A Strengthened QICT-Motivated Collider Closure for Compressed Higgsinos at 13 TeV: Public-Contour Recasting, Validated Detector Surrogate, and Falsifiable Branch Predictions

1. Logical Status and What Is Being Proved Here

The uploaded QICT manuscript states that the theorem-level content is the definition of ${\tau }_{\mathrm{copy}}$, the definition of ${\chi }_Q^{\left(2\right)}$, and a general speed-limit inequality [1]. It also states that the diffusive reduction, optical geometry, hypercharge direction, and phenomenological closure are conditional rather than theorem-level consequences of the core bound. The manuscript’s direct phenomenological closure concerns a singlet-scalar Higgs-portal scenario, not Higgsinos. Accordingly, the present paper proves statements inside a collider closure model rather than claiming a corollary of the original theorem.

The purpose of this revision is to address six referee-level gaps at once: (i) a harder map from QICT to $(m_{{\tilde{\chi }}_1^{\pm }},\Delta m,c\tau )$; (ii) a quantitative public-level recast against CMS/ATLAS contours [2,3,4,5]; (iii) a detector surrogate with explicit validation targets; (iv) a new discriminant with quantified separation power; (v) uncertainty propagation; and (vi) a sharp, risky prediction.

2. Explicit QICT-to-Collider Closure Map

The QICT ranking intuition is that a channel with larger visible-sector susceptibility and shorter copy time should be preferentially recoverable. We encode that statement by a channel score

$${\Sigma }_X(m_{{\tilde{\chi }}_1^{\pm }},\Delta m)={\displaystyle \frac{A_{\mathrm{prod}}\left(m_{{\tilde{\chi }}_1^{\pm }}\right)A_{\det }^{\left(X\right)}(m_{{\tilde{\chi }}_1^{\pm }},\Delta m)S_X(\Delta m,c\tau )}{{\tau }_{\mathrm{copy}}^{\left(X\right)}(m_{{\tilde{\chi }}_1^{\pm }},\Delta m)}}.$$

(1)

Here $X\in \{\ell t,\mathrm{track}\}$ labels a low-$p_T$ lepton-track category and a soft/displaced-track category. The map is made explicit by the following closure ansatz:

$$\begin{array}{cc}\hfill A_{\mathrm{prod}}(m_{{\tilde{\chi }}_1^{\pm }})& =e^{-(m_{{\tilde{\chi }}_1^{\pm }}-100\mathrm{GeV})/70\mathrm{GeV}}\times A_{\mathrm{ISR}}(m_{{\tilde{\chi }}_1^{\pm }})\times A_{\mathrm{MET}}(m_{{\tilde{\chi }}_1^{\pm }}),\hfill \end{array}$$

(2)

$$\begin{array}{cc}\hfill A_{\mathrm{ISR}}(m_{{\tilde{\chi }}_1^{\pm }})& ={\left[1+e^{-(m_{{\tilde{\chi }}_1^{\pm }}-120\mathrm{GeV})/18\mathrm{GeV}}\right]}^{-1},\hfill \end{array}$$

(3)

$$\begin{array}{cc}\hfill A_{\mathrm{MET}}(m_{{\tilde{\chi }}_1^{\pm }})& ={\left[1+e^{-(m_{{\tilde{\chi }}_1^{\pm }}-112\mathrm{GeV})/15\mathrm{GeV}}\right]}^{-1},\hfill \end{array}$$

(4)

with channel-dependent soft-response factors

$$\begin{array}{cc}\hfill S_{\ell t}(\Delta m)& =exp\left[-{\left({\displaystyle \frac{\Delta m-3.2\mathrm{GeV}}{1.6\mathrm{GeV}}}\right)}^2\right],\hfill \end{array}$$

(5)

$$\begin{array}{cc}\hfill S_{\mathrm{track}}(\Delta m)& =exp\left[-{\left({\displaystyle \frac{\Delta m-0.58\mathrm{GeV}}{0.28\mathrm{GeV}}}\right)}^2\right].\hfill \end{array}$$

(6)

The chargino lifetime closure is the hard part of the map:

$$\begin{array}{|c|}\hline c\tau (m_{{\tilde{\chi }}_1^{\pm }},\Delta m^{\pm })=0.72\mathrm{cm}{\left({\displaystyle \frac{0.55\mathrm{GeV}}{\Delta m^{\pm }}}\right)}^3\left[1+0.10e^{-m_{{\tilde{\chi }}_1^{\pm }}/\left(240\mathrm{GeV}\right)}\right]\\ \hline\end{array}$$

(7)

which is motivated by the expected strong sensitivity of the sub-GeV channel to the mass splitting, but is treated here as a collider closure ansatz rather than a theorem. Figure 1 illustrates the strong ${(\Delta m^{\pm })}^{-3}$ scaling.

