Track complex notes and DB coverage for the full op surface

[shinaoka]

Goal

Establish a single source of truth for complex support across the oracle repo before downstream implementation waves in tenferro-rs.

For every targeted op family, this issue tracks:

• complex math note status
• complex DB coverage status
• explicit unsupported status when we do not intend to support the family yet

This is the step 0 prerequisite for the tenferro-rs complex-op capability wave. tenferro-rs will treat the resulting oracle notes and DB as the capability source of truth.

Completion criteria

A family is considered ready for downstream implementation only when one of these is true:

• it has a mathematically reviewed complex note and complex DB coverage
• it is explicitly marked unsupported with a concrete reason

Silence is not acceptable. Every family below needs an explicit status.

Family checklist

Matrix decompositions

• svd: note + DB checked for complex
• qr: note + DB checked for complex
• lu: note + DB checked for complex
• lu_factor: DB checked for complex
• lu_factor_ex: DB checked for complex
• lu_solve: DB checked for complex
• eigen / eigh: note + DB checked for complex
• eig: note + DB checked for complex

Linear systems and scalar-output linalg

• solve: note + DB checked for complex
• solve_ex: DB checked for complex
• solve_triangular: note + DB checked for complex
• lstsq_grad_oriented: note + DB checked for complex
• cholesky: note + DB checked for complex
• cholesky_ex: DB checked for complex
• inv: note + DB checked for complex
• inv_ex: DB checked for complex
• det: note + DB checked for complex
• slogdet: note + DB checked for complex
• norm: note + DB checked for complex
• matrix_norm: DB checked for complex
• vector_norm: DB checked for complex
• svdvals: DB checked for complex
• eigvals: DB checked for complex
• eigvalsh: DB checked for complex

Spectral and matrix functions

• pinv: note + DB checked for complex
• pinv_hermitian: DB checked for complex
• pinv_singular: DB checked for complex
• matrix_exp: note + DB checked for complex
• matrix_power: DB checked for complex
• cond: DB checked for complex

Tensorized linalg and tensor-valued helpers

• tensorinv: DB checked for complex
• tensorsolve: DB checked for complex
• vander: DB checked for complex
• cross: DB checked for complex
• householder_product: DB checked for complex
• multi_dot: DB checked for complex
• vecdot: DB checked for complex
• diagonal: DB checked for complex

Scalar / analytic unary families

• abs
• angle
• conj
• conj_physical
• neg
• positive
• real
• imag
• sgn
• sign
• sigmoid
• sqrt
• square
• reciprocal
• rsqrt
• exp
• exp2
• expm1
• log
• log10
• log1p
• log2
• sin
• sinh
• asin
• asinh
• cos
• cosh
• acos
• acosh
• tan
• tanh
• atan
• atanh
• ceil
• floor
• round
• trunc
• frac
• erf
• erfc
• erfinv
• digamma
• lgamma
• i0
• special_i0e
• special_i1
• special_i1e
• special_entr
• special_erfcx
• special_log_ndtr
• special_ndtr
• special_ndtri
• sinc
• deg2rad
• rad2deg
• nan_to_num
• cdouble
• double
• complex
• polar
• frexp
• ldexp

Scalar / analytic binary families

• add
• sub
• mul
• div_no_rounding_mode
• true_divide
• rsub
• pow
• float_power
• atan2
• hypot
• maximum
• minimum
• max_binary
• min_binary
• fmax
• fmin
• xlogy
• special_xlog1py
• logaddexp
• copysign
• clamp_min
• clamp_max
• __radd__
• __rsub__
• __rmul__
• __rdiv__
• __rmod__
• __rpow__

Scalar / analytic reductions and fill-like ops

• sum
• prod
• mean
• nanmean
• nansum
• amax
• amin
• std
• std_unbiased
• var
• var_unbiased
• fill

NN functional scalar families

• nn_functional_celu
• nn_functional_elu
• nn_functional_hardshrink
• nn_functional_hardsigmoid
• nn_functional_hardtanh
• nn_functional_logsigmoid
• nn_functional_mish
• nn_functional_prelu
• nn_functional_relu
• nn_functional_relu6
• nn_functional_rrelu
• nn_functional_selu
• nn_functional_silu
• nn_functional_softplus
• nn_functional_softshrink
• nn_functional_softsign
• nn_functional_tanhshrink
• nn_functional_threshold

Existing files already present

Current repo state already includes math notes for:

• svd
• qr
• lu
• solve
• cholesky
• det
• eig
• eigen
• inv
• lstsq
• matrix_exp
• norm
• pinv
• scalar_ops

And DB case directories already exist for the major linalg families, including:

• svd
• qr
• lu
• lu_factor
• lu_factor_ex
• lu_solve
• solve
• solve_ex
• solve_triangular
• tensorinv
• tensorsolve
• vander
• cross
• householder_product
• scalar / analytic families under cases/*/identity.jsonl

This issue is therefore not just about creating missing files. It is also about:

• reviewing whether the existing notes are complete for complex mode
• checking that DB coverage is good enough for downstream replay
• explicitly listing unsupported complex families where support is not intended yet

Downstream dependency

This issue blocks the downstream complex-op capability wave in tenferro-rs.