feat(coprocessor): Phase 2a — FLINT FFI CAS backend

Adds `CoprocessorKind::FlintMath` and the full `FlintMathBackend` wired
via Rust FFI to the FLINT C library (LGPL-3).  FLINT is the only CAS
backend in ECHIDNA that links in-process rather than shelling out —
earning trust tier LibraryWrapped (Tier 3), same as `MathBackend`.

## What lands

**New `CoprocessorOp` variants** (polynomial algebra + enhanced integer ops):
- `FlintPolyGcd`     — primitive GCD of two polynomials over Z
- `FlintPolyMul`     — product of two polynomials over Z
- `FlintPolyRem`     — pseudo-remainder (lc(g)^d · f = q·g + r)
- `FlintPolyContent` — GCD of all coefficients of a polynomial
- `FlintNthRoot`     — exact integer k-th root (Empty if not exact)
- `FlintBinomial`    — binomial coefficient C(n, k)

**New `CoprocessorOutcome::Polynomial`** — wire format: space-separated
decimal coefficients in degree-ascending order; "0" for zero polynomial.

**`src/rust/coprocessor/flint.rs`** — RAII wrappers (`Fmpz`, `FmpzPoly`)
over `fmpz_t` / `fmpz_poly_t`; `extern "C"` declarations for 15 FLINT
functions; `FlintMathBackend` implementing `Coprocessor`; 8 unit tests.

**`--features flint`** — build.rs discovers system FLINT via pkg-config
or bare `-lflint`.  Without the feature, `CoprocessorFactory::native`
returns `None` for `FlintMath` — callers fall through gracefully.

**`julia_bridge.rs`** — exhaustive `kind_name` match extended for `FlintMath`.

## Tests

33 coprocessor tests pass.  New `flint_math_unavailable_without_feature`
confirms factory returns `None` without `--features flint`.  The 8
flint-specific tests (poly GCD, mul, rem, content, nth-root, binomial)
run only when `--features flint` is active and FLINT is installed.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

Author: hyperpolymath

.machine_readable/6a2/STATE.a2ml

@@ -42,9 +42,10 @@ target-claim-id = "echidna-phase1a-tptp-atps  /  echidna-phase1b-frontier-fol"
 [[expansion-roadmap.phase]]
 id = "phase-2"
 title = "Computer-algebra (FLINT FFI + subprocess CAS family)"
-status = "available-for-claim"
+status = "phase-2a-complete"
 adds-backends = ["FLINT", "PARI/GP", "Maxima", "Singular", "GAP", "Macaulay2"]
 target-claim-id = "echidna-phase2a-cas-libraries  /  echidna-phase2b-cas-subprocess"
+notes = "Phase 2a landed 2026-04-26: FLINT FFI coprocessor backend (CoprocessorKind::FlintMath, Tier 3 LibraryWrapped, --features flint). Adds FlintPolyGcd/Mul/Rem/Content + FlintNthRoot + FlintBinomial ops, Polynomial outcome variant. 8 unit tests; factory returns None gracefully without the feature. Phase 2b (subprocess CAS: PARI/GP, Maxima, Singular, GAP, Macaulay2) still available for claim."
 
 [[expansion-roadmap.phase]]
 id = "phase-3"

Cargo.toml

@@ -110,6 +110,7 @@ echidna-core = { path = "crates/echidna-core" }
 [features]
 default = []
 chapel = []       # Enable Chapel parallel proof search (requires Zig FFI library)
+flint = []        # Enable FLINT CAS coprocessor (requires system libflint, LGPL-3)
 spark = []        # Enable SPARK-verified axiom-policy (requires libechidna_spark from GPRbuild)
 verisim = [     # Enable VeriSimDB persistent proof storage (8-modality octads)
     "dep:ciborium",

build.rs

@@ -50,6 +50,46 @@ fn main() {
         println!("cargo:rerun-if-changed=src/zig/ffi/axiom_spark_bridge.zig");
     }
 
+    // FLINT CAS coprocessor (in-process, the only CAS we link rather than exec)
+    #[cfg(feature = "flint")]
+    {
+        // Try pkg-config first; fall back to a bare -lflint on the standard
+        // library path.  FLINT is LGPL-3 and compatible with the PMPL/MPL-2.0
+        // fallback licence under which ECHIDNA is distributed.
+        let found_via_pkg_config = std::process::Command::new("pkg-config")
+            .args(["--exists", "flint"])
+            .status()
+            .map(|s| s.success())
+            .unwrap_or(false);
+
+        if found_via_pkg_config {
+            // Let pkg-config emit the full set of link flags.
+            if let Ok(output) = std::process::Command::new("pkg-config")
+                .args(["--libs", "flint"])
+                .output()
+            {
+                let flags = String::from_utf8_lossy(&output.stdout);
+                for flag in flags.split_whitespace() {
+                    if let Some(path) = flag.strip_prefix("-L") {
+                        println!("cargo:rustc-link-search=native={path}");
+                    } else if let Some(lib) = flag.strip_prefix("-l") {
+                        println!("cargo:rustc-link-lib=dylib={lib}");
+                    }
+                }
+            }
+        } else {
+            // No pkg-config entry; attempt bare link on the system library path.
+            println!("cargo:rustc-link-lib=dylib=flint");
+            println!(
+                "cargo:warning=FLINT not found via pkg-config — \
+                 trying bare -lflint.  Install FLINT (LGPL-3) and ensure \
+                 its headers are on the include path."
+            );
+        }
+
+        println!("cargo:rerun-if-changed=src/rust/coprocessor/flint.rs");
+    }
+
     // Chapel parallel proof search bridge
     #[cfg(feature = "chapel")]
     {