Invariant Grammar · Uruk · P325352 · 2026-10-04
The UDU₃₉ Attractor Theorem
A finite projector proof of semantic-accounting invariance in the Late Uruk livestock ledger P325352. The source records 41 animals, marks two ewes with X, and preserves an accepted state of 39 through two independent reverse decompositions.
Recorded
41
X-marked residual
2
Accepted invariant
39
Python certificate
8 / 8 PASS
Finite projector
x = (5,6,4,1,3,3,6,2,2,7,2)ᵀ
P = diag(1,1,1,1,1,1,1,1,0,1,1)
1ᵀPx = 39
P = diag(1,1,1,1,1,1,1,1,0,1,1)
1ᵀPx = 39
Two decompositions, one accepted state
16 + 6 + 17 = 39
9 + 7 + 6 + 8 + 9 = 39
1ᵀA₁ = 1ᵀA₂ = 1ᵀPx = 39
9 + 7 + 6 + 8 + 9 = 39
1ᵀA₁ = 1ᵀA₂ = 1ᵀPx = 39
Executed certificate
obverse_total_41 PASS P_idempotent PASS excluded_X_state_2 PASS projected_state_39 PASS first_reconciliation_16_6_17 PASS second_reconciliation_9_7_6_8_9 PASS representations_distinct PASS common_invariant PASS ALL 8/8 CHECKS PASS
OVERALL: PASS
Academic boundary
This theorem certifies the finite arithmetic and projector identity encoded from the source reconstruction. Projector language is a modern analytical formalization. It does not claim that Late Uruk scribes possessed modern linear algebra, and it does not resolve the exact administrative semantics of the X sign.