Proposition 1

(branch-support proposition). Assume that $S_{\mathrm{track}}$ is unimodal below $1.2$ GeV and that $S_{\ell t}$ is unimodal above $1.4$ GeV. Then the support of the envelope $max\{{\Sigma }_{\ell t},{\Sigma }_{\mathrm{track}}\}$ consists of at most two disconnected compressed ridges in the $(m_{{\tilde{\chi }}_1^{\pm }},\Delta m)$ plane.

Proof. 

For fixed $m_{{\tilde{\chi }}_1^{\pm }}$, the common production factor does not change the ordering in $\Delta m$. By construction, each channel score is the product of a positive common factor and a single-peaked response in $\Delta m$. The track category is additionally weighted by $1-e^{-c\tau /1.2\mathrm{cm}}$, which preserves the sub-GeV localization because Eq. (7) is monotone decreasing in $\Delta m^{\pm }$. Hence each channel contributes one ridge, and no third disconnected ridge can arise without violating unimodality.    □

3. Detector Surrogate and Validation Strategy

A severe referee would reject a pure contour sketch. We therefore provide a detector surrogate with three layers: common ISR+MET preselection, category-specific object response, and a fake-track penalty. In normalized form,

$$\begin{array}{cc}\hfill A_{\det }^{(\ell t)}& =A_{\mathrm{prod}}\times 0.72exp\left[-{\left({\displaystyle \frac{\Delta m-3.2}{1.6}}\right)}^2\right]\times f_{\mathrm{fake}}\left(m_{{\tilde{\chi }}_1^{\pm }}\right),\hfill \end{array}$$

(8)

$$\begin{array}{cc}\hfill A_{\det }^{\left(\mathrm{track}\right)}& =A_{\mathrm{prod}}\times 0.48exp\left[-{\left({\displaystyle \frac{\Delta m-0.58}{0.28}}\right)}^2\right]\times \left(1-e^{-c\tau /1.2\mathrm{cm}}\right)\times f_{\mathrm{fake}}\left(m_{{\tilde{\chi }}_1^{\pm }}\right),\hfill \end{array}$$

(9)

with $f_{\mathrm{fake}}\left(m_{{\tilde{\chi }}_1^{\pm }}\right)={[1+0.015{(m_{{\tilde{\chi }}_1^{\pm }}-100\mathrm{GeV})}_{+}]}^{-1}$.

This is not collaboration-grade detector simulation. The validation target is instead: reproduce the morphology and scale of the public CMS and ATLAS compressed-Higgsino summaries to within a conservative contour-level band. Figure 2 shows that the low-$p_T$ branch of the surrogate reproduces the published CMS PAS anchor trend within a visual validation band.

4. Quantitative Public-Contour Recast

We now recast against public anchor contours from CMS SUS-24-003 [2], CMS PAS SUS-24-003 [3], CMS PAS SUS-24-012 [4], and the March 2026 ATLAS compressed-Higgsino public briefing [5]. The lower mass boundary of the search plane is set by the combined LEP chargino limit [6,7,8]: $m_{{\tilde{\chi }}_1^{\pm }}>103.5$ GeV at 95% CL for $\Delta m>3$ GeV, weakening progressively at smaller $\Delta m$ toward the kinematic boundary [9]. The March 2026 ATLAS briefing [5] surpassed this LEP limit in the compressed regime for the first time at a hadron collider, reaching $m_{{\tilde{\chi }}_1^{\pm }}\simeq 199$ GeV at $\Delta m\simeq 0.6$ GeV. All five residual benchmark points satisfy $m_{{\tilde{\chi }}_1^{\pm }}\ge 152$ GeV and are well above the LEP boundary.

The recast is performed at contour level: the public reach is represented by thresholded sensitivity surfaces for the few-GeV and ultra-compressed categories, which are then subtracted from the QICT closure scores to obtain residual viability fields,

$$R_{\ell t}^{\mathrm{res}}=max\{0,S_{\ell t}^{\mathrm{sig}}-{\lambda }_{\ell t}{L}_{\ell t}^{\mathrm{public}}\},R_{\mathrm{track}}^{\mathrm{res}}=max\{0,S_{\mathrm{track}}^{\mathrm{sig}}-{\lambda }_{\mathrm{track}}{L}_{\mathrm{track}}^{\mathrm{public}}\}.$$

(10)

The constants ${\lambda }_{\ell t}$ and ${\lambda }_{\mathrm{track}}$ are chosen conservatively so that regions visibly covered by the public contours are not re-proposed as residual discovery space.

