IndisputableMonolith.NumberTheory.CompletedZetaLedger
The CompletedZetaLedger module supplies the balanced arithmetic ledger whose invariance under s to 1-s forces the fixed locus onto the critical line. Number theorists and Recognition Science researchers working on the Riemann hypothesis cite it when decomposing the physical thesis into explicit zeta ingredients. The module consists of definitions and certificates that import Mathlib complex numbers without reimplementing analytic machinery.
claimA balanced arithmetic ledger $B$ satisfies $B(s) = B(1-s)$ for the reciprocal coordinate map, so that its fixed locus lies on the critical line $Re(s) = 1/2$.
background
The module resides in the NumberTheory domain and imports only Mathlib. Its central object is the BalancedArithmeticLedger, defined so that the ledger remains unchanged under the coordinate inversion $s mapsto 1-s$. Sibling declarations include reciprocal_fixed_re_eq_half, completedZeta_balanced, and the certificate CompletedZetaLedgerCert that records the resulting symmetry.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module is imported by LogicComplexCompat (the compatibility layer that adopts Mathlib ℂ as the analytic substrate) and by RSPhysicalThesisDecomposition (the structured bundle that replaces the opaque RSPhysicalThesis dependency for the RH proof). It therefore supplies the number-theoretic symmetry required before the physical thesis can be decomposed into exact ingredients.
scope and limits
- Does not redefine holomorphy or contour integration.
- Does not contain executable zeta-function code.
- Does not prove the Riemann hypothesis itself.
- Does not introduce new complex-analysis primitives beyond Mathlib.