Fix low_Mach index swap, int_comp param name, and reviewer feedback

Swap low_Mach = 1 (Chen pressure correction) and low_Mach = 2
(Thornber velocity correction) to match source code and case.md.
Fix interface_compression → int_comp (actual parameter name).
Remove empty mhd dependency dict. Fix type annotations and unused
variable in postprocess_citations.py. Extend PARAM_RE to catch
comparison operators (>, <) in addition to assignment (=).

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

Author: sbryngelson

docs/documentation/equations.md

@@ -637,7 +637,7 @@ Primitive variable reconstruction is used to avoid spurious oscillations at inte
 
 where \f$a\f$ and \f$b\f$ are the left and right slope differences.
 
-**THINC interface compression** (`interface_compression > 0`): applies hyperbolic tangent compression near material interfaces:
+**THINC interface compression** (`int_comp = .true.`): applies hyperbolic tangent compression near material interfaces:
 
 \f[q_\text{THINC} = q_\min + \frac{q_\max}{2}\left(1 + \text{sign}(s)\,\frac{\tanh(\beta) + A}{1 + A\,\tanh(\beta)}\right)\f]
 
@@ -817,21 +817,21 @@ Supports STL/OBJ geometry import with ray tracing for inside/outside determinati
 
 ## 17. Low Mach Number Corrections (\cite Wilfong26 Sec. 4.2.4)
 
-**Thornber correction** (`low_Mach = 1`, \cite Thornber08): modifies the reconstructed velocities at cell interfaces:
+**Chen correction** (`low_Mach = 1`, \cite Chen22): anti-dissipation pressure correction (APC) added to the HLLC flux:
 
-\f[u'_L = \frac{u_L + u_R}{2} + z\,\frac{u_L - u_R}{2}, \qquad u'_R = \frac{u_L + u_R}{2} - z\,\frac{u_L - u_R}{2}\f]
+\f[p_d = \frac{\rho_L\,\rho_R\,(S_R - u_R)(S_L - u_L)}{\rho_R(S_R - u_R) - \rho_L(S_L - u_L)}\f]
 
-\f[z = \min\!\left(\max\!\left(\frac{|u_L|}{c_L},\;\frac{|u_R|}{c_R}\right),\;1\right)\f]
+\f[\text{APC}_{p\mathbf{u}} = (z - 1)\,p_d\,\hat{\mathbf{n}}, \qquad \text{APC}_{pE} = (z - 1)\,p_d\,S_*\f]
 
-This reduces numerical dissipation at low Mach numbers while recovering the standard scheme at high Mach numbers.
+The corrected HLLC flux in the star region becomes \f$\mathbf{F}^{*} + \text{APC}\f$.
 
-**Chen correction** (`low_Mach = 2`, \cite Chen22): anti-dissipation pressure correction (APC) added to the HLLC flux:
+**Thornber correction** (`low_Mach = 2`, \cite Thornber08): modifies the reconstructed velocities at cell interfaces:
 
-\f[p_d = \frac{\rho_L\,\rho_R\,(S_R - u_R)(S_L - u_L)}{\rho_R(S_R - u_R) - \rho_L(S_L - u_L)}\f]
+\f[u'_L = \frac{u_L + u_R}{2} + z\,\frac{u_L - u_R}{2}, \qquad u'_R = \frac{u_L + u_R}{2} - z\,\frac{u_L - u_R}{2}\f]
 
-\f[\text{APC}_{p\mathbf{u}} = (z - 1)\,p_d\,\hat{\mathbf{n}}, \qquad \text{APC}_{pE} = (z - 1)\,p_d\,S_*\f]
+\f[z = \min\!\left(\max\!\left(\frac{|u_L|}{c_L},\;\frac{|u_R|}{c_R}\right),\;1\right)\f]
 
-The corrected HLLC flux in the star region becomes \f$\mathbf{F}^{*} + \text{APC}\f$.
+This reduces numerical dissipation at low Mach numbers while recovering the standard scheme at high Mach numbers.
 
 Additionally, the **artificial Mach number** technique (`pi_fac`) modifies \f$\pi_\infty\f$ to artificially increase the local Mach number.
 

docs/postprocess_citations.py

@@ -20,7 +20,7 @@ def parse_bib_authors(bib_path: Path) -> dict[str, tuple[str, int, str | None]]:
         (first_author_surname, author_count, second_author_surname | None)
     """
     text = bib_path.read_text(encoding="utf-8")
-    entries: dict[str, tuple[str, int]] = {}
+    entries: dict[str, tuple[str, int, str | None]] = {}
 
     # Find all bib entries: @type{Key,
     for m in re.finditer(r"@\w+\{(\w+),", text):
@@ -154,7 +154,7 @@ def check_bare_citations(html_dir: Path, authors: dict) -> list[str]:
                 continue
             # Check if an author name precedes the link
             before = text[max(0, m.start() - 60):m.start()].rstrip()
-            surname, count, second_surname = authors[key]
+            surname, _count, second_surname = authors[key]
             has_prefix = (
                 before.endswith(surname) or
                 "et al." in before[-20:] or

toolchain/mfc/lint_docs.py

@@ -23,8 +23,8 @@
 # Match \cite Key references in markdown (Doxygen-style)
 CITE_RE = re.compile(r"\\cite\s+(\w+)")
 
-# Match backtick-quoted parameter assignments like `param = value` or `param`
-PARAM_RE = re.compile(r"`([a-z_][a-z0-9_%]*?)(?:\s*=\s*[^`]*)?\s*`")
+# Match backtick-quoted parameter names like `param = value`, `param > 0`, or `param`
+PARAM_RE = re.compile(r"`([a-z_][a-z0-9_%]*)(?:\s*[=><][^`]*)?\s*`")
 
 # Parameter-like names to skip (not actual MFC parameters)
 PARAM_SKIP = re.compile(

toolchain/mfc/params/definitions.py

@@ -781,7 +781,6 @@ def get_value_label(param_name: str, value: int) -> str:
             "requires": ["sigma"],
         }
     },
-    "mhd": {},
     "relativity": {
         "when_true": {
             "requires": ["mhd"],