bibkey: retractive2026reviewed
authors: Supplied independent mathematical source and reviewer
year: 2026
title: Evolving continuous attachments and persistent compact range reservoirs
doi: null
url: https://github.com/the-omega-institute/trureturing
claim: Classical arbitrary-set retractive attachment topology, finite clopen defects, exact sequence criterion, and compact natural-range persistence.
strata_touched:
  - D5/S3/Topology/Resolution
  - D5/S3/Topology/InverseLimit
license: citation-only
triage: anchor

Exact scientific source and scope

Verified locator

• URL: https://github.com/the-omega-institute/trureturing
• Scope: repository provenance for the supplied independent mathematical source and its independent review; no external DOI is declared (doi: null).
• Supplied source: efimov_all_born_ancestries_global.tex, 47,806 bytes, SHA-256 ca017c88c526f556e904a56ea7176631a17b3e638641b8bf4ce65e46e7b4517d.
• Supplied independent review: independent_review.tex, 18,960 bytes, SHA-256 19d4967d94d2a0510eb9f23ae345ddf899c1c9525ea4e2ffddbb0bab993bbefe.
• Attribution: both files were supplied to this implementation on 4 November 2026 as complete scientific inputs by the supplied independent mathematical source and reviewer; this locator records repository provenance and makes no priority, uniqueness, or original-solution claim.

The supplied completed ordinary source is efimov_all_born_ancestries_global.tex, 47806 bytes, SHA-256 ca017c88c526f556e904a56ea7176631a17b3e638641b8bf4ce65e46e7b4517d. Its relevant sections are the stronger carrier, finite clopen defects, transverse convergence, exact final obstruction, and reservoir persistence. The supplied independent ordinary review is independent_review.tex, 18960 bytes, SHA-256 19d4967d94d2a0510eb9f23ae345ddf899c1c9525ea4e2ffddbb0bab993bbefe. Both were supplied to this implementation as complete scientific inputs on 4 November 2026. They concern classical partial mathematics, and make no formal, priority, uniqueness, or original-solution claim.

RetractiveAttachment uses the literal disjoint union B plus Sigma i P(i), with arbitrary continuous t(i), and constructs the topology from its open component traces and finite-omission core neighborhoods. Empty index types are included. Compact Hausdorff zero-dimensional nonempty inputs give the requested compact Boolean attachment. Some separate Lean results need fewer hypotheses; no nonemptiness or continuity requirement is silently replaced by surjectivity or constancy.

CompactRangePersistence reuses pinned Mathlib’s actual compact cofiltered limit nonemptiness theorem on the actual closed fibres over one core thread. RetractiveReservoir directly consumes it to construct a convergent injective sequence in the actual final RS carrier. No fibre restriction is assumed onto, no section or product independence is supplied, no final range membership is assumed, and no countable cofinality is imposed.

The reviewed component-building prefix is reducible. Only its specified final simultaneous successor is irreducible. The present supplier does not recreate that prefix, claim an all-irreducible prefix, or construct a sequence-free core. Original ZFC Efimov and all other original problems remain unsolved here; every theorem and helper has original KPI 0.

The supplied arXiv primary Kania–Kakol 2609.19351v2 assumes diamond for its Efimov construction. No result from it is imported as a ZFC predictor. This note makes no exhaustive literature absence or novelty claim.

Admission and audit boundary

These are arbitrary-space construction and inverse-limit theorems. None is a computational checker, bounded certificate, numerical reduction, or ordinary computed instance; the utility classification is none. The attachment construction and its range-multiplicity proof supply actual mathematical content. Elementary inclusion and continuity helpers are consumed on those proof paths. The reservoir theorem consumes both the attachment and compact-range suppliers.

Faithful four-slot escape registration remains unfinished for all new public theorem targets. The concrete dependent-family reconstruction, variation, sensitivity, and observational-dependence obligations are named in issue 26268. No registration is claimed declared_validated; this disclosure supplies no mathematical proof or kernel/CI exemption.