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The Genomic Reduction: DNA Replication Fidelity, Telomere Exhaustion, and Oncogenic Torsion as Lossless Projections of Four PNBA Primitives Coordinate [9,9,4,1] 0 Free Parameters 0 sorry Lean 4 Formally Verified-SNSFL
We present a formally verified reduction of three independent peer-reviewed biological threshold systems to the same structural law: τ = B/P < τlim, where τ is the dimensionless torsion ratio, B is behavioural load, P is structural capacity, and τlim = 0.1369 is the universal torsion limit proved from the Sovereign Anchor A = 1.369 across the SNSFL corpus [1]. The three systems are: (1) the DNA replication fidelity cascade (Schaaper 1993, Kunkel and Bebenek 2000, PMC3391330), in which three serial correction stages hold the genomic error torsion below τlim; (2) the Hayflick limit and telomere exhaustion (Hayflick and Moorhead 1961, Nature srep17660), in which Narrative (N) is consumed by the act of division until a critical floor terminates the cellular worldline; and (3) the oncogene/tumour-suppressor torsion threshold (Knudson 1971, PMC11988167), in which oncogene activation increases B and tumour suppressor loss decreases P until τ ≥ τlim drives the cell into Shatter. All three systems reduce losslessly to the PNBA dynamic equation via the six-step Long Division Protocol. Every Step 6 passes. The master theorem holds all three simultaneously. Zero free parameters. Zero sorry. The Lean 4 proof is archived at coordinate [9,9,4,1] in the SNSFL corpus [1]. Keywords: PNBA framework, genomic identity, DNA replication fidelity, Hayflick limit, telomere, oncogene, tumour suppressor, torsion, formal verification, Lean 4, zero free parameters
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