The Amplitude, Written Down: Veneziano's Beta-Function Construction, the Poles It Returns, and the Tachyon It Carries

Census pricing (row CC-119) of the founding step of Veneziano's 'Construction of a Crossing-Symmetric, Regge-Behaved Amplitude for Linearly Rising Trajectories,' Nuovo Cimento A 57, 190-197 (1968), against a fixed bench (what is postulated, what is derived, what the postulates return numerically, what they cannot reach). The step is one constructed amplitude -- the Euler beta function A(s,t) = Gamma(-alpha(s))Gamma(-alpha(t))/Gamma(-alpha(s)-alpha(t)) written down to meet the duality specification, not derived from any dynamics -- plus two fitted trajectory parameters (declared bench values alpha0 = 0.5, alpha' = 0.9 GeV^-2). Verified in the notebook (17 checks, exit 0): the pole ladder at s = 0.5556 / 1.6667 / 2.7778 / 3.8889 / 5.0000 GeV^2 with residues exactly the degree-n polynomials of the closed form; the Regge power law at 1.0001 and 0.9995 of its stated form at s = 1000 once the exact signature factor is divided out; crossing exact. Remainders at full size: the ladder's ground floor is a tachyon at s = -0.5556 GeV^2, unavoidable for any positive intercept; and the declared fit puts its spin-1 pole at 0.7454 GeV against the declared rho-mass input 0.770 GeV, a slack of 3.20%. Scout-grade verification disclosed on the manuscript's face (CC-91 form): no verbatim quotation, no page-specific claim. The author is living; the work is priced, the man is not addressed, and no contact was made. EXTENSION. Vacuum catastrophe NOT SOLVED; quantum gravity NOT SOLVED.