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@@ -2,80 +2,6 @@
 BUFFERED COMPARISON AND STOPPING-BAND RESOLUTION IN CRITICAL ISING
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-An expository, self-contained version, with no steps hidden.
-
-The original paper is a LaTeX article. Here every theorem, lemma, and
-corollary is restated in plain text and proved. Symbols are kept as in
-the original, but each is defined the moment it first appears.
-
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-PART 0. WHAT THIS PAPER PROVES, IN PLAIN WORDS
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-
-The critical Ising model is a random colouring of the square grid by two
-colours, call them + (up) and - (down). It is the model of a magnet, and
-at one special temperature, beta_c, it has long-range structure: the
-colours are correlated across huge distances, and interfaces (curves
-separating + from -) behave like random curves with a well-defined
-continuum limit.
-
-Version 1 of this picture: explore (reveal) spins near an interface. You
-discover a random jagged boundary. Later you care about spins FAR from
-that boundary, on the other side of a fixed band of positive width. What
-do those distant spins look like, given everything you revealed?
-
-The visible boundary may have many thin "slits" (excursions that poke
-toward you). Its signs may alternate. To say anything about the far side
-you must, it seems, remember an infinite amount of jagged detail. This
-paper proves that you do not. To a controlled total-variation error, the
-distant spine law depends only on which of FINITELY MANY regular
-("signed barrier") contours the visible boundary resembles, and the
-barriers and error tolerances are chosen BEFORE the mesh gets fine. The
-same approximation works uniformly for all bounded distant observables,
-even ones that change with the mesh, and the descriptors (the finite
-codes) converge in discrete total variation.
-
-The engine has two halves.
-
-Half A (comparison). Changing prescribed Ising spins on a set changes
-any outcome on another set by at most a factor exp(4 arctanh(q0)), where
-q0 is a zero-field random-cluster connection probability on the graph
-with the intermediate prescribed spins deleted. On the critical square
-lattice, q0 is tiny whenever a buffer of lattice separates the two sets,
-so "far apart" means "almost independent". This works with arbitrarily
-many common prescribed spins and mixed signs.
-
-Half B (transmission). If two joint laws are ordered pointwise, the
-effect of a small patch of changed boundary on a distant target is
-bounded by the change of a normalized magnetization on an intermediate
-"cut" contour. Summing over a cover of the cut turns the microscopic
-comparison into a macroscopic total-variation statement on the target.
-
-Then a geometric construction replaces the jagged visible boundary by a
-regular signed contour with ordered upper and lower approximations, uses
-incidence ordering to sandwich the actual transcript between them, and
-uses transmission to convert the small mean gap into a total-variation
-gap. A separable metric on boundary data plus a countable-cover argument
-reduce infinitely many possible boundaries to finitely many barriers.
-
-Everything rests on four imported truth-bricks, used as hypotheses and
-cited each time:
-
-  (C1) RSW / crossing and one-arm estimates for critical FK-Ising
-       [Duminil-Copin, Hongler, Nolin 2011].
-  (C2) The Ding-Song-Sun correlation inequality for Ising with
-       arbitrary external fields [2023].
-  (C3) Bulk one- and two-spin limits and two-spin fusion for critical
-       Ising [Chelkak, Hongler, Izyurov 2021].
-  (C4) The critical Ising interface scaling limit is nested CLE_3, with
-       simultaneous common-edge approximation of ALL macroscopic loops
-       [Benoist, Hongler 2019].
-  Plus the Edwards-Sokal and Fortuin-Kasteleyn-Ginibre cluster
-  machinery and the Karlin-Rinott total-positivity theory.
-
-
-
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 PART 1. THE ISING MODEL AND ITS RANDOM-CLUSTER FORM
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