Manuscript Em02-A@6 · Em02-A-v6.tex · section · cb2f0a9a

Seed constraints

Route B: geometry, support zeros, and the contribution ledger › Seed constraints · lines 553–579

Em02-A@6#eq:47-constraint, Em02-A@6#eq:5a-constraint, Em02-A@6#eq:5z-constraint, Em02-A@6#eq:response-constraint

On the scalar supports:

47 : 5 a : 5 z : response : u = 0, υ = - \frac{∣ ω ∣ ^{2}}{4 ( β - γ )} (β - γ > 0); u = 0, r past null; r, b - z future null, υ = \frac{β - γ}{β} u, ∣ ω ∣^{2} = \frac{4 γ ( β - γ )}{β} u (0 < γ < β); r = 0, u = 0.

For $5 a$ , directed nullness gives $γ, υ \leq 0$ . For $5 z$ , it gives $u \geq 0$ . The relations follow by equating the two expressions for $∣ ω ∣^{2}$ in (eq:internal-cones).

Displayed formulas in this passage

Em02-A@6#eq:47-constraint · line 556
$47 : 5 a : 5 z : response : u = 0, υ = - \frac{∣ ω ∣ ^{2}}{4 ( β - γ )} (β - γ > 0); u = 0, r past null; r, b - z future null, υ = \frac{β - γ}{β} u, ∣ ω ∣^{2} = \frac{4 γ ( β - γ )}{β} u (0 < γ < β); r = 0, u = 0.$
Em02-A@6#eq:5a-constraint · line 556
$47 : 5 a : 5 z : response : u = 0, υ = - \frac{∣ ω ∣ ^{2}}{4 ( β - γ )} (β - γ > 0); u = 0, r past null; r, b - z future null, υ = \frac{β - γ}{β} u, ∣ ω ∣^{2} = \frac{4 γ ( β - γ )}{β} u (0 < γ < β); r = 0, u = 0.$
Em02-A@6#eq:5z-constraint · line 556
$47 : 5 a : 5 z : response : u = 0, υ = - \frac{∣ ω ∣ ^{2}}{4 ( β - γ )} (β - γ > 0); u = 0, r past null; r, b - z future null, υ = \frac{β - γ}{β} u, ∣ ω ∣^{2} = \frac{4 γ ( β - γ )}{β} u (0 < γ < β); r = 0, u = 0.$
Em02-A@6#eq:response-constraint · line 556
$47 : 5 a : 5 z : response : u = 0, υ = - \frac{∣ ω ∣ ^{2}}{4 ( β - γ )} (β - γ > 0); u = 0, r past null; r, b - z future null, υ = \frac{β - γ}{β} u, ∣ ω ∣^{2} = \frac{4 γ ( β - γ )}{β} u (0 < γ < β); r = 0, u = 0.$