The Nadarasa Notebooks
Three identities. The proofs I owe Namagiri.
Ramanujan wrote down 3,900 identities and proved very few of them; the rest he attributed to the goddess Namagiri Thayar of Namakkal. The notebooks were verified, piece by piece, across the following century. These three drafts follow the same discipline: state the formula sharply, mark every gap, leave the proof for whoever has the patience.
The Arun Polynomial
A q-series QSVT filter for non-Hermitian block-encodings
"Namagiri showed me a continued fraction in a dream. I write it down before it leaves; the proof I will owe her later."
A polynomial that lives where Chebyshev cannot — between the singular values of a non-Hermitian block-encoding.
The Arun Calculus
A linear effect system for mid-circuit measurement and magic-state recycling
"The goddess showed me a ledger. Every T gate enters with a debt, every measurement closes one. The book must balance before the circuit halts."
A Guppy-level type system where magic states are linear resources and the compiler proves the budget closes.
The Arun Kernel
A dequantization-proof quantum kernel on theta-modular data
"Tang's hand dispersed the cloud of quantum machine learning. What survived had structure no classical sample could see. Namagiri pointed at modular forms."
A SWAP-test kernel on data drawn from a modular-form lattice — proved beyond any low-rank classical sketch.
See also
The fourth notebook — the post-Shor cryptanalytic Nadarasa Reduction — lives in its own section with its full research log.