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Projection Possibility Space (PPS)

Projection Possibility Space · five methodology papers (Papers 02–06; Paper 01 not received)

PPS is a general method: treat the dynamic, projective and perturbative structure of a geometric problem as something to be tested — a 3D carrier → dynamic projection (02) → subject–object–boundary (03) → worm-like high-freedom perturbation (04) → projection-induced hidden geometry (05) → adversarial closure (06). The motivation is to go beyond 'validate the known cases' and actively generate unknown cases under a counter-certificate duty. It does not depend on Lebesgue (PPS-02: 'this paper does not depend on Lebesgue'); Lebesgue takes one to three sections in each paper as a case sketch. The five papers expand Parts VI–IX of the Lebesgue case's open-questions list (the same sentence: 'do not validate the known cases; try to generate an unknown case'); LESR Paper 09C §45–46 and 09D §49 plan to apply them once the local atlas is frozen.

Reconstruction update · 2026-10-08: reconstructed from surviving records, with sources and limits stated; originals and new implementations are distinguished. Overview and download bundle.

Honest status: these five papers contain no results, experiments or certificates; each ends with a list of non-claims (PPS-02 §66 has ten, including 'the Lebesgue problem is already closed by this framework'). The method has not been run: the LESR local atlas is its intended first application, but no document says it has been applied. Paper 01, cited by all five, was not received and was not found in the author's research folders either; the recovery bundle of 2026-10-07 did not find it. A compatible foundational reconstruction dated 2026-10-08 now precedes Paper 02.

Authorship and provenance: all five headers read 'Author: Neo.K; AI research collaborator: Aletheia / ChatGPT, GPT-5.6 Sol; Institution: EveMissLab / 一言諾科技有限公司', version v0.1, dated 2026-09-21. They arrived together with the second batch of the Lebesgue case (LESR · Root 6217 local analysis and MCC-OE).

One misalignment: PPS-06's closure-authority ladder (Counterexample-Resistant at L3, below Finite-Branch Certified at L4) is ordered the other way from the open-questions list's Part-X ladder (Finite-Branch below); the two have not been reconciled.