⚑Derivation Flags (15)

• high
  Eq. (6) — The linear form is stated as a near-threshold approximation, but no derivation, validity interval, or truncation error is supplied for its use at x=1.462 or x≈3.09.

  If wrong: The estimated Z=164 deficit may be below 14 MeV, so the negative-barrier and terminal-fissility conclusions would no longer follow.

• high
  Eq. (6) and Remark 1 — The paper calibrates an approximate near-threshold linear form at Z=126, then asserts that its extrapolation gives a lower bound at much larger fissility. No liquid-drop saddle-point expression, proof of monotonicity, or cited result establishing this lower-bound property is supplied.

  If wrong: The claimed lower bound used for Z=164 is unavailable. Consequently, Eqs. (10)-(11) do not establish that the Z=164 barrier is necessarily negative, and the paper's terminal-fissility conclusion is unsupported by its displayed derivation.

• high
  Eqs. (10)-(11) — The negative-barrier inference for Z=164 is conditional on the unproved lower-bound extrapolation in Remark 1, rather than following from an independently displayed macroscopic fission-barrier calculation.

  If wrong: A negative barrier at Z=164 is not demonstrated, so the conclusion that Z=126 is the last positive-barrier candidate among those examined does not follow.

• high
  Remark 1 (justifying Eq. 10) — The claim that the macroscopic/Strutinsky penalty grows at least as fast as the linear extrapolation for x >> 1 is asserted without derivation from the liquid-drop saddle-point energy; it is the sole basis for treating the Z=164 and α=1/50 numbers as lower bounds rather than uncontrolled extrapolations of a one-point fit.

  If wrong: If the true macroscopic penalty at x = 1.462 falls below the ≲14 MeV maximum shell correction, Eq. (11) no longer forces B_f(Z=164) < 0 and the paper's central 'terminal fissility limit at Z = 126' conclusion would be unsupported by its own model, resting only on the cited B_f(Z=164) ≈ 0 MeV from [13].

• high
  Remark 1 following Eq. (7) — The assertion that the true macroscopic penalty must grow at least as rapidly as the fitted linear expression is not derived from the equations shown or from a stated theorem with applicable hypotheses.

  If wrong: The labels Δ_LDM(Z=164)≥21.9 MeV and Δ_LDM|_{α=1/50}≥82.9 MeV are not justified as lower bounds; they are only extrapolated point estimates.

• medium
  Eq. (12) — The counterfactual alpha calculation extrapolates the Eq. (6) fit from x=1.126 to x≈3.09, far outside the stated near-threshold calibration region.

  If wrong: The specific 82.9 MeV counterfactual and the quantitative sensitivity narrative are unreliable, although a larger alpha would still increase E_C and x under the stated fissility formula.

• medium
  Eq. (13) and Remark 2 — The critical-alpha sensitivity result is derived entirely within the phenomenological extrapolation of Eq. (6). Its status should therefore be conditional on the validity of that extrapolation over the required alpha_EM range, rather than presented as a model-independent stability threshold.

  If wrong: The quoted critical-coupling sensitivity threshold is not established. This affects the counterfactual sensitivity discussion, but not the basic conditional state-count result for the Z=126 shell closure.

• medium
  Eq. (6), Δ_LDM ≈ c(x−1)·2E_S — The linear approximation for the Coulomb deficit above unit fissility is introduced with the statement 'well approximated by a linear function' but the underlying justification (e.g., from the Myers–Swiatecki saddle-point energy formula) is not shown. The calibration constant c is determined from a single point (Z=126).

  If wrong: If the linear approximation underestimates the growth of Δ_LDM with x, the lower-bound argument in Remark 1 would fail, and the Z=164 conclusion would be weakened (though the paper argues the linear fit is a lower bound, so the conclusion is conservative). If the approximation overestimates, the Z=126 conclusion could be affected, but the calibration at Z=126 anchors that point exactly.

• medium
  Eq. (7) and its use in Eq. (8) — The coefficient c is calibrated from the same Z=126 shell correction and published barrier later used to claim a positive Z=126 barrier, so Eq. (8) is a fitted reproduction rather than an independent check.

  If wrong: The paper's claimed non-trivial Z=126 UV–IR consistency check reduces to consistency with the inputs used to calibrate the model; it cannot independently test the UAIC-derived alpha value.

• medium
  Eqs. (7)–(9) — Single-point calibration loop: c is fitted from the published Z=126 barrier and then used to 'compute' the Z=126 Coulomb deficit and barrier, so Eqs. (8)–(9) return their own input rather than providing an independent check. Disclosed, but presented in the summary box as a consistency result.

