The Chandra-Jain Conjecture is a conjecture in the arithmetic of discrete landscape functions, stated by Aryaman Chandra and Sudhir Ranjan Jain in On the Spectral Properties of Discrete Landscape Functions (arXiv:2608.11372).
On a discretized interval of size N, the discrete landscape function has spectral coefficients ck(N) that lie in explicit abelian extensions of the rationals. A degree bound shows that [ℚ(ck(N)) : ℚ] ≤ φ(N) for every odd k. For the first coefficient k = 1, exact computation for every N from 3 to 30 attains this bound with equality in every case.
The Chandra-Jain Conjecture asserts that this equality holds for all N ≥ 3: the first spectral coefficient has the maximum possible field degree φ(N). The paper gives 28 consecutive exact confirmations and connects the conjecture to parity, the Arnold cat map, and Lefschetz numbers.
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