elreal Phase 5: infinite summation

[Ravenwater]

Parent epic: #923
Depends on: Phase 4 (addition)

Goal

Implement infinite summation: given a co-list of `ZBCL` (a stream of streams), produce a single `ZBCL` representing the sum. This is the workhorse for Taylor series and other transcendentals in Phase 7.

Primitives

• `sum(colist<ZBCL> series) -> ZBCL`

Convergence story

The dissertation defines summation only for series whose partial-sum sequence is Cauchy. The library must:

• Trust the caller for non-trivial series (transcendentals know their own convergence)
• Provide guard rails for ill-formed series (e.g., divergence detection that aborts at some configurable depth budget)

Acceptance criteria

• `sum` implemented per dissertation 4.2.3
• Tests on geometric series `sum (1/2)^n` -> 2, `sum (1/3)^n` -> 3/2, etc.; check first N blocks against high-precision oracle
• Tests on alternating series `sum (-1)^n / (2n+1)` -> pi/4 (slow convergence -- exercises lazy refinement)
• Tests on Taylor series of exp(1) -> e -- a Phase 7 preview
• Depth budget guard: `sum` with a max-depth knob, aborts if not Cauchy-stable within budget
• Tests live in `elastic/elreal/summation/`

Out of scope

• Specific transcendental implementations (Phase 7)
• Acceleration techniques (Aitken, Wynn epsilon) -- defer

Reference

McCleeary 2019 dissertation, Section 4.2.3 (infinite summation).

[Ravenwater]

Precondition: #1022 -- port the exact dyadic oracle (dyadic_exact.hpp) to elreal and re-assert the Phase 1-4 building blocks bit-exactly before building infinite summation on top. The current Phase 1-4 value checks rest on long double, which is not an exact oracle (and aliases double on MSVC/ARM/RISC-V). Should be closed/green before Phase 5 work proceeds.