[Rafael-SOWNet]

Five of family 1's last six unsolved rows, by four mechanisms:

• A linear beside a power of a block P^q, q >= 2 (1.3.1:568 and 569), inside IntegrateOverAPowerOfALinearBesideABlock. The root -d/e is named while the series and the rest are computed. The rest is summed over one denominator in powers of the block's base, split into Q_q/P^q + … + Q_1/P, and each piece is integrated with named coefficients. Carried as -d/e, the coefficients reached about 14,000 characters, the lowest-terms step gave up on the expanded (a + c ρ^4)^6, and 568's answer came to 203,000 characters.
• A sum of powers of x times a symbolic power of a linear in a root of x (1.2.3.2:621), as a new rule. The answer is G L T(u) with u = x^(1/k). T's coefficients are solved from the highest power down, and the one equation left over decides whether the sum is elementary. The answer is differentiated back before it is returned.
• Under t = sqrt(L1)/sqrt(L2) (1.2.1.4:1097), inside SolveByAQuotientOfTwoLinearRadicals. Powers of a - c t^q and of t are stripped and the compound coefficients named. This runs only where the denominator has a complete quadratic factor with a symbol in it, since a + c x^2 rows got longer when named.
• A polynomial over the cube root of a quadratic beside another with the same axis (1.2.1.6:232). It is shifted to y = x + b/(2c) and written in depressed form, which turns it into a row master already answers.

Measured on 8270086f, branch against master:

Run	Problems	Master	Branch
Pocket: Rubi's 1.3.1, 1.2.1.4–1.2.1.6, 1.2.3.2 and 1.1.1.4, whole	1,980	1,959 solved	1,965 solved
Family 1, 40 a file	1,381	1,368	1,368
Family 0, whole	1,814	1,789	1,789
Families 2 to 8, sampled	2,410	2,380	2,381

Re-run alone, against master:

Row	Master	Branch
1.2.1.4:1097	timed out	0.7 s
1.2.1.6:232	unevaluated	4.2 s
1.2.3.2:621	unevaluated	51 ms
1.3.1:569	timed out	1.0 s
1.2.1.4:1100	16.7 s, 25 GB	0.3 s, 0.07 GB
1.3.1:568	23 s, 24 GB	0.9 s, 0.7 GB

1.2.1.5:155 is the sixth row; #1992 answered it.

The other two moves, 3.2.1:292 and 7.4.1:369, are answered on both builds at a 60 s budget, with the same allocation to 0.001%. Every answer was checked at four or five pin sets on both signs, and by quadrature. 232 reads wrong under the probe's principal cube root at c < 0. With the library's real odd roots, its derivative matches the integrand to 100 digits; the test asserts it at c = -0.8.

Rebased on #1992, which changed the same family's answers: AX's six rows and #1992's rows (1.2.1.5:18, 19, 148, 154 and 155) all answer on the combined build, and both PRs' 367 tests pass. Of AX's 125 neighbours, no verdict is lost, and every unchanged answer is the same character for character. None of the problems answered on both builds allocates more on the branch.

Four new test classes differentiate the answers back. BREAKING-CHANGES.md has four entries, with the 2.5.0 column measured on v2.5.0.

Part of #233.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura