Difference between revisions of "Sandbox"
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| − | <div class="thumb tright" style="float:right; margin:-72px 0px 8px 18px"> |
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| + | [[Swift enforcement of the Budapest Memorandum]] is a [[gedankenexperiment]] describing |
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| − | {{pic|Tetreal10bx10d.png|300px}} |
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| + | how the guarantees given to Ukraine in 1994 could have been implemented if the |
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| − | <small><center>\(y=\mathrm{tet}_b(x)\) versos \(x\) for various values of base \(b\).<br> |
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| + | United States and its allies had decided to enforce them consistently and |
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| − | [[Superfunctions]]<ref name="en"/>, Fig.17.2, p.239.</center></small> |
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| + | rapidly. |
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| − | </div> |
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| + | |||
| − | <div class="thumb tright" style="float:right; background-color:#fff; margin:2px 0px 8px 8px; width:300px; line-height:9px"> |
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| + | The scenario is intentionally simplified in order to make the causal logic |
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| − | {{pic|Ackerplot.jpg|300px}}<small><center>First five [[ackermann]]s.<!-- [[Natural tetration]] |
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| + | explicit. |
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| − | refers to dashed line.!--><br>[[Superfunctions]]<ref name="en"> |
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| + | |||
| − | https://www.amazon.co.jp/Superfunctions-Non-integer-holomorphic-functions-superfunctions/dp/6202672862<br> |
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| + | This [[emulation]] is generated by [[ChatGPT]] in order to explain the sense of the [[Budapest memorandum]] - under condition, that initially, it was not a fraud, nor a bluff, nor a trick since the beginning, and initially, its signing by the American President was not an attempt to destroy the International Law, nor an attempt to show that America again becomes a poor colony with external government - as it was 3 centures ago. |
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| − | https://mizugadro.mydns.jp/BOOK/468.pdf |
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| + | |||
| − | Dmitrii Kouznetsov. Superfunctions: Non-integer iterates of holomorphic functions. Tetration and other superfunctions. Formulas,algorithms,tables,graphics ペーパーバック – 2020/7/28 |
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| + | I such a way, the emulation below is constructed under fantastic assumption, that |
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| − | </ref>, p.266. Fig.19.7. |
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| + | the [[Moscovia]]n [[war crime]]s do not menace the world with the [[nuclear weapon]], and, at this conditions, the [[Budapest memorandum]] still could have been implemented. |
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| − | </div> |
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| − | <div class="thumb tright" style="float:right; margin: |
+ | <div class="thumb tright" style="float:right; margin:2px 0px 0px -24px; width:300px; background-color:#fff; line-height:1em"> |
| − | {{pic| |
+ | {{pic|AP_9412050636-min_(1).jpg|300px}} <small><center><p style="0px 0px 0px 8px; line-height:1em; width:300px"> |
| + | Russian President Boris Yeltsin, left, American President Bill Clinton, Ukrainian President Leonid Kuchma, and British Prime Minister John Major, extreme right, sign the [[Budapest memorandum]] 1994.12.05 <ref> |
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| − | See Figure 4.12 at page 203 of book [[Superfunctions]]<ref name="en"/></center></small> |
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| + | https://www.belfercenter.org/event/ukraines-nuclear-disarmament-25-years-after-budapest-memorandum |
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| + | Ukraine’s Nuclear Disarmament: 25 Years After the [[Budapest memorandum|Budapest Memorandum]]. Fri., Dec. 6, 2019 | 8:30am - 5:30pm. |
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| + | </ref></p></center></small> |
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</div> |
</div> |
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| + | ==Premise== |
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| − | [[Tetration]] ([[Тетрация]]) is the [[superfunction]] of the [[exponential]] map. |
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| + | In 1994 [[Ukraine]] agreed to give up the nuclear weapons inherited from the [[USSR]]. |
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| − | For a given base \(b\), the tetration \(\operatorname{tet}_b\) is defined as the function satisfying the transfer equation |
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| + | In exchange, the United States, the United Kingdom and the Russian Federation |
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| − | \[ |
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| + | signed the [[Budapest memorandum]], promising to respect the sovereignty and |
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| − | \operatorname{tet}_b(z+1) = b^{\operatorname{tet}_b(z)} |
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| + | territorial integrity of Ukraine. |
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| − | \] |
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| − | together with additional normalization and regularity conditions that select a unique solution among infinitely many possible superfunctions. |
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| − | For real values of the argunet, the explicit plots of \(\operatorname{tet}_b(x)\) versos \(x\) |
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| − | for various real values of base \(b\) is shown in figure at right. |
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| + | The thought experiment below assumes that the US administration interprets these |
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| − | The inverse function [[ArcTetration]] is denoted with symbol ate; \( \mathrm{ate}_b = \mathrm{tet}_b^{-1} \).<br> |
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| + | assurances not merely as diplomatic language but as commitments affecting the |
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| − | The iterates of [[Exponential]] can be expressed as follows: |
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| + | national interests and credibility of the United States. |
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| − | \( |
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| − | \exp_b^{\ n}=\operatorname{tet}_b\big(n+\operatorname{ate}_b(z)\big) |
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| − | \). |
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| − | Here, number \(n\) of the iterate has no need to be integer. In particular, \(\varphi=\exp^{1/2}\) |
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| − | appears as solution of equation \( \varphi(\varphi(x))=\mathrm e^x \); this equation had been considered by [[Hellmuth Kneser]] <ref name="k"> |
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| − | http://www.digizeitschriften.de/dms/img/?PID=GDZPPN002175851&physid=phys63#navi |
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| − | [[Hellmuth Kneser]]. Reelle analytische Lösungen der Gleichung \( \varphi(\varphi(x))=\mathrm e^x \) und verwandter Funktionalgleichungen. |
