Factual entropy and structural irreversibility in the Sistema Vectorial SV: pre-ternary dispersion, transport law along the foundational chain and asymmetric conservation of factual content

Abstract: A structural magnitude of factual dispersion is established in the Sistema Vectorial SV as an intrinsic companion of every admissible trajectory throughout the foundational chain of the corpus, from the pre-ternary domain Ωpre to the final verdict {m0, χ0, U}. The magnitude is derived natively from the accumulations Ai(n) of §3 in Lloret Egea (2026j) and from the total pre-ternary variation of the polar bias δi. It is proved that, under the append-only discipline and coordinate honesty, the magnitude is non-decreasing on every admissible segment of the trajectory. Non-decrease is a structural property of the system and is not a consequence of external temporal ordering. The transport law of the magnitude through the five canonical operators of the chain is fixed, and a theorem of asymmetric conservation of factual content in the entropic regime is proved. The magnitude is identified as the factual entropy of the system, denoted HSV. Its relation to ρU, κU, Tpre, RΓ and the exact basal sector is established. A visible consistency pass over the canonical cell SV(3,9) confirms operational coherence without introducing founding probability, statistics as a criterion of truth, or sovereign time. --- Note: Canonical material source on GitHub: https://github.com/juantoniolloretegea/SV-matematica-semantica/tree/main/documentos/adendas/matematica-fisica-factual-contemporanea-sv/termodinamica-gases-fluidos-sv/entropia-factual-irreversibilidad-estructural-sv. Supplementary reproducible laboratories preserved in Zenodo: https://doi.org/10.5281/zenodo.19897700. Concept DOI for all laboratory versions: https://doi.org/10.5281/zenodo.19897699. These canonical sources are provided to facilitate direct consultation of the living textual record, reproducible laboratory verification and reader-side translation through standard browser translation tools when required.