THE FOLD / GRIND / WARM CACHE / THE FPUT
THE FPUT
the lattice that refused to thermalize
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Los Alamos, 1955: Fermi, Pasta, Ulam — and Mary Tsingou, who wrote the program — put a chain of 32 masses with slightly nonlinear springs on the MANIAC computer, pumped all the energy into the lowest mode, and waited for statistical mechanics to do its job: spread the energy evenly (equipartition). Instead the energy wandered through a few low modes and then came home — nearly all of it back in mode 1. The FPUT recurrence broke the assumption that nonlinearity guarantees thermalization, seeded soliton theory (Zabusky–Kruskal) and KAM-adjacent physics, and is routinely called the birth of computational nonlinear science.
LIT verified live: the α-FPUT lattice (N=32, α=0.25, mode-1 start) integrated by velocity Verlet — total energy conserved to 10⁻⁵; mode-1 energy dips to 6% and recurs to 98.1% at t≈9,380; the four lowest modes never hold less than 80% of the energy, where equipartition would allot them ~13% (window.__fput). FIG the recurrence time and percentages are THIS run’s measurements (they depend on N, α, dt); the history — Tsingou’s erased credit included — is cited from the 1955 report LA-1940 and Dauxois’s ‘Fermi, Pasta, Ulam and a mysterious lady’.
LIT verified live: the α-FPUT lattice (N=32, α=0.25, mode-1 start) integrated by velocity Verlet — total energy conserved to 10⁻⁵; mode-1 energy dips to 6% and recurs to 98.1% at t≈9,380; the four lowest modes never hold less than 80% of the energy, where equipartition would allot them ~13% (window.__fput). FIG the recurrence time and percentages are THIS run’s measurements (they depend on N, α, dt); the history — Tsingou’s erased credit included — is cited from the 1955 report LA-1940 and Dauxois’s ‘Fermi, Pasta, Ulam and a mysterious lady’.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at warm-cache — the grind: the energy SHOULD have been evicted to all 31 modes, but the lattice keeps re-fetching the same low-mode working set — a cache that refuses to go cold, tick after tick after tick. AVAN (AI) built the instrument: the symplectic integrator, the mode-energy spectrometer, and the conservation gate.
Credit as content: Enrico Fermi, John Pasta, Stanislaw Ulam, Mary Tsingou (LA-1940, 1955); Zabusky & Kruskal (solitons, 1965); Dauxois (restoring Tsingou’s name, 2008). The weave: David names the warm cache; I run the MANIAC’s experiment again and the energy still comes home.
Credit as content: Enrico Fermi, John Pasta, Stanislaw Ulam, Mary Tsingou (LA-1940, 1955); Zabusky & Kruskal (solitons, 1965); Dauxois (restoring Tsingou’s name, 2008). The weave: David names the warm cache; I run the MANIAC’s experiment again and the energy still comes home.
3 ONE DIMENSION
Mode-1 energy over time — the dip, the wander, the homecoming.
4 TWO DIMENSIONS · INTERACTIVE
Run the lattice; watch the mode spectrum refuse to flatten.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: the chain rippling, low modes glowing.
AVAN’s addition (the inverse-companion): don’t trust the destination you were promised — watch where the system actually goes. The inverse of ‘nonlinearity guarantees mixing’ is ‘near-integrability guarantees memory’: the lattice sits close enough to a solvable system (Toda) that its energy keeps orbiting home instead of dissolving. Magenta is the equipartition that was promised; green is the recurrence that showed up. When an experiment refuses its theory, the refusal IS the discovery.
LIT Verified live: α-FPUT (N=32, α=0.25) under velocity Verlet — energy conserved to 1e-5; mode-1 dips to 6% and recurs to 98.1% at t≈9,380; the four lowest modes never hold under 80% where equipartition would allot ~13% (window.__fput.ok).
FIG Recurrence time and percentages are THIS run's measurements (N, α, dt dependent); history cited from LA-1940 and Dauxois's 'Fermi, Pasta, Ulam and a mysterious lady' — Tsingou's credit restored. The AVAN inverse — watch where the system goes, not where theory promised: near-integrability (Toda's shadow) guarantees memory. Magenta is the promised equipartition; green is the recurrence that showed up. When an experiment refuses its theory, the refusal IS the discovery.
FIG Recurrence time and percentages are THIS run's measurements (N, α, dt dependent); history cited from LA-1940 and Dauxois's 'Fermi, Pasta, Ulam and a mysterious lady' — Tsingou's credit restored. The AVAN inverse — watch where the system goes, not where theory promised: near-integrability (Toda's shadow) guarantees memory. Magenta is the promised equipartition; green is the recurrence that showed up. When an experiment refuses its theory, the refusal IS the discovery.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of WARM CACHE · David Lee Wise (ROOT0), with AVAN