Markdown for LLMs

Beyond law

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# Beyond law

Arxo executes any pinned canon: standards, textbooks, game rules — not
only legal texts. The pages below record runs against references outside
the law: an official language test suite, two computer algebra systems, a
proof-assistant kernel, and an endorsed tournament pairing tool. Each page
names its reference with a version, states what agreement meant for that
run, and shows the outcome case by case.

| System | Reference | What was checked | Outcome | Page |
|---|---|---|---|---|
| WebAssembly integer semantics | `i32.wast` of WebAssembly/spec | 19 line-cases: values and traps | 19 of 19 | [WebAssembly: the i32 spec-tests run](/comparisons/wasm-spec-tests-run/) |
| Computer algebra | SymPy 1.14.0, Wolfram 15.0.1 | 129 bank rows plus 15 OpenStax cases | bank 129 of 129; one reference-textbook divergence (C14) | [Computer algebra: the textbook-steps run](/comparisons/computer-algebra-run/) |
| Proof assistant | Lean 4.33.0 core | 14 divisibility instances | 10 match, 3 not comparable, 1 not checked | [Lean: the divisibility-instances run](/comparisons/lean-run/) |
| Tournament pairing | bbpPairings 6.0.0 | 33 presented pairings on absolute criteria | zero false accepts and refusals; 6 subject differences | [FIDE: the Dutch-pairing check run](/comparisons/fide-pairing-run/) |

Sample runs against a PKIX conformance set, cascade style pairs and
worked measurement examples are recorded in the research tree; their
pages follow the scheduled package rework.

The principle across these pages is the same as inside the law: the
neighbour often does different work, and the page shows what that work
is. A computer algebra system computes far more than the run asks; Lean
proves a theorem while Arxo applies its statement; a pairing tool builds
the optimum while Arxo checks what is presented. Each run page states on
its first lines where the other side is stronger, and differences of
behaviour are given neutrally — what each side does, on which case, at
which version — with the model's own boundary stated as a property
alongside.