core: BraKetSymmetry of a Tensor deduced from indices' field + Hermiticity; drop Context::braket_symmetry

[evaleev]

Summary

A tensor's bra↔ket exchange symmetry is its own physical fact — the
composition of its abstract Hermiticity with the scalar field over which
its bra/ket vector pairing is defined (base_field(bra, ket)). It is not
a property of the active Context. This PR removes Context::braket_symmetry
and teaches the legacy Tensor ctors to derive their BraKetSymmetry default
the same way the field-agnostic Hermiticity-taking ctors already do.

What changes

1. Tensor ctors: default bks deduced from indices, not Context (86a613b3c)

The 6 legacy Tensor ctors (the two primary reserved_tag ones + 4 public
delegators) previously defaulted BraKetSymmetry bks to
get_default_context().braket_symmetry(). They now take
std::optional<BraKetSymmetry> bks_opt = std::nullopt and the primary ctors'
init lists resolve it via

braket_symmetry_(bks_opt.value_or(to_braket_symmetry(
    Hermiticity::Hermitian, sequant::base_field(bra_, ket_))))

Member declaration order guarantees bra_/ket_ are constructed before
braket_symmetry_, so reading them in the init expression is well-defined.

Callers that pass an explicit BraKetSymmetry (e.g. BraKetSymmetry::Nonsymm
for amplitudes) implicitly construct the optional and behave as before.
Callers that previously relied on the Context-derived default (C tensors
built by csv_transform_impl, overlap factories, etc.) now derive directly
from the indices' fields:

• real field → Symm
• complex field → Conjugate

2. Remove Context::braket_symmetry (69b11265c)

Removals:

• Context::braket_symmetry() accessor and braket_symmetry_ member
• Context::Options::braket_symmetry field
• Context::Defaults::braket_symmetry constant
• Context::set(BraKetSymmetry) setter
• braket_symmetry() comparison in Context::operator==

Updates to the remaining users:

• v1/deserialize.cpp::to_default_symms: fallback initialized to
  BraKetSymmetry::Conjugate (later relaxed — see commit 3).
• v3.cpp dummy-edge strict-assert: the per-edge upper bound on bra/ket
  endpoints can no longer be selected by a single Context value (per-tensor
  BraKetSymmetry would require per-vertex resolution); uses the looser
  nbra + nket <= 2 bound that subsumes both old branches.
• Tests: drop the braket_symmetry option / set(BraKetSymmetry::Symm) chain
  links in test_runtime, test_canonicalize, test_main, test_wick,
  benchmarks/main.cpp.

3. Deserialization fallback matches the new programmatic default (50513fd76)

The deserializer's BraKet fallback (when the serialized form omits it and
the caller didn't pin DeserializationOptions::def_braket_symm) should match
the programmatic ex<Tensor>(label, bra, ket) default — otherwise the same
expression built two ways ends up with two different braket_symmetry_
values and the ResultExprs compare unequal.

Change:

• v1/ast_conversions.hpp: DefaultSymmetries' BraKet slot is now
  std::optional<BraKetSymmetry>. std::nullopt means "defer to the
  Tensor ctor's derive-from-indices+Hermitian default". to_symmetries
  returns the optional through to the ex<Tensor> call.
• v1/deserialize.cpp: to_default_symms initializes BraKet to
  std::nullopt. Callers who want a fixed fallback (e.g. CSE tests using
  BraKetSymmetry::Nonsymm for amplitudes) still set
  options.def_braket_symm explicitly and that wins, unchanged.

Test snapshot rebaselines:

• test_mbpt: C{;;x_1,x_2} now spelled :N-S-S — empty bra/ket ⇒ Real
  field ⇒ Symm under the new default.
• test_wick: the two -1/2 terms swap order in the canonicalized Sum
  (canonical sort key changed under the new default).
• test_tensor_network: index canonical order for the two G/T pairs swaps
  in the V3 backend (V1 unchanged).