  If wrong: Nothing numerically breaks, but the 'non-triviality' argument of Sec. 4.3(b) and summary item (i) lose force: only the Z=164 branch and the α-sensitivity estimate carry genuine model content.

• medium
  Remark 1, lower bound claim: 'the macroscopic energy penalty grows at least as fast as the linear extrapolation' — The claim that the Strutinsky penalty cannot decrease relative to the linear fit as fissility increases further above unity is asserted without derivation. This is a monotonicity/convexity claim about the liquid-drop saddle-point energy as a function of x.

  If wrong: If the penalty grows more slowly than linearly, the lower bound on Δ_LDM(Z=164) would be weaker, but the paper's conclusion (Δ_LDM ≥ 22 MeV > 14 MeV shell correction) would still hold given the large margin. If the penalty grows faster, the conclusion is strengthened. The lower-bound claim is load-bearing for the rigor of the Z=164 conclusion but the margin is large enough that the conclusion is robust.

• low
  Eq. (10) cross-reference — Eq. (10) directs the reader to 'Remark 2' for the lower-bound justification, but the lower-bound argument is Remark 1; Remark 2 is the α_EM sensitivity calculation.

  If wrong: Navigational only; no mathematical consequence.

• low
  Eq. (11) — The shell correction δE_shell(Z=164) = 2–4 MeV is introduced without explicit citation or derivation, while the maximum ≲14 MeV is separately cited from [13].

  If wrong: Only the magnitude of the negative barrier changes; the sign conclusion is protected by the separately cited ≲14 MeV ceiling.

• low
  Eq. (13), sensitivity factor f — The derivation of f = 1.18 is shown in one line. The algebra is straightforward but compressed.

  If wrong: This is a sensitivity analysis, peripheral to the main conclusion. An error here would not affect the central consistency check.

• low
  Table 1, fissility values — The fissility values x = 1.006, 1.065, 1.126, 1.462 are stated as 'independently verifiable' from Eqs. (1)–(3) but the intermediate arithmetic is not shown.

  If wrong: These values are inputs to the calibration and conclusions. An error here would propagate, but the values are independently verifiable and correct.

⚑Derivation Flags (15)

• high
  Eq. (6) — The linear form is stated as a near-threshold approximation, but no derivation, validity interval, or truncation error is supplied for its use at x=1.462 or x≈3.09.

  If wrong: The estimated Z=164 deficit may be below 14 MeV, so the negative-barrier and terminal-fissility conclusions would no longer follow.

• high
  Eq. (6) and Remark 1 — The paper calibrates an approximate near-threshold linear form at Z=126, then asserts that its extrapolation gives a lower bound at much larger fissility. No liquid-drop saddle-point expression, proof of monotonicity, or cited result establishing this lower-bound property is supplied.

  If wrong: The claimed lower bound used for Z=164 is unavailable. Consequently, Eqs. (10)-(11) do not establish that the Z=164 barrier is necessarily negative, and the paper's terminal-fissility conclusion is unsupported by its displayed derivation.

• high
  Eqs. (10)-(11) — The negative-barrier inference for Z=164 is conditional on the unproved lower-bound extrapolation in Remark 1, rather than following from an independently displayed macroscopic fission-barrier calculation.

  If wrong: A negative barrier at Z=164 is not demonstrated, so the conclusion that Z=126 is the last positive-barrier candidate among those examined does not follow.

• high
  Remark 1 (justifying Eq. 10) — The claim that the macroscopic/Strutinsky penalty grows at least as fast as the linear extrapolation for x >> 1 is asserted without derivation from the liquid-drop saddle-point energy; it is the sole basis for treating the Z=164 and α=1/50 numbers as lower bounds rather than uncontrolled extrapolations of a one-point fit.

  If wrong: If the true macroscopic penalty at x = 1.462 falls below the ≲14 MeV maximum shell correction, Eq. (11) no longer forces B_f(Z=164) < 0 and the paper's central 'terminal fissility limit at Z = 126' conclusion would be unsupported by its own model, resting only on the cited B_f(Z=164) ≈ 0 MeV from [13].

• high
  Remark 1 following Eq. (7) — The assertion that the true macroscopic penalty must grow at least as rapidly as the fitted linear expression is not derived from the equations shown or from a stated theorem with applicable hypotheses.

