fix(solve): keep the remaining plan in view after each step fold

[KKandLL-Forever]

Description

solve_finish_step folds the finished step's tool chatter (intended), but the same cut also dropped the solve_plan result and the step's own next pointer. From step 2 onward the model only saw [S1] <goal> — done. and had to reconstruct the remaining steps from memory; the persisted model turn lost the plan too.

This PR:

• lets a context checkpoint carry an optional state next to summary. Summaries still accumulate before the fold boundary; state is one system message after it, so each fold replaces it instead of stacking stale copies;
• has solve_finish_step pass SolveSession.progress_text() (every step marked done / next / todo) as that state, so the current plan, including after a replan, stays in view and is persisted with the model turn.

Checkpoints without state behave exactly as before; _context_checkpoint is only emitted by solve.

Related Issues

• Closes [Bug]: deep_solve's context checkpoint deletes the remaining plan the model is following #1968

Module(s) Affected

• agents
• tests
• Other: capabilities (solve)

Validation

• New tests: test_context_checkpoint_state_replaces_instead_of_stacking and test_solve_checkpoint_fold_keeps_remaining_plan (tests/agents/chat/test_agent_loop.py); test_session_progress_text_marks_each_step, test_session_progress_text_after_last_step_and_replan, test_finish_step_checkpoint_carries_plan_state (tests/capabilities/test_solve_capability.py). All five fail on dev and pass here; the existing test_context_checkpoint_folds_completed_tool_rounds passes unchanged.
• Full suite as in CI (pytest -q tests deeptutor/learning/tests, server + partners requirements, LightRAG/GraphRAG on 3.12): 10,325 passed, 11 skipped, 2 failed. Both failures fail identically on untouched dev (e60fb158) on my macOS machine and are unrelated: tests/runtime/test_launcher.py::test_noninteractive_restart_recovers_an_actual_orphaned_backend_listener, tests/services/sandbox/test_sandbox.py::test_runner_server_executes_and_truncates_output.
• ruff check ., ruff format --check . (0.16.0), lint-imports (3 kept, 0 broken) and scripts/check_architecture.py pass.
• pre-commit run --all-files: all hooks pass on the changed files; end-of-file-fixer flags web/public/provider-icons/onomeo.svg (missing trailing newline, from 47e10db), which this PR leaves untouched.
• No live-model calls; the reproduction uses the suite's scripted client.

Checklist

• This PR targets dev (not main)
• I have read and followed the contribution guidelines.
• My code follows the project's coding standards.
• I have run pre-commit run --all-files and fixed any issues. (One pre-existing finding in an unrelated file, noted above.)
• I have added relevant tests for my changes.
• I have updated the documentation where necessary (module docstrings in solve/session.py and solve/tools.py).
• My changes do not introduce any known new security vulnerabilities.

[KKandLL-Forever]

Real-model check, in addition to the scripted tests: I ran the same open-ended deep_solve prompt 5 times on dev (e60fb158) and 5 times on this branch.

Setup

• Model: deepseek-flash; identical settings; a separate data home per arm.
• Command: deeptutor run deep_solve "<prompt>" -l zh, with the prompt "Fully study f(x) = (x³ − 3x² + 4)/(x² − 1) and sketch it; verify every key value". The model chooses its own decomposition, so the remaining steps are not recoverable from the question.
• exec was unavailable in this CLI setup for both arms.

	dev (n=5)	this PR (n=5)
Failed turns	1 (two rounds of reasoning-only output)	0
Turns that re-planned (solve_plan > 1)	5/5 (6, 4, 2, 7, 2 calls)	0/4 (one run answered without planning)
Steps finished again after a re-plan	17 (one run finished S1 six times)	0
Final plan finished (completed turns)	2/4	4/4
Median time	177 s	95 s
Median tokens	147,635	88,392
Median tool calls	13	7
Answer checklist (hole at (−1, −4.5), asymptotes x = 1 / y = x − 3, extrema, no inflection)	24/24 on completed turns	30/30

What this shows

• On dev, once the first fold removes the plan, the model calls solve_plan again, which overwrites the session, and it redoes S1.
• With this PR, it plans once and walks the steps in order.
• Answers stay correct on both sides for this model, so the gain here is fewer wasted rounds (about 40% fewer tokens). Correctness did not change.

Limitations

• n = 5 per arm.
• The arms ran concurrently, so timings are noisy.
• The PR column's medians include the one run that skipped planning. Without it, the medians are 107 s and 89,590 tokens; the conclusion is unchanged.
• Whether the failed dev turn was caused by the lost plan is plausible but not proven.