diffexp-mpl.md

Remaining DiffExp multiple-polylogarithm profiles

The pinned DiffExp notebook's trailing-zero, complex-letter and weight-20 examples pass independent native transport and original Wolfram comparisons at 20 decimal digits. Together with mpl-101-4.json, these cover every numerical MPL profile in MultiplePolylogarithms.nb at commit 784c8229bf92369a03f011a48e161522c8c54bbd.

The new input sequences are G(1,-10,0;4), G(10,-10+i,-1/2,-50;1), and G(1,2,...,20;21). Native code builds the triangular differential equation directly. The first case obtains its logarithmic boundary from exact regularized constants and native generalized Frobenius recurrence; the other cases start from exact finite constants at zero. No original numerical value enters a native boundary. The frozen native ordinary solver accepts the complex letter using an exact symbolic parameter mapped to MPFR i. A literal complex polynomial coefficient was rejected by that frozen version; its failed probe remains recorded. The production compiler now encodes exact complex literals before rational-polynomial conversion. Its integrated MPL regression supplies the literal complex letter directly; the historical timings below remain those of the frozen symbolic-input implementation.

The original harness executes the GPL notebook's own helper definitions from the pinned checkout, including shuffle/logarithm extraction. This is oracle execution, not source copied into the MIT library. It uses the notebook's 250-digit working precision, chop 225, Mobius transformation, division 3, and orders 50/75 or 100, with parallel execution disabled. Native settings and continuation contours differ, and the trailing-zero computation solves a different number of systems, so the following single-core measurements do not establish a matched-algorithm speedup. They were collected on CPU 28 of a shared host while other scientific jobs ran on different cores.

Case	Original order	Original helper seconds	Native digits/order	Native boundary+compile+transport seconds	Native/original absolute difference
trailing	50	0.768252	80/50	0.512075	3.998e-25
trailing	75	0.926068	100/75	0.355881	6.140e-38
complex	50	0.443258	80/50	0.085049	8.781e-28
complex	75	0.510206	100/75	0.060672	2.368e-40
weight20	100	33.669108	100/100	5.974607	5.504e-57

The weight-20 independent refinement used 140 digits/order 140 and took 10.181645 seconds internally. All native basis components were checked against increased working precision and order; maximum differences were 2.96e-76, 1.13e-79 and 8.27e-96 respectively. These small differences are evidence of stability, not a claim that working precision certifies the same accuracy. Both absolute and nonzero-MPL relative 20-digit checks pass.

Every original component retains its recorded Precision and absolute Accuracy; comparison uncertainty estimates round absolute accuracy downward. The weight-20 imaginary output is a finite-accuracy zero (absolute accuracy 56.5038), and is checked with an absolute bound only. The original shuffle helper's signed pm error coefficient may cancel and is retained as an estimate, not a rigorous bound. Two early harness-only decoding failures introduced a machine zero via pm -> 0; the accepted runs extract the exact coefficient of pm^0 instead. They do not alter DiffExp's algorithm.

reports/diffexp/mpl-additional-validation.json retains all output arrays, component metadata, source/binary hashes, internal phase times and step counts. Two-second process polling can overestimate short-run wall time and miss the RSS peak, so internal phase timings are reported independently. The offline regressions need no Wolfram installation:

source .dev-env
cargo test --locked --release -p symbolica-amflow --test mpl_additional

To regenerate one original profile, use a fresh existing output directory and the pinned DiffExp checkout. MPL_CASE is trailing, complex, or weight20; MPL_ORDER is 50, 75, or 100 respectively. The harness checks package/notebook hashes and preserves native Wolfram output alongside JSON:

mkdir -p target/mpl-original-new
DIFFEXP_ROOT=/common/dev/diffexp MPL_OUTPUT="$PWD/target/mpl-original-new" \
MPL_CASE=trailing MPL_ORDER=50 OMP_NUM_THREADS=1 OPENBLAS_NUM_THREADS=1 \
MKL_NUM_THREADS=1 timeout --signal=TERM --kill-after=5s 600s \
  bern-wolfram -noinit -noprompt -script scripts/diffexp_mpl_additional_oracle.wl

The larger weight-20 oracle used a 1800-second cap and 4 GiB process-tree RSS limit in the recorded run. It completed in 33.669108 seconds in the original helper (36.012178 seconds including launch/polling).