  If wrong: The labels Δ_LDM(Z=164)≥21.9 MeV and Δ_LDM|_{α=1/50}≥82.9 MeV are not justified as lower bounds; they are only extrapolated point estimates.

• medium
  Eq. (12) — The counterfactual alpha calculation extrapolates the Eq. (6) fit from x=1.126 to x≈3.09, far outside the stated near-threshold calibration region.

  If wrong: The specific 82.9 MeV counterfactual and the quantitative sensitivity narrative are unreliable, although a larger alpha would still increase E_C and x under the stated fissility formula.

• medium
  Eq. (13) and Remark 2 — The critical-alpha sensitivity result is derived entirely within the phenomenological extrapolation of Eq. (6). Its status should therefore be conditional on the validity of that extrapolation over the required alpha_EM range, rather than presented as a model-independent stability threshold.

  If wrong: The quoted critical-coupling sensitivity threshold is not established. This affects the counterfactual sensitivity discussion, but not the basic conditional state-count result for the Z=126 shell closure.

• medium
  Eq. (6), Δ_LDM ≈ c(x−1)·2E_S — The linear approximation for the Coulomb deficit above unit fissility is introduced with the statement 'well approximated by a linear function' but the underlying justification (e.g., from the Myers–Swiatecki saddle-point energy formula) is not shown. The calibration constant c is determined from a single point (Z=126).

  If wrong: If the linear approximation underestimates the growth of Δ_LDM with x, the lower-bound argument in Remark 1 would fail, and the Z=164 conclusion would be weakened (though the paper argues the linear fit is a lower bound, so the conclusion is conservative). If the approximation overestimates, the Z=126 conclusion could be affected, but the calibration at Z=126 anchors that point exactly.

• medium
  Eq. (7) and its use in Eq. (8) — The coefficient c is calibrated from the same Z=126 shell correction and published barrier later used to claim a positive Z=126 barrier, so Eq. (8) is a fitted reproduction rather than an independent check.

  If wrong: The paper's claimed non-trivial Z=126 UV–IR consistency check reduces to consistency with the inputs used to calibrate the model; it cannot independently test the UAIC-derived alpha value.

• medium
  Eqs. (7)–(9) — Single-point calibration loop: c is fitted from the published Z=126 barrier and then used to 'compute' the Z=126 Coulomb deficit and barrier, so Eqs. (8)–(9) return their own input rather than providing an independent check. Disclosed, but presented in the summary box as a consistency result.

  If wrong: Nothing numerically breaks, but the 'non-triviality' argument of Sec. 4.3(b) and summary item (i) lose force: only the Z=164 branch and the α-sensitivity estimate carry genuine model content.

• medium
  Remark 1, lower bound claim: 'the macroscopic energy penalty grows at least as fast as the linear extrapolation' — The claim that the Strutinsky penalty cannot decrease relative to the linear fit as fissility increases further above unity is asserted without derivation. This is a monotonicity/convexity claim about the liquid-drop saddle-point energy as a function of x.

  If wrong: If the penalty grows more slowly than linearly, the lower bound on Δ_LDM(Z=164) would be weaker, but the paper's conclusion (Δ_LDM ≥ 22 MeV > 14 MeV shell correction) would still hold given the large margin. If the penalty grows faster, the conclusion is strengthened. The lower-bound claim is load-bearing for the rigor of the Z=164 conclusion but the margin is large enough that the conclusion is robust.

• low
  Eq. (10) cross-reference — Eq. (10) directs the reader to 'Remark 2' for the lower-bound justification, but the lower-bound argument is Remark 1; Remark 2 is the α_EM sensitivity calculation.

  If wrong: Navigational only; no mathematical consequence.

• low
  Eq. (11) — The shell correction δE_shell(Z=164) = 2–4 MeV is introduced without explicit citation or derivation, while the maximum ≲14 MeV is separately cited from [13].

  If wrong: Only the magnitude of the negative barrier changes; the sign conclusion is protected by the separately cited ≲14 MeV ceiling.

• low
  Eq. (13), sensitivity factor f — The derivation of f = 1.18 is shown in one line. The algebra is straightforward but compressed.

  If wrong: This is a sensitivity analysis, peripheral to the main conclusion. An error here would not affect the central consistency check.

• low
  Table 1, fissility values — The fissility values x = 1.006, 1.065, 1.126, 1.462 are stated as 'independently verifiable' from Eqs. (1)–(3) but the intermediate arithmetic is not shown.

  If wrong: These values are inputs to the calibration and conclusions. An error here would propagate, but the values are independently verifiable and correct.