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| − | Journal für die reine und angewandte Mathematik / Zeitschriftenband (1950) / Artikel / 56 - 67 |
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| − | </ref>, 1950. |
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| + | ==Phase 1: Intelligence Assessment (1994–2000)== |
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| − | ==Notations== |
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| + | 1994.12.01 |
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| − | The name [[tetration]] reflects its role as the next operation after exponentiation within the [[hyperoperation]] hierarchy:<br> |
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| − | [[Ackermann]]\(_1\), id est, the [[Addition]] appears as [[superfunction]] of [[unity increment]];<br> |
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| − | [[Ackermann]]\(_2\), id est, the [[Multiplication]] appears as [[superfunction]] of additon; <br> |
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| − | [[Ackermann]]\(_3\), id est, the [[Exponential]] \(\exp\) appears as [[superfunction]] of multiplication;<br> |
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| − | [[Ackermann]]\(_4\), id est, the [[Tetration]] \(\mathrm{tet}\) appears as [[superfunction]] of [[exponential]];<br> |
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| − | [[Ackermann]]\(_5\), id est, the [[Pentation]] \(\mathrm{pen}\) appears as [[superfunction]] of [[tetration]];<br> |
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| − | and so on. These functions are qualified as [[ackermann]]s after the last name of |
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| − | mathematician [[Wilhelm Ackermann]]. |
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| + | US intelligence services deliver an analytical memorandum to the President and |
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| − | The most studied case is the [[Natural tetration]] |
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| + | to Congress. |
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| − | <ref name="analuxp"> |
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| − | https://www.ams.org/journals/mcom/2009-78-267/S0025-5718-09-02188-7/home.html <br> |
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| − | http://mizugadro.mydns.jp/PAPERS/2009analuxpRepri.pdf |
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| − | Dmitrii Kouznetsov. Solution of F(z+1)=exp(F(z)) in complex z-plane. |
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| − | Mathematics of Computation, 2009, V.78, p.1647-1670. |
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| − | </ref><ref name="vladi"> |
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| − | https://mizugadro.mydns.jp/PAPERS/2010vladie.pdf<br> |
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| − | https://www.vmj.ru/articles/2010_2_4.pdf <br> |
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| − | https://mizugadro.mydns.jp/PAPERS/2010_2_4.pdf |
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| − | D.Kouznetsov. Tetration as special function. (In Rusian) [[Vladikavkaz Mathematical Journal]], 2010, v.12, issue 2, p.31-45. |
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| − | </ref>. It corresponds to base \(b=\mathrm e\); it can be written simply as |
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| − | \[ |
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| − | \operatorname{tet}(z)=\operatorname{tet}_{\mathrm e}(z). |
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| − | \] |
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| − | For base \(\mathrm e\) the first five [[ackermann]]s are shown in figure at right.<br> |
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| − | The dashed line refers to the [[natural tetration]]. |
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| + | The report states that: |
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| − | In such a way, all the [[ackermann]]s are numerated. <br> |
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| − | In notation [[Ackermann]]\(_m (z)\), the number \(m\) is supposed to be positive integer (natural number). <br> |
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| − | To year 2025, the generalization of [[Ackermann]]\(_m(z)\) for non-integer values of \(m\) is not yet developed. |
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| − | However, the argument \(z\) may have complex values. |
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| + | * After the collapse of the USSR, the Russian Federation may attempt to restore influence over former Soviet territories. |
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| − | ==Definition== |
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| + | * Military pressure against neighboring states is considered plausible. |
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| − | Let \(T_b(z)=b^z\). |
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| − | A function \(F\) is a ''[[superexponential]]'' (a [[superfunction]] of \(T_b\)) if |
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| − | \[ |
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| − | F(z+1) = T_b(F(z)). |
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| − | \] |
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| + | * Potential targets include weak or politically unstable former Soviet republics. |
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| − | A [[tetration]] to real base \(b\) is real-holomorphic superexponential \(F\) |
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| − | such that \(F(x+\mathrm i y)\) remains bounded at \(y\to\pm\infty\) and \(F(0)=1\). |
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| + | The report also evaluates two strategic scenarios. |
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| − | Such a solution is believed to exists and to be unique <ref> |
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| − | https://link.springer.com/article/10.1007/s00010-010-0021-6 |
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| − | https://mizugadro.mydins.jp/2011uniabel.pdf |
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| − | H.Trappmann, D.Kouznetsov. Uniqueness of holomorphic Abel functions at a complex fixed point pair. |
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| − | [[Aequationes Mathematicae]], v.81, p.65-76 (2011) |
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| − | </ref><ref> |
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| − | https://math.stackexchange.com/questions/284868/uniqueness-of-tetration |
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| − | Let 𝑓(0)=1 |
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| − | and 𝑓(𝑥+1)=2^𝑓(𝑥) // |
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| − | Also let f be infinitely differentiable. Then does f exist and is it unique? // |
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| − | If f is merely continuous, then any continuous function such that f(0)=1 f(1)=2 satisfies the conditions(if f is defined in [0,1] ,we can use the property to define it everywhere else). Similar things can be said for differentiability. But I don't how to solve the problem if it's infinitely differentiable. |
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| − | </ref>. |
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| + | Scenario A: |
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| − | ==Special cases== |
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| + | Ukraine keeps nuclear weapons. |
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| − | <div class="thumb tright" style="float:right; margin:-6px 0px 4px 8px; background-color:#fff; width:480px; line-height:8px;"> |
