Add the holonomy-signature paper to Selected Publications

New first entry, linking papers/holonomy-signatures.pdf with a six-bullet
abstract and a teaser thumbnail at public_html/respic/holonomy-small.jpg
(1024x1024 JPEG, 333 KB, matching the other entries).

The paper is "Which Holonomy Signatures Are Realizable?  A Complete Answer for
Closed Surfaces", 28 pages, built without a date on the title page.  Source
lives in the seamless_prove repository; only the PDF is here.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_016S2cnn5bdgDG8Fu9r62tnC

Author: claude

index.html

@@ -1568,6 +1568,33 @@ <h1 data-en="Leyi Zhu" data-zh="朱乐宜">Leyi Zhu</h1>
         <section class="publications" id="publications">
             <h2 class="section-title" data-en="Selected Publications" data-zh="代表性论文">Selected Publications</h2>
 
+            <!-- Pub 0 -->
+            <div class="pub-item">
+                <img class="pub-thumb" src="./public_html/respic/holonomy-small.jpg"
+                    alt="Which Holonomy Signatures Are Realizable?"
+                    width="160" height="160">
+                <div class="pub-details">
+                    <p class="pub-title">Which Holonomy Signatures Are Realizable? A Complete Answer for Closed Surfaces</p>
+                    <p class="pub-venue">Preprint</p>
+                    <div class="pub-buttons">
+                        <a class="pub-btn" href="./papers/holonomy-signatures.pdf" target="_blank"
+                            data-en="Paper" data-zh="论文">Paper</a>
+                        <button class="pub-btn" onclick="toggleAbstract('abstractHolonomy')" data-en="Abstract"
+                            data-zh="摘要">Abstract</button>
+                    </div>
+                    <div id="abstractHolonomy" class="abstract">
+                        <ul>
+                            <li>A seamless parametrization carries a discrete invariant, its holonomy signature: the cone angles, all multiples of &pi;/2, together with the rotational holonomy of the induced cross field. This is the datum a quadrangulation prescribes, and it decides whether any parametrization exists at all.</li>
+                            <li>A Reduction Lemma shows that the mapping class group acts on signatures with fixed cone angles with orbits classified by the subgroup im&nbsp;&rho; alone, so at most three cases survive per angle multiset instead of 4<sup>2g</sup>.</li>
+                            <li>A dictionary identifies seamless parametrizations with meromorphic 4-differentials, under which im&nbsp;&rho; measures primitivity, and realizability becomes non-emptiness of a stratum of primitive k-differentials.</li>
+                            <li>Exactly five families of signatures fail to be realizable; every other admissible signature is realizable, in every genus. Two of the five appear to be new, and both live in genus two.</li>
+                            <li>Four of the five lie outside the gcd condition of the SIGGRAPH 2022 paper below, and the whole region that condition leaves open is settled here.</li>
+                            <li>The non-emptiness half is also made constructive, via an explicit one-vertex square-tiled surface in every genus together with a local surgery that splits one cone into two of prescribed angles.</li>
+                        </ul>
+                    </div>
+                </div>
+            </div>
+
             <!-- Pub 1 -->
             <div class="pub-item">
                 <img class="pub-thumb" src="./public_html/respic/bijective-gemini-small.jpg"