⚑Derivation Flags (15)

• high
  Eq. (6) — The linear form is stated as a near-threshold approximation, but no derivation, validity interval, or truncation error is supplied for its use at x=1.462 or x≈3.09.

  If wrong: The estimated Z=164 deficit may be below 14 MeV, so the negative-barrier and terminal-fissility conclusions would no longer follow.

• high
  Eq. (6) and Remark 1 — The paper calibrates an approximate near-threshold linear form at Z=126, then asserts that its extrapolation gives a lower bound at much larger fissility. No liquid-drop saddle-point expression, proof of monotonicity, or cited result establishing this lower-bound property is supplied.

  If wrong: The claimed lower bound used for Z=164 is unavailable. Consequently, Eqs. (10)-(11) do not establish that the Z=164 barrier is necessarily negative, and the paper's terminal-fissility conclusion is unsupported by its displayed derivation.

• high
  Eqs. (10)-(11) — The negative-barrier inference for Z=164 is conditional on the unproved lower-bound extrapolation in Remark 1, rather than following from an independently displayed macroscopic fission-barrier calculation.

  If wrong: A negative barrier at Z=164 is not demonstrated, so the conclusion that Z=126 is the last positive-barrier candidate among those examined does not follow.

• high
  Remark 1 (justifying Eq. 10) — The claim that the macroscopic/Strutinsky penalty grows at least as fast as the linear extrapolation for x >> 1 is asserted without derivation from the liquid-drop saddle-point energy; it is the sole basis for treating the Z=164 and α=1/50 numbers as lower bounds rather than uncontrolled extrapolations of a one-point fit.

  If wrong: If the true macroscopic penalty at x = 1.462 falls below the ≲14 MeV maximum shell correction, Eq. (11) no longer forces B_f(Z=164) < 0 and the paper's central 'terminal fissility limit at Z = 126' conclusion would be unsupported by its own model, resting only on the cited B_f(Z=164) ≈ 0 MeV from [13].

• high
  Remark 1 following Eq. (7) — The assertion that the true macroscopic penalty must grow at least as rapidly as the fitted linear expression is not derived from the equations shown or from a stated theorem with applicable hypotheses.

  If wrong: The labels Δ_LDM(Z=164)≥21.9 MeV and Δ_LDM|_{α=1/50}≥82.9 MeV are not justified as lower bounds; they are only extrapolated point estimates.

• medium
  Eq. (12) — The counterfactual alpha calculation extrapolates the Eq. (6) fit from x=1.126 to x≈3.09, far outside the stated near-threshold calibration region.

  If wrong: The specific 82.9 MeV counterfactual and the quantitative sensitivity narrative are unreliable, although a larger alpha would still increase E_C and x under the stated fissility formula.

• medium
  Eq. (13) and Remark 2 — The critical-alpha sensitivity result is derived entirely within the phenomenological extrapolation of Eq. (6). Its status should therefore be conditional on the validity of that extrapolation over the required alpha_EM range, rather than presented as a model-independent stability threshold.

  If wrong: The quoted critical-coupling sensitivity threshold is not established. This affects the counterfactual sensitivity discussion, but not the basic conditional state-count result for the Z=126 shell closure.

• medium
  Eq. (6), Δ_LDM ≈ c(x−1)·2E_S — The linear approximation for the Coulomb deficit above unit fissility is introduced with the statement 'well approximated by a linear function' but the underlying justification (e.g., from the Myers–Swiatecki saddle-point energy formula) is not shown. The calibration constant c is determined from a single point (Z=126).

  If wrong: If the linear approximation underestimates the growth of Δ_LDM with x, the lower-bound argument in Remark 1 would fail, and the Z=164 conclusion would be weakened (though the paper argues the linear fit is a lower bound, so the conclusion is conservative). If the approximation overestimates, the Z=126 conclusion could be affected, but the calibration at Z=126 anchors that point exactly.

• medium
  Eq. (7) and its use in Eq. (8) — The coefficient c is calibrated from the same Z=126 shell correction and published barrier later used to claim a positive Z=126 barrier, so Eq. (8) is a fitted reproduction rather than an independent check.

  If wrong: The paper's claimed non-trivial Z=126 UV–IR consistency check reduces to consistency with the inputs used to calibrate the model; it cannot independently test the UAIC-derived alpha value.

• medium
  Eqs. (7)–(9) — Single-point calibration loop: c is fitted from the published Z=126 barrier and then used to 'compute' the Z=126 Coulomb deficit and barrier, so Eqs. (8)–(9) return their own input rather than providing an independent check. Disclosed, but presented in the summary box as a consistency result.