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| + | This creates a regional balance of power but complicates nuclear |
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| − | {{pic|E1efig09abc1a150.png|480px}}<small><center>[[Complex map]]s of [[tetration]] \(\mathrm{tet}_b\) to base \(b\!=\!1.5\) , left; \(b\!=\!\exp(1/\mathrm e)\) , center and \(b\!=\!\sqrt{2}\) , right.<br> |
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| + | non-proliferation policy. |
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| − | From: Fig.17.4, p.245 in [[Superfunctions]] <ref name="en"/></center></small> |
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| − | </div> |
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| − | <div class="thumb tright" style="float:right; margin:4px 0px 8px 8px"> |
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| − | {{pic|Tetsheldonmap03.png|480px}}<small><center>[[Tetration to Sheldon base]]. [[Superfunctions]], p.250, top picture of Fig.18.3.</center></small> |
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| − | </div> |
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| + | Scenario B: |
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| − | [[Decimal tetration]], \(b=10\). The routine for the evaluation is loaded as [[F4ten.cin]]. |
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| + | Ukraine gives up nuclear weapons in exchange for credible security guarantees |
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| − | It is used to plot the top picture. |
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| + | from nuclear powers. |
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| + | The report concludes that Scenario B is viable only if the guarantees are considered enforceable. |
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| − | [[Natural tetration]], \(b=\mathrm e\). The [[complex map]] for this case is shown in figure above. The original description <ref name="analuxp"/> and the fast C++ implementation <ref name=vladie"> |
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| − | https://www.emis.ams.org/journals/VMJ/articles/2010_2_4.pdf <br> |
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| − | https://mizugadro.mydns.jp/PAPERS/2010_2_4.pdf<br> |
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| − | https://mizugadro.mydns.jp/PAPERS/2010vladie.pdf<br> |
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| − | Д.Кузнецов. Тетрация как специальная функция. Владикавказский математический журнал, 2010, т.12, вып. 2, стр.31-45.<br> |
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| − | D.Kouznetsov, Tetration as special function. Vladikavkaz Mathematical Journal, 2010, |
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| − | v.12, Issue 2, p.33-45. |
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| − | </ref> are published and mentioned in book [[Superfunctions]] <ref name="en"/> |
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| + | 1994.12.02 |
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| − | [[Binary tetration]], \(b=2\), see [[Base 2]] |
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| + | The President acknowledges the report and instructs intelligence agencies to |
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| − | [[tetration to base 1.5]], see [[Base 1.5]] |
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| + | monitor Russian military and political developments closely. |
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| + | ==Phase 2: Early Warning Signals (1994–2008)== |
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| − | [[Crytical tetration]], \(b= \mathrm e^{1/\mathrm e}\), see [[Base e1e]] |
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| + | {{fig|Pu01puppetmaster.jpg|100|-44|1|8|}} |
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| + | In subsequent years intelligence monitoring identifies several patterns: |
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| + | * Military operations against [[Ichkeria]] ([[First Chechen War]]). |
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| + | * Russian political rhetoric emphasizing influence over the “near abroad”. |
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| + | * Gradual increase of military presence of Russia and frozen conflicts in territories such as [[Transnistria]], [[Abkhazia]] and [[South Ossetia]]. |
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| + | Analysts warn that these conflicts demonstrate a strategic method of RF:<br> |
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| − | [[Tetration to base sqrt2]], \(b= \sqrt{2}\), see [[Base sqrt2]] |
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| + | 1. Create or maintain unstable regions in neighboring states.<br> |
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| + | 2. Use military presence to influence political outcomes.<br> |
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| + | 3. Prevent integration of these states into Western institutions. |
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| + | The assessment concludes that Ukraine may eventually face similar pressure. |
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| − | [[Tetration to Sheldon base]] \(b=1.52598338517+0.0178411853321\ \mathrm i\). |
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| − | The original algorithm <ref name="analuxp"/> allows the straight-forward generalization for the case of complex values of base \(b\). After the request by [[Sheldon Levenstain]], the complex map of this tetration had been generated; it is shown in figure at right. |
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| + | 2008.08.08, the [[Russian invasion into Georgia]] confirms this pattern |
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| − | ==Continuity at base b=exp(1/e)== |
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| − | <div class="thumb tright" style="float:right; margin:0 0 8px 8px; width:280px; line-height:10px"> |
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| − | {{pic|BlackSheep.png|280px}} |
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| − | <small><center>"half-sheep" illustration. [[Суперфункции]]<ref name="ru"> |
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| − | https://mizugadro.mydns.jp/BOOK/202.pdf |
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| − | Дмитрий Кузнецов. [[Суперфункции]]. [[Lambert Academic Publishing]], 2014 |
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| − | </ref>, p.218, Fig.15.6; [[Superfunctions]] <ref name="en"/>, p.215, Fig.15.6</center></small> |
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| − | </div> |
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| + | Intelligence briefings warn that the Georgian war could represent a precedent |
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| − | This cartoon at right illustrates a philosophical point in tetration theory:<br> |
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| + | for future operations against other neighbors, including Ukraine. |
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| − | <b>"The only we may conclude, that in this county, there is at least one sheep, |
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| − | and at least the right-hand side of this animal is black"</b>. <br> |
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| − | The heuristic assumptions that appear “obvious’’ (e.g., that the right side of a sheep has the same color as its left side) appears without rigorous proof and, from point of a mathematician, may happen to be wrong. |
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| + | ==Phase 3: Pre-Crisis Alert (2008–2014)== |
