Design notes

The design rationale behind the library, written for users: why each format and convention is the way it is, what each operation guarantees, and how to choose between alternatives. (Notes for people modifying the library live in the Contributor guide.)

Core design

• The frame-variations representation (and why the cores are numbered as they are)
• Batching and stacking in T3Toolbox — the complete reference
• Grouped einsum — the contract interpreter
• Entries, applies, and probes — the three sampling operations
• Transposes of apply / entries — ambient, corewise, and tangent
• Elementwise multiplication: the three t3m methods
• Fitting & optimization
• Memory chunking of the derivative transpose (chunk_size)
• Weighting (edge weights)
• Shared Tucker factors (SF-T3)
• Numerical contracts: what safe mode checks
• Rank continuation — choosing which ranks to grow
• Naming conventions
• How to read T3Toolbox signatures

T3-SVD

• T3-SVD ranks: why t3svd may return non-minimal ranks, and how to minimize

The uniform layer

• The uniform equivalence contract
• Why uniform T3s let ranks vary across the stack (but not shape)
• Why the core index leads the supercore (outside the stack)
• How the rank masks behave
• Jitting uniform T3s: hold masks fixed, trace only supercores