  If wrong: Nothing numerically breaks, but the 'non-triviality' argument of Sec. 4.3(b) and summary item (i) lose force: only the Z=164 branch and the α-sensitivity estimate carry genuine model content.

• medium
  Remark 1, lower bound claim: 'the macroscopic energy penalty grows at least as fast as the linear extrapolation' — The claim that the Strutinsky penalty cannot decrease relative to the linear fit as fissility increases further above unity is asserted without derivation. This is a monotonicity/convexity claim about the liquid-drop saddle-point energy as a function of x.

  If wrong: If the penalty grows more slowly than linearly, the lower bound on Δ_LDM(Z=164) would be weaker, but the paper's conclusion (Δ_LDM ≥ 22 MeV > 14 MeV shell correction) would still hold given the large margin. If the penalty grows faster, the conclusion is strengthened. The lower-bound claim is load-bearing for the rigor of the Z=164 conclusion but the margin is large enough that the conclusion is robust.

• low
  Eq. (10) cross-reference — Eq. (10) directs the reader to 'Remark 2' for the lower-bound justification, but the lower-bound argument is Remark 1; Remark 2 is the α_EM sensitivity calculation.

  If wrong: Navigational only; no mathematical consequence.

• low
  Eq. (11) — The shell correction δE_shell(Z=164) = 2–4 MeV is introduced without explicit citation or derivation, while the maximum ≲14 MeV is separately cited from [13].

  If wrong: Only the magnitude of the negative barrier changes; the sign conclusion is protected by the separately cited ≲14 MeV ceiling.

• low
  Eq. (13), sensitivity factor f — The derivation of f = 1.18 is shown in one line. The algebra is straightforward but compressed.

  If wrong: This is a sensitivity analysis, peripheral to the main conclusion. An error here would not affect the central consistency check.

• low
  Table 1, fissility values — The fissility values x = 1.006, 1.065, 1.126, 1.462 are stated as 'independently verifiable' from Eqs. (1)–(3) but the intermediate arithmetic is not shown.

  If wrong: These values are inputs to the calibration and conclusions. An error here would propagate, but the values are independently verifiable and correct.

⚑Derivation Flags (15)

• high
  Eq. (6) — The linear form is stated as a near-threshold approximation, but no derivation, validity interval, or truncation error is supplied for its use at x=1.462 or x≈3.09.

  If wrong: The estimated Z=164 deficit may be below 14 MeV, so the negative-barrier and terminal-fissility conclusions would no longer follow.

• high
  Eq. (6) and Remark 1 — The paper calibrates an approximate near-threshold linear form at Z=126, then asserts that its extrapolation gives a lower bound at much larger fissility. No liquid-drop saddle-point expression, proof of monotonicity, or cited result establishing this lower-bound property is supplied.

  If wrong: The claimed lower bound used for Z=164 is unavailable. Consequently, Eqs. (10)-(11) do not establish that the Z=164 barrier is necessarily negative, and the paper's terminal-fissility conclusion is unsupported by its displayed derivation.

• high
  Eqs. (10)-(11) — The negative-barrier inference for Z=164 is conditional on the unproved lower-bound extrapolation in Remark 1, rather than following from an independently displayed macroscopic fission-barrier calculation.

  If wrong: A negative barrier at Z=164 is not demonstrated, so the conclusion that Z=126 is the last positive-barrier candidate among those examined does not follow.

• high
  Remark 1 (justifying Eq. 10) — The claim that the macroscopic/Strutinsky penalty grows at least as fast as the linear extrapolation for x >> 1 is asserted without derivation from the liquid-drop saddle-point energy; it is the sole basis for treating the Z=164 and α=1/50 numbers as lower bounds rather than uncontrolled extrapolations of a one-point fit.

  If wrong: If the true macroscopic penalty at x = 1.462 falls below the ≲14 MeV maximum shell correction, Eq. (11) no longer forces B_f(Z=164) < 0 and the paper's central 'terminal fissility limit at Z = 126' conclusion would be unsupported by its own model, resting only on the cited B_f(Z=164) ≈ 0 MeV from [13].

• high
  Remark 1 following Eq. (7) — The assertion that the true macroscopic penalty must grow at least as rapidly as the fitted linear expression is not derived from the equations shown or from a stated theorem with applicable hypotheses.