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| − | The similar heuristic assumption refers to the continuity of [[tetration]] \(\mathrm{tet}_b(z) \) being considered as function of base \(b\) at point \(b=\exp(1/\mathrm e)\). |
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| + | After the Georgian war, US intelligence agencies intensify monitoring of |
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| − | The maps above for \(b=1.5\), \(b=\exp(1/\mathrm e)\approx 1.44\) and \(b=\sqrt{2}\approx 1.41\) |
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| + | Russian military modernization and political strategy. |
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| − | as well as the explicit plot at the top make an impression, that the [[tetration]] is continuous and perhaps holomorphic with respect to \(b\) at this point: the variation in the 3d significant figure causes small change of the view of the curves; at least for moderate valies of argument \(z\) |
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| + | {{fig|BackInTheUSSR.png|144|0|2|2|[[Back in the USSR]]}} |
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| + | Analysts warn that: |
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| + | * Crimea has strategic value because of the Black Sea Fleet. |
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| − | As in the case of the sheep in the cartoon, this assumptions about tetration |
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| + | * Political instability in Ukraine could create an opportunity for intervention. |
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| − | is not obvious and require careful justification. |
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| + | * Hybrid methods (covert troops, irregular forces, propaganda) may be used to obscure responsibility. |
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| + | By early 2014 intelligence reports conclude that military intervention in Ukraine is highly probable. |
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| − | The prelimninary numerical analysis indicates, that |
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| − | \(tet_b(z)\) for \(\Re(b)<\exp(1/\mathrm e)\) |
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| − | is not analytical extension of |
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| − | \(tet_b(z)\) for \(\Re(b)>\exp(1/\mathrm e)\); |
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| − | in the simplest way, the cut line along line \(\Re(b)=\exp(1/\mathrm e)\) |
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| − | divides the complex plane to two almost independent parts, |
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| − | and only in point \(Re(b)=\exp(1/\mathrm e)\), these two tetrqations have the same limiting |
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| − | tetration. <br> |
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| − | However, the cut at the complex \(b\)-plane has no need to follow the vertical line \(\Re(b)=\exp(1/\mathrm e)\); but this choice is simplest and has priority (following the last, 6th of the [[TORI axioms]].) |
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| + | ==Phase 4: Immediate Response (2014)== |
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| − | ==Applications== |
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| + | {{fig|PuSanctions.jpeg|160|-20|4|8|}} |
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| − | The obvious application of the tetration may refer to representation of huge numbers.<br> |
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| + | {{fig|107253_original.jpg|100|4|0|8|}} |
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| − | For example the [[Googolplex]] number <ref> |
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| + | When armed forces without insignia appear in Crimea in February 2014, |
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| − | https://en.wikipedia.org/wiki/Googolplex |
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| + | the United States and the United Kingdom interpret the event as a violation of |
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| − | A '''googolplex''' is the [[large number]] \(10^{10^{100}}\), that is, 10 raised to the power of a [[googol]]. If written out in ordinary [[decimal notation]], it would be 1 followed by a [[googol]] (10<sup>100</sup>) zeroes – a physically impossible number to write explicitly. |
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| + | the [[Budapest memorandum]]. |
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| − | </ref> can be expressed as follows: |
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| − | \[ |
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| − | 10^{10^{100}}=\mathrm{tet}_{10}^3(2) |
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| − | \] |
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| − | However, up to year 2025, Editor have not yet found any [[scientific concept]] |
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| − | that deals with such a huge number. |
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| + | Within days they take several coordinated actions. |
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| − | The more realistic application may refer to the approximation of processes that |
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| − | grows faster than any polynomial but slower than any exponential. |
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| − | The non-integer iterates greatly extend the arsenal of functions available for |
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| − | construction of efficient fits, involving less fitting parameters and/or providing better precision and/or having wider range of approximation. |
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| + | Diplomatic action: |
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| − | The \(n\)-th iterate of the exponential: |
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| + | An official warning is delivered to the Russian leadership stating that |
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| − | \[ |
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| + | continued occupation of Ukrainian territory will trigger collective responses. |
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| − | \exp_b^{\ n}(z) = \operatorname{tet}_b\!\big(n + \operatorname{ate}_b(z)\big), |
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| − | \] |
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| − | for real \(n\). One example of such a function is mentioned in the Preamble. |
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| + | Legal action: |
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| − | An additional extension could be generalization of [[ackermann]]\(m\) |
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| + | The issue is immediately raised in the United Nations and international courts. |
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| − | to non-integer values of \(m\), looking for the real-holomorphic solition \(A\) of equations |
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| + | |||
| − | \[ |
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| + | Military deterrence: |
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| − | A_m(z+1)=A_{m-1}(A_m(z)) \\ |
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| + | NATO rapidly deploys naval and air units to the region as a defensive measure. |
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| − | A_2(z)= \mathrm e\ z \\ |
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| + | |||
| − | Z_m(0)=1 \text{ for } m>2 |
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| + | Economic pressure: |
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| − | \] |
