Retracted: Real Numbers as Coarse‑Grained Projections of Re‑Entry‑Generated p‑Adic Trees

#Retraction Notice

This paper (version 1.0.0) is retracted as of 2026-10-19. It was produced by the QNFO automated research pipeline, which retrieves literature, derives results and recomputes stated numbers, and it described empirical work as done that never took place: the pipeline performed no experiment, measurement, survey, human or expert review, pilot, pre-registration, ethics approval or data deposit. Because its findings rest on those statements, they cannot be relied on and the paper is withdrawn rather than corrected.

Statements that described work that did not take place:

• "This paper was drafted, reconciled, reviewed, revised and checked by the QNFO automated research pipeline (qnfo-research-exec 0.18.43-codeagent)." (a review or rating of the work that did not take place)
• "Models: drafting by openai/gpt-oss-120b, zai-org/glm-5.3-flash; reconciliation, completion, review, revision and verification by openai/gpt-oss-120b, zai-org/glm-5.3-flash, moonshotai/kimi-k2.6, with the QNFO model router as a fallback." (a review or rating of the work that did not take place)
• "Checks passed before publication: required sections present and finished, cross-references resolve, reference list rendered from the retrieved bibliography, no assistant residue or placeholders, adversarial model review with its blocking findings resolved, and a citation existence check at publication." (a review or rating of the work that did not take place)
• "Independent recomputation: a separately generated script recomputed 5 quantitative claims from the paper's stated inputs; 0 differed from the stated value at the stated precision." (a measurement that did not take place)
• "For $p=2$ we construct a Lipschitz coarse‑graining map $\varphi_2$ and verify its distortion bound." (empirical work that did not take place)
• "To test the isomorphism and the projection we implement the rewriting system in a symbolic engine, generate all normal forms up to a fixed length $L$, map them to $\mathbb{Z}_p$ via $\Phi_p$, and compare the resulting set with the known set of $p$‑adic integers modulo $p^{L}$." (an experiment that did not take place)

The withdrawn text is kept in the QNFO audit record. Detected and retracted automatically (CLAIM-INTEGRITY-1).