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Fix gramcover gauge dependence for coupled W#37

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timholy merged 1 commit into
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teh/gram-gauge
Jul 20, 2026
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Fix gramcover gauge dependence for coupled W#37
timholy merged 1 commit into
mainfrom
teh/gram-gauge

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@timholy timholy commented Jul 20, 2026

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A nondiagonal W can couple distinct support components, which gramcover merges into a group. The bound over a group is built from the per-block sums M[p,q], each weighted by sqrt(M[p,p]/M[q,q]), rather than from a single uniform total over the group. Every term then scales as γ[p]^2 under the componentwise gauge a -> γ*a, b -> b/γ, so s depends on (a, b) only through the products a[i]*b[j], as it already did for diagonal W.

Where a component's own block vanishes, its weight propagates along the coupling as M[p,q]^2/M[q,q]. A group in which every block vanishes admits no such weight: the surviving data fixes each product s[j]*s[k] across two components but not how it divides between them, and the group takes the uniform total.

Assisted-by: Claude Opus 4.8 noreply@anthropic.com

A nondiagonal W can couple distinct support components, which gramcover
merges into a group. The bound over a group is built from the per-block
sums M[p,q], each weighted by sqrt(M[p,p]/M[q,q]), rather than from a
single uniform total over the group. Every term then scales as γ[p]^2
under the componentwise gauge a -> γ*a, b -> b/γ, so s depends on (a, b)
only through the products a[i]*b[j], as it already did for diagonal W.

Where a component's own block vanishes, its weight propagates along the
coupling as M[p,q]^2/M[q,q]. A group in which every block vanishes admits
no such weight: the surviving data fixes each product s[j]*s[k] across
two components but not how it divides between them, and the group takes
the uniform total.

Assisted-by: Claude Opus 4.8 <noreply@anthropic.com>
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codecov Bot commented Jul 20, 2026

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Codecov Report

❌ Patch coverage is 97.82609% with 2 lines in your changes missing coverage. Please review.
✅ Project coverage is 98.74%. Comparing base (e8d8379) to head (bd97f42).

Files with missing lines Patch % Lines
src/gram_covers.jl 97.82% 2 Missing ⚠️
Additional details and impacted files
@@            Coverage Diff             @@
##             main      #37      +/-   ##
==========================================
- Coverage   98.78%   98.74%   -0.05%     
==========================================
  Files          14       14              
  Lines        2306     2383      +77     
==========================================
+ Hits         2278     2353      +75     
- Misses         28       30       +2     

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@timholy
timholy merged commit 7323137 into main Jul 20, 2026
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@timholy
timholy deleted the teh/gram-gauge branch July 20, 2026 12:33
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