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| + | Assets connected to the Russian state and key political figures are frozen. |
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| − | treating \(A_m(z)\) as holomorphic function of two variables \(m\) and \(z\).<br> |
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| + | |||
| − | Such a generalization can be matter for the future research. |
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| + | These measures are presented not as escalation but as enforcement of previously |
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| + | agreed commitments. |
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| + | |||
| + | ==Phase 5: Resolution Scenario== |
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| + | |||
| + | Under coordinated diplomatic, economic and military pressure the Russian |
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| + | leadership faces a strategic choice: |
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| + | |||
| + | continue escalation with severe international consequences, |
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| + | or withdraw forces and negotiate. |
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| + | |||
| + | In this simplified scenario the crisis ends with withdrawal of occupying |
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| + | forces and restoration of Ukrainian control over its territory. |
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| + | |||
| + | ==Consequences== |
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| + | {{fig|Mvn78red1.jpg|144|-20|2|2|}} |
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| + | The rapid enforcement of the [[Budapest memorandum]] produces several effects: |
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| + | * international agreements gain credibility; |
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| + | * aggressive territorial revisionism becomes less attractive; |
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| + | * states that renounced nuclear weapons see that security guarantees can work. |
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| + | |||
| + | ==Methodological note== |
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| + | |||
| + | This article describes a hypothetical scenario rather than a prediction or a |
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| + | historical claim. |
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| + | |||
| + | Its purpose is to illustrate how intelligence analysis, diplomatic pressure, |
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| + | economic tools and military deterrence could theoretically interact in the |
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| + | enforcement of international security guarantees. |
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| + | |||
| + | ==Notes by Editor== |
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==References== |
==References== |
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{{ref}} |
{{ref}} |
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| − | https:// |
+ | https://en.wikipedia.org/wiki/Budapest_Memorandum |
| − | P. Fatou. Sur les ´equations fonctionnelles. Bulletin de la Soci´et´e |
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| − | Math´ematique de France, 47 (1919), p. 161-271. |
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| − | https:// |
+ | https://treaties.un.org/doc/Publication/UNTS/Volume%203007/Part/volume-3007-I-52241.pdf |
| + | Memorandum on security assurances in connection with Ukraine’s accession to the Treaty on the Non-Proliferation of Nuclear Weapons. Budapest, 5 December 1994 // |
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| − | Wilhelm Ackermann. Zum Hilbertschen Aufbau der reellen Zahlen. [[Mathematische Annalen]] 99, Number 1(1928), Z.118-133. |
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| + | Entry into force: 5 December 1994 by signature // |
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| + | Authentic texts: English, Russian and Ukrainian // |
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| + | Registration with the Secretariat of the United Nations: Ukraine, 2 October 2014 |
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| + | https://www.gutenberg.org/files/236/236-h/236-h.htm#link2H_4_0001 [[Rudyard Kipling]]. THE JUNGLE BOOK. Release Date: January 16, 2006 [EBook #236] Last Updated: October 6, 2016. .. Akela lifted his head again and said, “He has eaten our food. He has slept with us. He has driven game for us. He has broken no word of the Law of the Jungle.”// “Also, I paid for him with a bull when he was accepted. The worth of a bull is little, but Bagheera’s honor is something that he will perhaps fight for,” said Bagheera in his gentlest voice.// “A bull paid ten years ago!” the Pack snarled. “What do we care for bones ten years old?” .. |
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| − | <small>https://projecteuclid.org/journals/acta-mathematica/volume-100/issue-3-4/Regular-iteration-of-real-and-complex-functions/10.1007/BF02559539.full |
||
| − | </small> |
||
| − | G.Szekeres. Regular iteration of real and complex functions. Acta Mathematica 1958, Volume 100, Issue 3-4, pp 203-258. |
||
| + | 2015.11.10. |
||
| − | https://www.ams.org/journals/bull/1993-29-02/S0273-0979-1993-00432-4/S0273-0979-1993-00432-4.pdf |
||
| + | https://www.youtube.com/watch?v=qA8kaGnf4ro [[Marco Rubio]]: Putin Is A Gangster. Published on Nov 10, 2015. Fox Business Debate 11.10.15. |
||
| − | W.Bergweiler. Iteration of meromorphic functions. Bulletin (New Series) of the American Mathematical society, v.29, No.2 (1993) p.151-188. |
||
| + | 2017.04.06. |
||
| − | https://www.tandfonline.com/doi/full/10.1080/10652460500422247 |
||
| + | https://www.youtube.com/watch?v=i1RSG2TeHAU Rubio: 'Putin is a war criminal' CNN Apr 6, 2017 |
||
| − | M.H.Hooshmand, (2006). Ultra power and ultra exponential functions. Integral [[Transforms and Special Functions]] 17 (8): 549–558 |
||
| + | 2022.03.04. <small> |
||
| − | https://www.proquest.com/openview/cb7af40083915e275005ffca4bfd4685/1?pq-origsite=gscholar&cbl=18750 |
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| + | https://news.sky.com/story/russian-invasion-wouldnt-have-happened-if-ukraine-still-had-nuclear-weapons-ukrainian-political-adviser-says-12556811 |
||
| − | [[Samuel Cowgill]]. EXPLORING TETRATION IN THE COMPLEX PLANE |
||
| + | </small>Russian invasion 'wouldn't have happened' if Ukraine still had nuclear weapons, Ukrainian political adviser says |
||
| − | EXPLORING TETRATION IN THE COMPLEX PLANE |
||
| + | [[Svitlana Zalishchuk]], a foreign policy adviser to the Ukrainian deputy prime minister, told Sky News that Ukraine giving up its nuclear weapons was "without a doubt" a mistake. By [[Alexa Phillips]], news reporter Friday 4 March 2022 13:10, UK |
||
| − | A Thesis presented to the faculty of Arkansas State University in partial. |
||
| − | fulfillment of the requirements for the Degree of |
||
| − | MASTER OF SCIENCE IN MATHEMATICS |
||
| − | ARKANSAS STATE UNIVERSITY //MAY 2017 |
||
| − | Approved by: |
||
| − | Dr. [[William Paulsen]], Thesis Advisor |
||
| − | Dr. [[Jie Miao]], Committee Member |
||
| − | Dr. [[Jeongho Ahn]], Committee MemberPREVIE |
||
| + | 2022.11.01. |
||
| − | https://link.springer.com/article/10.1007/s10444-018-9615-7 |
||
| + | https://www.newyorker.com/news/our-columnists/why-vladimir-putin-would-use-nuclear-weapons-in-ukraine |
||
| − | William Paulsen. Tetration for complex bases. |
||
| + | Why Vladimir Putin Would Use Nuclear Weapons in Ukraine.. |
||
| − | Advances in Computational Mathematics. |
||
| + | The more the Kremlin has signalled its readiness to drop a nuclear bomb, the more the rest of the world has sought a reason to believe that it will not. By [[Masha Gessen]] November 1, 2022. |
