Modernize legendre_convert Boost usage

[egull]

Summary

• add deterministic golden regression coverage for legendre_convert
• replace Boost.Random with the C++ standard <random> implementation
• replace boost::math::factorial with a small local product
• replace boost::math::legendre_p with the standard three-term recurrence
• intentionally retain Boost spherical Bessel and Boost.Program_options

Verification

• Debug build with warnings-as-errors passes
• legendre_convert regression passes in Debug and Release
• transform and convergence outputs are bit-identical; back-continuation differs only by 5.1e-18
• complete regression-fast label passes
• git diff --check passes

[Copilot]

Copilot review overview

🟡 Changes recommended

Unresolved moderate issues remain in the implementation and regression tolerance configuration.

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Review effort: Lite
Findings: 1

Open (1)

• Avoid constructing normal distribution with zero deviation · New

What changed in this PR

Modernizes legendre_convert by replacing selected Boost functionality with standard C++ implementations and adding deterministic regression coverage.

Changes:

• Replaces Boost.Random, factorial, and Legendre polynomial usage.
• Adds regression inputs, references, tolerances, and CTest integration.
• Documents migration progress and reference provenance.

File	Review summary
test/​regression/​tolerances.json	Moderate, 1 vote: Tolerance key does not match the generated legendre_convert_transform:<dataset> keys.
test/​regression/​REFERENCE_CHANGES.md	Reviewed; no final comment.
test/​regression/​README.md	Reviewed; no final comment.
test/​regression/​PROVENANCE.md	Reviewed; no final comment.
test/​regression/​manifest.py	Reviewed; no final comment.
test/​regression/​MANIFEST.md	Reviewed; no final comment.
test/​regression/​make_inputs.py	Reviewed; no final comment.
test/​regression/​inputs/​legendre_convert_transform/​input.dat	Reviewed; no final comment.
test/​regression/​generate.py	Nit, 1 vote: The missing-program diagnostic suggests an invalid underscore-form option.
test/​regression/​compare.py	Reviewed; no final comment.
test/​regression/​CMakeLists.txt	Reviewed; no final comment.
test/​regression/​cases.py	Reviewed; no final comment.
legendre_convert/​legendre_convert.cpp	Moderate, 1 vote: Required standard headers are not included directly. Moderate, 3 votes: Zero error bars create std::normal_distribution with an invalid zero standard deviation.
ALPS3_MIGRATION_PLAN.md	Reviewed; no final comment.

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[Copilot]

Copilot review overview

🔵 Needs a closer look

The migrated random-distribution path is not exercised by the regression coverage.

Review effort: Lite
Findings: None

Resolved since last review (1)

• Avoid constructing normal distribution with zero deviation

Previously missed (1)

In code that hasn't changed since last review

Add shell continuation to multiline command example

test/​regression/​generate.py:7

This newly added command example is not shell-continuable: without a trailing \\ here, the next [--provenance ...] line is executed as a separate command. Add the continuation character so the documented invocation can be copied verbatim.

[Copilot]

Copilot review overview

🟢 Approval recommended

Only documentation nits remain; no blocking issues were identified.

Review effort: Lite
Findings: None