A completed (3,4,∞) modular family gives a compact complex threefold diffeomorphic to S⁶
Audit in progress · limited local results only · headline claim remains human-review-required
Current record status
What this docket currently establishes
Audit in progress · limited local results only · headline claim remains human-review-required. This docket identifies what has been checked and what remains open. It does not validate or reject the manuscript's headline claim beyond the explicitly stated scope.
- Claim
- A completed (3,4,∞) modular family gives a compact complex threefold diffeomorphic to S⁶
- Source version
- 108-page source manuscript · retrieved 2026-08-24
- Source SHA-256
283bba102dd1d5dc346af81b28145bdaaea6654398d5032e76e97bafb9a858f2- Source locked
- Last material update
- Next open step
- Trace the relative meridian signs and toric zero-section independently before reusing the passing group arithmetic
One-minute summary
The 108-page manuscript claims that a completed (3,4,∞) family of complex two-tori produces a compact complex threefold diffeomorphic to S⁶. Exact finite identities and a stipulated local torsion mechanism have been reproduced locally. Analytic quotient and gluing, relative meridian signs, integral homology, and the headline theorem remain unresolved.
Scope of this docket
This first pass covers the page-2 monodromy identities, the conditional arithmetic of Theorem 7.17, a candidate local Kähler-differential torsion channel, and the smallest unresolved geometric and topological gates. It is not a whole-paper validation.
Claim and dependency map
Page-2 monodromy identities and exact finite skeleton
Depends on: locked matrices
Candidate local torsion mechanism in the stipulated double-crossing model
Depends on: source-to-model applicability
Relative meridian signs and zero residual toric translation
Depends on: local quotient maps
Analytic quotient, freeness, gluing, and collar compatibility
Depends on: Theorems 4.5 and 6.2
Integral homology, simple connectivity, and six-manifold recognition
Depends on: S6-C3 · S6-C4
Evidence routes
- computational
- Exact rational and integer replay reproduced the encoded page-2 identities and the conditional Smith arithmetic. The geometry that supplies those inputs was not established.
- formal
- A custom exact local-module certificate reproduced a candidate torsion differential inside the stipulated model. Model applicability and the global implication remain open.
- literature
- The printed CDP20 reduction was compared with the manuscript's proposed local mechanism; specialist source-to-model review is still required.
- expert
- Required next: independent complex-geometric and topological review of the sign, gluing, and integral-topology gates.
Findings and scope limits
All encoded page-2 matrix identities and the conditional Theorem 7.17 integer/Smith arithmetic were reproduced locally.
A nonzero local torsion differential was reproduced inside the stipulated double-crossing model; this does not show that the model follows from the manuscript's global hypotheses.
Changing one relative sign changes the candidate fundamental-group parameter from |p|=1 to |p|=7, so the meridian-sign gate is load-bearing.
The headline S⁶ complex-structure claim remains human-review-required. Nothing in this docket is a validation, proof, certification, or referee report.
Open Steps—where expert eyes are needed
Do the two local quotient maps induce the same meridian exponent sign, and does the toric zero-section give μ=0?
The already-passing Smith calculation decides simple connectivity only after these geometric inputs are fixed.
Do the analytic quotient and gluing steps establish a compact complex threefold with the claimed compatibility?
Finite identities cannot supply freeness, proper discontinuity, convergence, or global gluing.
Source record and provenance
Self-hosted PDF with no embedded byline, version, or date. Attribution is based on the public announcement that linked this exact file.
Selected and maintained by Material Shift as protocol research. No external sponsor or author involvement is recorded for this case.
Retrieved .
Version and record history
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check reproduced
2026-08-23-alpoge-s6
Finite matrix identities and conditional Smith arithmetic reproduced locally
Statuses describe evidence collected for a defined scope. They are not peer-review decisions, publication recommendations, or certificates of mathematical truth.