||
| − | Published: 02 June 2018// |
||
| − | Volume 45, pages 243–267, (2019) |
||
| + | 2023.03.17.<small> |
||
| − | https://www.researchgate.net/publication/325532999_Tetration_for_complex_bases |
||
| + | https://www.icc-cpi.int/news/situation-ukraine-icc-judges-issue-arrest-warrants-against-vladimir-vladimirovich-putin-and |
||
| − | <br> |
||
| + | </small> Today, 17 March 2023, Pre-Trial Chamber II of the [[International Criminal Court]] (“ICC” or “the Court”) issued warrants of arrest for two individuals in the context of the situation in Ukraine: Mr Vladimir Vladimirovich Putin and Ms Maria Alekseyevna Lvova-Belova. .. |
||
| − | https://www.researchgate.net/figure/Level-curves-for-Rk-b-z-and-Ik-b-z-0-1-2-3-4-for-b-i_fig1_325532999 |
||
| − | [[William Harold Paulsen]]. Tetration for complex bases. |
||
| − | Advances in Computational Mathematics 45(6), |
||
| − | February 2019 |
||
| − | DOI:10.1007/s10444-018-9615-7 |
||
| + | 2024.04.20. https://www.theguardian.com/us-news/2024/apr/20/us-house-approves-61bn-aid-ukraine [[Robert Tait]], Joan E Greve and Chris Michael. US House approves $61bn in military aid for Ukraine after months of stalling. Sat 20 Apr 2024 22.46 BST |
||
| − | http://myweb.astate.edu/wpaulsen/tetration2.pdf |
||
| + | |||
| − | [[William Paulsen]] and [[Samuel Cowgil]]. |
||
| + | 2024.11.13. |
||
| − | Solving F(z+1)=bF(z) in the complex plane. |
||
| + | https://unn.ua/en/news/ukraine-may-restore-nuclear-status-if-us-aid-is-cut-off-the-times |
||
| + | Ukraine may restore nuclear status if US aid is cut off - The Times |
||
| + | Kyiv • UNN November 13 2024, 08:54 PM .. |
||
| + | The Times reports on the possibility that Ukraine could develop a [[nuclear weapon]] in a few months if US military aid is cut. .. |
||
| + | |||
| + | 2025.03.12. |
||
| + | https://www.japantimes.co.jp/commentary/2025/03/12/world/ukraine-security-nuclear-proliferation/ |
||
| + | Lessons from Ukraine: Allies are fickle, nukes are forever// |
||
| + | If Kyiv is left to capitulate, others will see security as stemming from power, not assurances. BY THOMAS O. FALK .. Mar 12, 2025 |
||
| + | |||
| + | 2025.04.21.<small> |
||
| + | https://global.espreso.tv/military-news-ukraine-could-technically-restore-nuclear-status-in-just-four-years-experts-say |
||
| + | </small> Ukraine could technically restore nuclear status in just four years, experts say// 21 april, 2025 monday 11:16 |
||
| + | |||
| + | 2025.07.01. <small> |
||
| + | https://united24media.com/latest-news/uk-must-help-ukraine-regain-nuclear-arms-retired-british-commander-says-8787 |
||
| + | </small>[[Roman Kohanets]]. |
||
| + | UK Must Help Ukraine Regain Nuclear Arms, Retired British Commander Says |
||
| + | May 31, 2025 16:42 Updated Jul 01, 2025 00:25. |
||
| + | </small> |
||
{{fer}} |
{{fer}} |
||
==Keywords== |
==Keywords== |
||
| − | «[[ |
+ | «[[Advices for Trump]]», |
| − | «[[ |
+ | «[[]]», |
| − | «[[ |
+ | «[[Alternative Math]]», |
| − | «[[ |
+ | «[[Annexation of Canada]]», |
| − | «[[ |
+ | «[[Annexation of Crimea]]», |
| − | «[[ |
+ | «[[Annexation of Greenland]]», |
| − | «[[ |
+ | «[[Annexation of Ichkeria]]», |
| − | «[[ |
+ | «[[Appeasing aggression]]», |
| − | «[[ |
+ | «[[Barack Obama]]», |
| − | «[[ |
+ | «[[Bill Clinton]]», |
| − | «[[ |
+ | «[[Budapest memorandum]]», |
| − | «[[ |
+ | «[[CIA]]», |
| + | «[[CIA methodology]]», |
||
| + | «[[ChatGPT]]», |
||
| + | «[[Collapse of RF]]», |
||
| + | «[[Collapse of USA]]», |
||
| + | «[[Collapse of USSR]]», |
||
| + | «[[Corruption]]», |
||
| + | «[[Designate Russia as state sponsor of terrorism]]», |
||
| + | «[[Designate Russia as terrorist state]]», |
||
| + | «[[Donald Trump]]», |
||
| + | «[[Donroe Doctrine]]», |
||
| + | «[[Duration]]», |
||
| + | «[[Dvizhuha]]», |
||
| + | «[[Fascism]]», |
||
| + | «[[Gedankenexperment]]», |
||
| + | «[[Hybrid war]]», |
||
| + | «[[Jinping]]», |
||
| + | «[[Joe Biden]]», |
||
| + | «[[Moscovia]]», |
||
| + | «[[Mystic weakness]]», |
||
| + | «[[New World Order]]», |
||
| + | «[[Pahanat]]», |
||
| + | «[[Propaganda]]», |
||
| + | «[[Putin]]», |
||
| + | «[[Putin world war]]», |
||
| + | «[[Realpolitik]]», |
||
| + | «[[Russian Agent Governs America]]», |
||
| + | «[[Russian invasion into Ichkeria]]», |
||
| + | «[[Russian invasion into Ukraine]]», |
||
| + | «[[Russki mir]]», |
||
| + | «[[Sabotage]]», |
||
| + | «[[Small Victorious War]]», |
||
| + | «[[Small victorious war]]», |
||
| + | «[[TROI]]», |
||
| + | «[[Trump as KGB agent]]», |
||
| + | «[[Two concepts of collapse of the USSR]]», |
||
| + | «[[USA]]», |
||
| + | «[[Witkoff-Lavrov Pact Emulation]]», |
||
| + | «[[Wreckage of Crimea]]», |
||
| + | |||
| + | «[[Аннексия Ичкерии]]», |
||
| + | «[[Аннексия Крыма]]», |
||
| + | «[[Будапештский меморандум]]», |
||
| + | «[[Гибридная война]]», |
||
| + | «[[Движуха]]», |
||
| + | «[[Ихтамнет]]», |
||
| + | «[[Кисельные берега]]», |
||
| + | «[[Коррупция]]», |
||
| + | «[[Маленькая победоносная война]]», |
||
| + | «[[Московия]]», |
||
| + | «[[Мы попадём в рай а они сдохнут]]», |
||
| + | «[[Мысленный эксперимент]]», |
||
| + | «[[Новый Мировой Порядок]]», |
||
| + | «[[Остов Крым]]», |
||
| + | «[[Остров Крым]]», |
||
| + | «[[От Аляски до Одесы]]», |
||
| + | «[[Паханат]]», |
||
| + | «[[Путинский план спецоперации]]», |
||
| + | «[[Российское вторжение в Грузию]]», |
||
| + | «[[Российское вторжение в Украину]]» |
||
| + | «[[Саботаж]]», |
||
| + | «[[Синий вертолёт]]», |
||
| + | «[[Спецоперация]]», |
||
| + | «[[]]», |
||
| + | «[[Трамп Дональд Фредович]]», |
||
| + | «[[Умиротворение агрессора]]», |
||
| + | «[[Утопия]]», |
||
| + | «[[Фашизм]]», |
||
| + | «[[Эмуляция]]», |
||
| − | [[Category: |
+ | [[Category:Advices for Trump]] |
| − | [[Category: |
+ | [[Category:Annexation of Canada]] |
| − | [[Category: |
+ | [[Category:Annexation of Crimea]] |
| − | [[Category: |
+ | [[Category:Annexation of Greenland]] |
| − | [[Category: |
+ | [[Category:Annexation of Ichkeria]] |
| − | [[Category: |
+ | [[Category:Anti-Putin coalition]] |
| − | [[Category: |
+ | [[Category:Appeasing aggression]] |
| + | [[Category:Barack Obama]] |
||
| + | [[Category:Bill Clinton]] |
||
| + | [[Category:Budapest memorandum]] |
||
| + | [[Category:CIA]] |
||
| + | [[Category:ChatGPT]] |
||
| + | [[Category:Collapse of RF]] |
||
| + | [[Category:Collapse of USA]] |
||
| + | [[Category:Collapse of USSR]] |
||
| + | [[Category:Corruption]] |
||
| + | [[Category:Designate Russia as state sponsor of terrorism]] |
||
| + | [[Category:Designate Russia as terrorist state]] |
||
| + | [[Category:Donald Trump]] |
||
| + | [[Category:Donroe Doctrine]] |
||
| + | [[Category:Dvizhuha]] |
||
| + | [[Category:Fascism]] |
||
| + | [[Category:Gedankenexperment]] |
||
| + | [[Category:History]] |
||
| + | [[Category:Hybrid war]] |
||
| + | [[Category:Joe Biden]] |
||
| + | [[Category:Moscovia]] |
||
| + | [[Category:New World Order]] |
||
| + | [[Category:Pahanat]] |
||
| + | [[Category:Propaganda]] |
||
| + | [[Category:Putin]] |
||
| + | [[Category:Putin world war]] |
||
| + | [[Category:Realpolitik]] |
||
| + | [[Category:Russian Agent Governs America]] |
||
| + | [[Category:Russian invasion into Ichkeria]] |
||
| + | [[Category:Russian invasion into Ukraine]] |
||
| + | [[Category:Russki mir]] |
||
| + | [[Category:Sabotage]] |
||
| + | [[Category:Sci-fi]] |
||
| + | [[Category:Trump as KGB agent]] |
||
| + | [[Category:USA]] |
||
| + | [[Category:Utopia]] |
||
| + | [[Category:Witkoff-Lavrov Pact Emulation]] |
||
| + | [[Category:Wreckage of Crimea]] |
||
Latest revision as of 20:34, 12 March 2026
Swift enforcement of the Budapest Memorandum is a gedankenexperiment describing how the guarantees given to Ukraine in 1994 could have been implemented if the United States and its allies had decided to enforce them consistently and rapidly.
