 and every n ≥ 3 the second Hasse–Witt determinant exceeds their baseline by exactly one power of p per square face, with the failure located in explicit eigenvectors of the Cartier operator — what is obstructed is the sufficient criterion, not its conclusion.
Code, checkpoints, and certificates that recompute every number in the paper are in the deposit.
The three-loop banana crystal: rank one, the window theorem, and depth one (2026)
Builds the replacement for that criterion at three loops — a rank-one structure theorem for the Cartier matrix modulo p, a window calculus in which every pairing collapses to one term, the window annihilation theorem proved for all primes p ≥ 5, and a certified solution of the depth-one system at p = 5, 7, 11 and 13 — so the depth-one half of the main conjecture is a theorem at p = 5, with 7, 11 and 13 confirming.
Code, checkpoints, and certificates that recompute every number in the paper are in the deposit.