Validation

All SeQuant C++ unit tests pass locally. Pre-existing failures unrelated
to this PR: btas/unit/*, tiledarray/unit/*, sequant/unit/python/basic/run.

Verified downstream in mpqc4 PNO-CCSD eval trace on c4h10/cc-pVDZ: the
previously-distinct half-PNO-transformed g(μ̃,μ̃,Κ) · C(μ̃; a^{ij})
intermediates now share a single cache key (180…8566) instead of two
separate ones, halving the materialized tile memory from 3.32 GB to 1.66 GB.

[Copilot]

Pull request overview

This PR redefines bra↔ket exchange symmetry as an intrinsic per-tensor property (derived from indices’ scalar field + Hermiticity) rather than a Context setting, removing Context::braket_symmetry and updating construction/serialization/test behavior accordingly. It also introduces an explicit EvalOp::Adjoint IR node to represent adjointed Nonsymm tensors (label-marked with ⁺) as a unary evaluation operation instead of a leaf-label artifact.

Changes:

• Remove Context::braket_symmetry (options/defaults/setter/equality) and update tests/benchmarks that previously configured it.
• Update legacy Tensor constructors to accept std::optional<BraKetSymmetry> and derive the default from base_field(bra, ket) + Hermiticity::Hermitian (with a special-case for empty bra/ket).
• Add EvalOp::Adjoint to the eval IR, including binarization, evaluation dispatch, export handling, and TiledArray backend support.

Reviewed changes

Copilot reviewed 19 out of 19 changed files in this pull request and generated 4 comments.

Show a summary per file

File	Description
tests/unit/test_wick.cpp	Rebases expectations and adjusts context setup by forcing index spaces to Field::Real rather than setting braket symmetry on Context.
tests/unit/test_runtime.cpp	Removes braket-symmetry context option assertions and setters from context runtime tests.
tests/unit/test_parse.cpp	Updates expectations for deserialization fallback braket symmetry (now asserted as Conjugate).
tests/unit/test_main.cpp	Drops braket symmetry from default context initialization.
tests/unit/test_eval_expr.cpp	Adds coverage for representing adjointed Nonsymm tensors as EvalOp::Adjoint nodes during binarization.
tests/unit/test_canonicalize.cpp	Removes reliance on Context braket symmetry for canonicalization tests; uses explicit per-tensor symmetry instead.
SeQuant/core/io/serialization/v1/deserialize.cpp	Changes default-symmetry fallback logic now that Context::braket_symmetry is removed.
SeQuant/core/io/serialization/v1/ast_conversions.hpp	Refines braket symmetry parsing to preserve concrete v1 encodings and introduces new Hermiticity spellings (H/A).
SeQuant/core/expressions/tensor.hpp	Updates legacy ctor defaults to derive BraKetSymmetry from indices’ field + Hermiticity instead of Context.
SeQuant/core/export/export.hpp	Adds export-side handling for EvalOp::Adjoint nodes.
SeQuant/core/eval/result.hpp	Extends Result with a virtual adjoint() op used by the new eval IR node.
SeQuant/core/eval/eval.hpp	Adds EvalOp::Adjoint evaluation dispatch; updates logging/bytes accounting for unary nodes.
SeQuant/core/eval/eval_node.hpp	Updates linearization and cost models for unary adjoint nodes.
SeQuant/core/eval/eval_expr.hpp	Extends EvalOp enum and EvalExpr API to recognize adjoint nodes.
SeQuant/core/eval/eval_expr.cpp	Teaches binarize(Tensor) to translate label-marked adjoints into EvalOp::Adjoint nodes with a sentinel right child.
SeQuant/core/eval/backends/tiledarray/result.hpp	Implements Result::adjoint() for TiledArray tensor and tensor-of-tensors results.
SeQuant/core/context.hpp	Removes Context braket symmetry defaults/options/accessors/setters.
SeQuant/core/context.cpp	Removes braket symmetry from equality and context construction/setters.
benchmarks/main.cpp	Drops braket symmetry from benchmark context setup.

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