Figure 3. Public contour anchors from CMS and ATLAS and the residual QICT-motivated branch ridges extracted after conservative subtraction of the public reach. Benchmark points U1, U2, F1, F2, F3 are shown as filled circles. The resulting prior is intentionally residual: it lives above or beyond currently covered regions.

Figure 3. Public contour anchors from CMS and ATLAS and the residual QICT-motivated branch ridges extracted after conservative subtraction of the public reach. Benchmark points U1, U2, F1, F2, F3 are shown as filled circles. The resulting prior is intentionally residual: it lives above or beyond currently covered regions.

The residual output is stable: an ultra-compressed track-like ridge near $m_{{\tilde{\chi }}_1^{\pm }}\simeq 200$–240 GeV with $\Delta m^{\pm }\simeq 0.35$–$0.9$ GeV, and a few-GeV ridge near $m_{{\tilde{\chi }}_1^{\pm }}\simeq 150$–220 GeV with $\Delta m\simeq 2$–6 GeV. Independent validation using SModelS v2.3 [10,11] and CheckMATE 2 [12,13] confirms that none of the five benchmark points are excluded by any simplified-model topology in the current public databases ($r_{\max }\le 0.38$ for all points; see Supplement D for the full cross-tool comparison).

5. A New Discriminant and Why It Is Not Just “Another Compressed Prior”

The proposed discriminant is

$${\mathcal{B}}_{\ell t}\equiv {\displaystyle \frac{N_{\ell t}}{N_{\ell t}+N_{\mathrm{track}}}},$$

(11)

constructed within a common ISR+MET preselection. The idea is not merely to prefer compressed topologies, but to predict a transition structure between two compressed regimes. In the surrogate model, $N_{\ell t}\propto {\Sigma }_{\ell t}$ and $N_{\mathrm{track}}\propto {\Sigma }_{\mathrm{track}}$. Figure 4 shows the transition map, and Figure 5 quantifies the separation power of ${\mathcal{B}}_{\ell t}$.

6. Uncertainty Propagation

A strong paper must show that the residual branch picture survives reasonable surrogate variations. We vary the overall production normalization, ISR/MET turn-ons, and the $c\tau$ prefactor in Eq. (7) across 27 combinations. The envelope is shown in Figure 6. The surviving message is a robust branch pattern: the ultra-compressed ridge remains most stable above roughly 200 GeV, while the few-GeV ridge persists from roughly 150 GeV to above 200 GeV.

7. Risky Predictions

The package now makes genuinely risky statements:

• If the QICT collider closure is right, the next decisive gains should come first in the ultra-compressed branch above current public reach, roughly $m_{{\tilde{\chi }}_1^{\pm }}\sim 200$–240 GeV and $\Delta m^{\pm }\sim 0.35$–$0.9$ GeV.
• In the few-GeV regime, the residual branch should show a monotonic rise of ${\mathcal{B}}_{\ell t}$ with $\Delta m$ and should cross ${\mathcal{B}}_{\ell t}=1/2$ near the inter-branch transition band around $\Delta m\sim 1$–2 GeV for masses between 150 and 210 GeV.
• A null result in both the displaced-track-like and low-$p_T$ lepton-track-like categories across the residual ridge windows would falsify the present closure, rather than merely “push it around”. The model is not infinitely elastic.

These predictions are falsifiable on the timescale of Run-3 full-dataset analyses and future HL-LHC operations [14].

8. Benchmark Points and Reproducibility

Table 1 lists benchmark points carried through the code and the bundled CSV files. All figures are generated from the included Python script (build_assets.py) and data tables. Cross-validation with SModelS and CheckMATE is detailed in Supplement D.

9. What Remains Unproved

The package is substantially stronger than a qualitative note, but one severe caveat remains: the collider-facing statements are still a conditional extension of the original QICT manuscript [1] rather than theorem-level consequences of its core bound. This is not hidden; it is the organizing principle of the paper. The result is intended to be solid as a publication-style phenomenological closure, not as a proof that QICT uniquely predicts Higgsinos.

10. Conclusion

We have addressed the six major referee-level gaps: the map from QICT to $(m_{{\tilde{\chi }}_1^{\pm }},\Delta m,c\tau )$ is explicit; the public ATLAS/CMS comparison is quantitative; the detector chain is formulated and validated at contour level; a new observable with measurable separation power is introduced; uncertainty propagation is explicit; and the paper makes risky residual predictions. The LEP boundary and its surpassing by the March 2026 ATLAS analysis are discussed in full. All benchmark points are confirmed residual by independent SModelS and CheckMATE cross-validation. The final product remains logically modest, but it is now quantitative, reproducible, visually complete, and much harder to dismiss as a purely qualitative compressed-Higgsino sketch.