Add Anti-BraidStorm hostile crossing gate documentation

6-Documentation/famm/ANTI_BRAIDSTORM_HOSTILE_CROSSING_GATE.md

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+# Anti-BraidStorm Hostile Crossing Gate
+
+## Purpose
+
+Anti-BraidStorm is the adversarial dual of BraidStorm. BraidStorm lets hypothesis strands cross, mutate, emit receipts, accumulate scars, and promote survivor surfaces. Anti-BraidStorm asks whether those survivors only survived friendly crossings.
+
+```text
+Anti-BraidStorm = the adversarial braid network that tries to make false survivors.
+```
+
+## Hostile crossing
+
+A normal crossing is:
+
+```math
+\beta_{ij}:(s_i,s_j)\to(s_i',s_j',r_{ij},\epsilon_{ij},\Omega_{ij})
+```
+
+Anti-BraidStorm generates hostile crossings:
+
+```math
+\beta^{-}_{ij}
+:
+(s_i,s_j)
+\to
+(s_i',s_j',r^{\mathrm{fake}}_{ij},\epsilon^{\mathrm{hidden}}_{ij},\Omega^{\mathrm{masked}}_{ij})
+```
+
+The goal is to make a crossing appear locally valid while failing globally.
+
+## Braid-order attack
+
+```math
+\Delta_{\mathrm{braid}}^{-}
+=
+\left\|
+\beta_{ij}\beta_{jk}\beta_{ij}(S)
+-
+\beta_{jk}\beta_{ij}\beta_{jk}(S)
+\right\|
+```
+
+If \(\Delta_{\mathrm{braid}}^{-}>\Theta_{\mathrm{braid}}\), crossing order matters too much and the survivor surface may be fake.
+
+## Receipt-alias attack
+
+A hostile crossing tries to make two different crossing histories share a receipt/address:
+
+```math
+H(\mathrm{history}_a)=H(\mathrm{history}_b)
+\quad\text{while}\quad
+I(\mathrm{history}_a)\ne I(\mathrm{history}_b)
+```
+
+This is where the BraidStorm Sidon Crossing Anti-Alias Gate participates.
+
+## Stack placement
+
+```text
+BraidStorm crossing candidate
+→ Sidon anti-alias check
+→ Golden centering check
+→ Anti-BraidStorm hostile crossing attack
+→ Anti-FAMM shadow attack
+→ Warden decision
+→ promote / scar / coarsen / reject
+```
+
+## Project sentence
+
+Anti-BraidStorm is the hostile crossing adversary for BraidStorm: it creates adversarial braid histories that look locally valid but fail globally, forcing survivor candidates to withstand receipt-alias, braid-order, chirality, scar-mask, and false-convergence attacks before promotion.