1. Condition (“if there is no peace deal…”)
   Early Russian–Ukrainian negotiations in spring 2022 (Istanbul talks, etc.) did not produce a lasting peace agreement, and the full‑scale war has continued through 2024–2025.(en.wikipedia.org) This means the condition for the prediction (“no peace deal in the near term following March 2022”) was met.

2. Russian escalation and heavy bombing of Ukrainian cities
   After March 19, 2022, Russia conducted extensive strikes against Ukrainian cities, consistent with the forecast:

• March–April 2022 saw major attacks such as the Mariupol theatre airstrike (March 16), the Kyiv Retroville shopping‑centre missile strike (March 20), the Kramatorsk railway‑station missile attack (April 8), and repeated cluster‑munition bombardments of Kharkiv and Mykolaiv, all hitting urban civilian areas.(en.wikipedia.org)
• From autumn 2022 onward, Russia launched large, repeated missile and drone salvos on cities and energy infrastructure across Ukraine (Kyiv, Lviv, Zaporizhzhia and others), with power plants and dense urban areas struck and large parts of the grid disabled.(en.wikipedia.org)
  This clearly matches the prediction of an escalation featuring “heavy bombing of Ukrainian cities.”

3. Increased political pressure on the U.S. to escalate its military role
   As Russian attacks intensified and atrocities became visible, political pressure on Washington to do more militarily rose sharply:

• President Zelenskyy repeatedly appealed for stronger U.S. and NATO action, including additional aircraft and air defenses, both in private calls with lawmakers and in his March 16, 2022 address to the U.S. Congress, where he urged creation of a no‑fly zone or, failing that, advanced systems and planes.(pbs.org)
• U.S. and allied debates over a Western‑enforced no‑fly zone—explicitly rejected by the Biden administration because it would mean direct combat with Russian forces—became a major political issue; lawmakers such as Senator Rob Portman and others publicly advocated “closing the skies” over Ukraine.(theguardian.com)
• Opinion polling cited in the no‑fly zone analysis found large majorities of Americans in favor of a no‑fly zone when asked in early March 2022, underscoring mass‑political pressure for more direct military measures.(en.wikipedia.org)
  While the Biden administration ultimately resisted direct intervention (no U.S./NATO troops or aircraft in combat), it did respond to this environment by steadily escalating the scale and sophistication of U.S. military aid (artillery, HIMARS, air defense systems, tanks, long‑range missiles) as part of a broader NATO effort.(nato.int)
  This is consistent with the prediction’s narrower claim that intensified Russian attacks would “step up the pressure” on Washington to increase its military involvement.

4. Heightened risk of the conflict “spinning out of control”
   Strategic analysts and officials repeatedly warned in 2022–2023 that the combination of Russia’s invasion and NATO’s growing military support for Ukraine significantly raised the danger of inadvertent or deliberate escalation into a wider NATO–Russia war, including nuclear use:

• The Atlantic Council’s work on escalation management in Ukraine explicitly states that Russia’s invasion and NATO’s response “increase the possibility of purposeful or inadvertent escalation in Europe.”(atlanticcouncil.org)
• Detailed studies of the proposed no‑fly zone stressed that enforcing it would likely mean U.S. and Russian forces shooting at each other, with a serious risk of nuclear confrontation; senior U.S. officials publicly cited this escalation risk as the main reason for rejecting the idea.(en.wikipedia.org)
• CSIS analyses document how Russian nuclear signaling and Western responses around Ukraine created significant concern about nuclear escalation, prompting efforts to build “off‑ramps” in crisis management.(csis.org)
  Thus, while the war has not yet “spun out of control” into direct NATO–Russia combat, expert and governmental assessments confirm that the risk of such an outcome rose markedly—matching the predictor’s framing (“could still spin out of control,” not that it necessarily would).

5. Overall assessment
   Given that: (a) no peace deal was reached in the near term; (b) Russia did escalate with sustained, heavy bombing of Ukrainian cities; (c) this escalation generated intense political pressure in Washington and among allies for riskier forms of U.S./NATO military involvement; and (d) the perceived risk of uncontrollable escalation between Russia and NATO materially increased, the conditional prediction closely matches subsequent events.

Accordingly, the prediction is best evaluated as right.