The scenario is intentionally simplified in order to make the causal logic explicit.
This emulation is generated by ChatGPT in order to explain the sense of the Budapest memorandum - under condition, that initially, it was not a fraud, nor a bluff, nor a trick since the beginning, and initially, its signing by the American President was not an attempt to destroy the International Law, nor an attempt to show that America again becomes a poor colony with external government - as it was 3 centures ago.
I such a way, the emulation below is constructed under fantastic assumption, that the Moscovian war crimes do not menace the world with the nuclear weapon, and, at this conditions, the Budapest memorandum still could have been implemented.
Russian President Boris Yeltsin, left, American President Bill Clinton, Ukrainian President Leonid Kuchma, and British Prime Minister John Major, extreme right, sign the Budapest memorandum 1994.12.05 [1]
Premise
In 1994 Ukraine agreed to give up the nuclear weapons inherited from the USSR. In exchange, the United States, the United Kingdom and the Russian Federation signed the Budapest memorandum, promising to respect the sovereignty and territorial integrity of Ukraine.
The thought experiment below assumes that the US administration interprets these assurances not merely as diplomatic language but as commitments affecting the national interests and credibility of the United States.
Phase 1: Intelligence Assessment (1994–2000)
1994.12.01
US intelligence services deliver an analytical memorandum to the President and to Congress.
The report states that:
- After the collapse of the USSR, the Russian Federation may attempt to restore influence over former Soviet territories.
- Military pressure against neighboring states is considered plausible.
- Potential targets include weak or politically unstable former Soviet republics.
The report also evaluates two strategic scenarios.
Scenario A: Ukraine keeps nuclear weapons. This creates a regional balance of power but complicates nuclear non-proliferation policy.
Scenario B: Ukraine gives up nuclear weapons in exchange for credible security guarantees from nuclear powers.
The report concludes that Scenario B is viable only if the guarantees are considered enforceable.
1994.12.02
The President acknowledges the report and instructs intelligence agencies to monitor Russian military and political developments closely.
Phase 2: Early Warning Signals (1994–2008)
In subsequent years intelligence monitoring identifies several patterns:
- Military operations against Ichkeria (First Chechen War).
- Russian political rhetoric emphasizing influence over the “near abroad”.
- Gradual increase of military presence of Russia and frozen conflicts in territories such as Transnistria, Abkhazia and South Ossetia.
Analysts warn that these conflicts demonstrate a strategic method of RF:
1. Create or maintain unstable regions in neighboring states.
2. Use military presence to influence political outcomes.
3. Prevent integration of these states into Western institutions.
The assessment concludes that Ukraine may eventually face similar pressure.
2008.08.08, the Russian invasion into Georgia confirms this pattern
Intelligence briefings warn that the Georgian war could represent a precedent for future operations against other neighbors, including Ukraine.
Phase 3: Pre-Crisis Alert (2008–2014)
After the Georgian war, US intelligence agencies intensify monitoring of Russian military modernization and political strategy.
Analysts warn that:
- Crimea has strategic value because of the Black Sea Fleet.
- Political instability in Ukraine could create an opportunity for intervention.
- Hybrid methods (covert troops, irregular forces, propaganda) may be used to obscure responsibility.
By early 2014 intelligence reports conclude that military intervention in Ukraine is highly probable.
Phase 4: Immediate Response (2014)
When armed forces without insignia appear in Crimea in February 2014, the United States and the United Kingdom interpret the event as a violation of the Budapest memorandum.
Within days they take several coordinated actions.
Diplomatic action: An official warning is delivered to the Russian leadership stating that continued occupation of Ukrainian territory will trigger collective responses.
Legal action: The issue is immediately raised in the United Nations and international courts.
Military deterrence: NATO rapidly deploys naval and air units to the region as a defensive measure.
Economic pressure: Assets connected to the Russian state and key political figures are frozen.
These measures are presented not as escalation but as enforcement of previously agreed commitments.
Phase 5: Resolution Scenario
Under coordinated diplomatic, economic and military pressure the Russian leadership faces a strategic choice:
continue escalation with severe international consequences, or withdraw forces and negotiate.
In this simplified scenario the crisis ends with withdrawal of occupying forces and restoration of Ukrainian control over its territory.
Consequences
The rapid enforcement of the Budapest memorandum produces several effects:
- international agreements gain credibility;
- aggressive territorial revisionism becomes less attractive;
- states that renounced nuclear weapons see that security guarantees can work.
Methodological note
This article describes a hypothetical scenario rather than a prediction or a historical claim.
Its purpose is to illustrate how intelligence analysis, diplomatic pressure, economic tools and military deterrence could theoretically interact in the enforcement of international security guarantees.
Notes by Editor
References
- ↑ https://www.belfercenter.org/event/ukraines-nuclear-disarmament-25-years-after-budapest-memorandum Ukraine’s Nuclear Disarmament: 25 Years After the Budapest Memorandum. Fri., Dec. 6, 2019 | 8:30am - 5:30pm.
https://en.wikipedia.org/wiki/Budapest_Memorandum
https://treaties.un.org/doc/Publication/UNTS/Volume%203007/Part/volume-3007-I-52241.pdf Memorandum on security assurances in connection with Ukraine’s accession to the Treaty on the Non-Proliferation of Nuclear Weapons. Budapest, 5 December 1994 // Entry into force: 5 December 1994 by signature // Authentic texts: English, Russian and Ukrainian // Registration with the Secretariat of the United Nations: Ukraine, 2 October 2014
https://www.gutenberg.org/files/236/236-h/236-h.htm#link2H_4_0001 Rudyard Kipling. THE JUNGLE BOOK. Release Date: January 16, 2006 [EBook #236] Last Updated: October 6, 2016. .. Akela lifted his head again and said, “He has eaten our food. He has slept with us. He has driven game for us. He has broken no word of the Law of the Jungle.”// “Also, I paid for him with a bull when he was accepted. The worth of a bull is little, but Bagheera’s honor is something that he will perhaps fight for,” said Bagheera in his gentlest voice.// “A bull paid ten years ago!” the Pack snarled. “What do we care for bones ten years old?” ..