  If wrong: The labels Δ_LDM(Z=164)≥21.9 MeV and Δ_LDM|_{α=1/50}≥82.9 MeV are not justified as lower bounds; they are only extrapolated point estimates.

• medium
  Eq. (12) — The counterfactual alpha calculation extrapolates the Eq. (6) fit from x=1.126 to x≈3.09, far outside the stated near-threshold calibration region.

  If wrong: The specific 82.9 MeV counterfactual and the quantitative sensitivity narrative are unreliable, although a larger alpha would still increase E_C and x under the stated fissility formula.

• medium
  Eq. (13) and Remark 2 — The critical-alpha sensitivity result is derived entirely within the phenomenological extrapolation of Eq. (6). Its status should therefore be conditional on the validity of that extrapolation over the required alpha_EM range, rather than presented as a model-independent stability threshold.

  If wrong: The quoted critical-coupling sensitivity threshold is not established. This affects the counterfactual sensitivity discussion, but not the basic conditional state-count result for the Z=126 shell closure.

• medium
  Eq. (6), Δ_LDM ≈ c(x−1)·2E_S — The linear approximation for the Coulomb deficit above unit fissility is introduced with the statement 'well approximated by a linear function' but the underlying justification (e.g., from the Myers–Swiatecki saddle-point energy formula) is not shown. The calibration constant c is determined from a single point (Z=126).

  If wrong: If the linear approximation underestimates the growth of Δ_LDM with x, the lower-bound argument in Remark 1 would fail, and the Z=164 conclusion would be weakened (though the paper argues the linear fit is a lower bound, so the conclusion is conservative). If the approximation overestimates, the Z=126 conclusion could be affected, but the calibration at Z=126 anchors that point exactly.

• medium
  Eq. (7) and its use in Eq. (8) — The coefficient c is calibrated from the same Z=126 shell correction and published barrier later used to claim a positive Z=126 barrier, so Eq. (8) is a fitted reproduction rather than an independent check.

  If wrong: The paper's claimed non-trivial Z=126 UV–IR consistency check reduces to consistency with the inputs used to calibrate the model; it cannot independently test the UAIC-derived alpha value.

• medium
  Eqs. (7)–(9) — Single-point calibration loop: c is fitted from the published Z=126 barrier and then used to 'compute' the Z=126 Coulomb deficit and barrier, so Eqs. (8)–(9) return their own input rather than providing an independent check. Disclosed, but presented in the summary box as a consistency result.

  If wrong: Nothing numerically breaks, but the 'non-triviality' argument of Sec. 4.3(b) and summary item (i) lose force: only the Z=164 branch and the α-sensitivity estimate carry genuine model content.

• medium
  Remark 1, lower bound claim: 'the macroscopic energy penalty grows at least as fast as the linear extrapolation' — The claim that the Strutinsky penalty cannot decrease relative to the linear fit as fissility increases further above unity is asserted without derivation. This is a monotonicity/convexity claim about the liquid-drop saddle-point energy as a function of x.

  If wrong: If the penalty grows more slowly than linearly, the lower bound on Δ_LDM(Z=164) would be weaker, but the paper's conclusion (Δ_LDM ≥ 22 MeV > 14 MeV shell correction) would still hold given the large margin. If the penalty grows faster, the conclusion is strengthened. The lower-bound claim is load-bearing for the rigor of the Z=164 conclusion but the margin is large enough that the conclusion is robust.

• low
  Eq. (10) cross-reference — Eq. (10) directs the reader to 'Remark 2' for the lower-bound justification, but the lower-bound argument is Remark 1; Remark 2 is the α_EM sensitivity calculation.

  If wrong: Navigational only; no mathematical consequence.

• low
  Eq. (11) — The shell correction δE_shell(Z=164) = 2–4 MeV is introduced without explicit citation or derivation, while the maximum ≲14 MeV is separately cited from [13].

  If wrong: Only the magnitude of the negative barrier changes; the sign conclusion is protected by the separately cited ≲14 MeV ceiling.

• low
  Eq. (13), sensitivity factor f — The derivation of f = 1.18 is shown in one line. The algebra is straightforward but compressed.

  If wrong: This is a sensitivity analysis, peripheral to the main conclusion. An error here would not affect the central consistency check.

• low
  Table 1, fissility values — The fissility values x = 1.006, 1.065, 1.126, 1.462 are stated as 'independently verifiable' from Eqs. (1)–(3) but the intermediate arithmetic is not shown.

  If wrong: These values are inputs to the calibration and conclusions. An error here would propagate, but the values are independently verifiable and correct.