2015.11.10. https://www.youtube.com/watch?v=qA8kaGnf4ro Marco Rubio: Putin Is A Gangster. Published on Nov 10, 2015. Fox Business Debate 11.10.15.
2017.04.06. https://www.youtube.com/watch?v=i1RSG2TeHAU Rubio: 'Putin is a war criminal' CNN Apr 6, 2017
2022.03.04. https://news.sky.com/story/russian-invasion-wouldnt-have-happened-if-ukraine-still-had-nuclear-weapons-ukrainian-political-adviser-says-12556811 Russian invasion 'wouldn't have happened' if Ukraine still had nuclear weapons, Ukrainian political adviser says Svitlana Zalishchuk, a foreign policy adviser to the Ukrainian deputy prime minister, told Sky News that Ukraine giving up its nuclear weapons was "without a doubt" a mistake. By Alexa Phillips, news reporter Friday 4 March 2022 13:10, UK
2022.11.01. https://www.newyorker.com/news/our-columnists/why-vladimir-putin-would-use-nuclear-weapons-in-ukraine Why Vladimir Putin Would Use Nuclear Weapons in Ukraine.. The more the Kremlin has signalled its readiness to drop a nuclear bomb, the more the rest of the world has sought a reason to believe that it will not. By Masha Gessen November 1, 2022.
2023.03.17. https://www.icc-cpi.int/news/situation-ukraine-icc-judges-issue-arrest-warrants-against-vladimir-vladimirovich-putin-and Today, 17 March 2023, Pre-Trial Chamber II of the International Criminal Court (“ICC” or “the Court”) issued warrants of arrest for two individuals in the context of the situation in Ukraine: Mr Vladimir Vladimirovich Putin and Ms Maria Alekseyevna Lvova-Belova. ..
2024.04.20. https://www.theguardian.com/us-news/2024/apr/20/us-house-approves-61bn-aid-ukraine Robert Tait, Joan E Greve and Chris Michael. US House approves $61bn in military aid for Ukraine after months of stalling. Sat 20 Apr 2024 22.46 BST
2024.11.13. https://unn.ua/en/news/ukraine-may-restore-nuclear-status-if-us-aid-is-cut-off-the-times Ukraine may restore nuclear status if US aid is cut off - The Times Kyiv • UNN November 13 2024, 08:54 PM .. The Times reports on the possibility that Ukraine could develop a nuclear weapon in a few months if US military aid is cut. ..
2025.03.12. https://www.japantimes.co.jp/commentary/2025/03/12/world/ukraine-security-nuclear-proliferation/ Lessons from Ukraine: Allies are fickle, nukes are forever// If Kyiv is left to capitulate, others will see security as stemming from power, not assurances. BY THOMAS O. FALK .. Mar 12, 2025
2025.04.21. https://global.espreso.tv/military-news-ukraine-could-technically-restore-nuclear-status-in-just-four-years-experts-say Ukraine could technically restore nuclear status in just four years, experts say// 21 april, 2025 monday 11:16
2025.07.01. https://united24media.com/latest-news/uk-must-help-ukraine-regain-nuclear-arms-retired-british-commander-says-8787 Roman Kohanets. UK Must Help Ukraine Regain Nuclear Arms, Retired British Commander Says May 31, 2025 16:42 Updated Jul 01, 2025 00:25.
Keywords
«Advices for Trump», «[[]]», «Alternative Math», «Annexation of Canada», «Annexation of Crimea», «Annexation of Greenland», «Annexation of Ichkeria», «Appeasing aggression», «Barack Obama», «Bill Clinton», «Budapest memorandum», «CIA», «CIA methodology», «ChatGPT», «Collapse of RF», «Collapse of USA», «Collapse of USSR», «Corruption», «Designate Russia as state sponsor of terrorism», «Designate Russia as terrorist state», «Donald Trump», «Donroe Doctrine», «Duration», «Dvizhuha», «Fascism», «Gedankenexperment», «Hybrid war», «Jinping», «Joe Biden», «Moscovia», «Mystic weakness», «New World Order», «Pahanat», «Propaganda», «Putin», «Putin world war», «Realpolitik», «Russian Agent Governs America», «Russian invasion into Ichkeria», «Russian invasion into Ukraine», «Russki mir», «Sabotage», «Small Victorious War», «Small victorious war», «TROI», «Trump as KGB agent», «Two concepts of collapse of the USSR», «USA», «Witkoff-Lavrov Pact Emulation», «Wreckage of Crimea»,
«Аннексия Ичкерии», «Аннексия Крыма», «Будапештский меморандум», «Гибридная война», «Движуха», «Ихтамнет», «Кисельные берега», «Коррупция», «Маленькая победоносная война», «Московия», «Мы попадём в рай а они сдохнут», «Мысленный эксперимент», «Новый Мировой Порядок», «Остов Крым», «Остров Крым», «От Аляски до Одесы», «Паханат», «Путинский план спецоперации», «Российское вторжение в Грузию», «Российское вторжение в Украину» «Саботаж», «Синий вертолёт», «Спецоперация», «[[]]», «Трамп Дональд Фредович», «Умиротворение агрессора», «Утопия», «Фашизм», «Эмуляция»,
- Advices for Trump
- Annexation of Canada
- Annexation of Crimea
- Annexation of Greenland
- Annexation of Ichkeria
- Anti-Putin coalition
- Appeasing aggression
- Barack Obama
- Bill Clinton
- Budapest memorandum
- CIA
- ChatGPT
- Collapse of RF
- Collapse of USA
- Collapse of USSR
- Corruption
- Designate Russia as state sponsor of terrorism
- Designate Russia as terrorist state
- Donald Trump
- Donroe Doctrine
- Dvizhuha
- Fascism
- Gedankenexperment
- History
- Hybrid war
- Joe Biden
- Moscovia
- New World Order
- Pahanat
- Propaganda
- Putin
- Putin world war
- Realpolitik
- Russian Agent Governs America
- Russian invasion into Ichkeria
- Russian invasion into Ukraine
- Russki mir
- Sabotage
- Sci-fi
- Trump as KGB agent
- USA
- Utopia
- Witkoff-Lavrov Pact Emulation
- Wreckage of Crimea