What question did this study set out to answer?

The aim is to improve the readability and auditability of mathematical proofs in the Quantum Sphaera framework.

April 26, 20260 citationsOpen Access

Quantum Sphaera Companion: A Structure-First Mathematical Unfolding

Key Points

The aim is to improve the readability and auditability of mathematical proofs in the Quantum Sphaera framework.
Restructured into split-bundle architecture for improved human readability.
Introduced internal RAID-like reading modes to enhance data handling.
Conducted a thorough audit of the previous working line to ensure accuracy.
Successfully separated active proof line from preserved historical material to enhance usability.
Achieved zero undefined references and duplicate labels in the active core review.
Improved reader architecture led to better accessibility and maintenance of mathematical interfaces.

Abstract

Quantum Sphaera Companion v3. 34. 0 A Structure-First Mathematical Unfolding Version DOI: 10. 5281/zenodo. 19746821Concept DOI: 10. 5281/zenodo. 19210728 Release summary This v3. 34. 0 release is a readability, infrastructure, and packaging release of the Quantum Sphaera Companion. It promotes the previous local audit-clean/split-bundle working line into the next public Zenodo version after v3. 33. 0. The release restructures the Companion into a split-bundle architecture: Active Core PDF — the governing current proof line, reader architecture, QAM/MML/MMA infrastructure, Sphaera array layer, OP-status material, audit frontmatter, and current release-facing mathematical interface. Historical Witness PDF — the preserved historical Part II / proof-memory material, retained as reconstruction support and archival continuity. Release Bundle ZIP — complete archive containing PDFs, TeX sources, manifest, audit report, release notes, checksums, and release description. The split does not delete or discard historical material. It separates the active proof line from the preserved historical witness to improve human readability while retaining the precision and auditability needed for LLM-assisted reconstruction and verification. Main changes in v3. 34. 0 Public version normalized to v3. 34. 0, following the previous public v3. 33. 0 Zenodo release. Version DOI 10. 5281/zenodo. 19746821 inserted into the version/DOI history. Concept DOI 10. 5281/zenodo. 19210728 retained as the main concept-level DOI. Monolithic working line split into: QuantumSphaeraCompanionᵥ3₃4₀ₐctivecore. pdf QuantumSphaeraCompanionᵥ3₃4₀ₕistoricalwitness. pdf Added and stabilized the QAM/MML/MMA store layer. Added and stabilized the Sphaera array extension. Introduced an internal RAID-like reading via mirror, stripe, and parity/residual modes, while explicitly avoiding technical RAID overclaim. Improved the human/LLM reader architecture in the frontmatter. Preserved explicit non-overclaim language for all open OP branches. Cleaned metadata-symbol hygiene: no version numbers are used as mathematical object indices; the audit-freeze object is written as Ffreezeᵃudit, not with a version number as subscript; QAM/MML/MMA interface version labels remain prose metadata, not mathematical exponents. Status and non-claims This release is conservative. It does not claim: closure of OP 1/4; closure of OP 5 (B) ; Turing-completeness of QAM/MML/MMA; technical RAID reconstruction; vanishing of parity/residual witnesses merely from their existence; theorematic promotion of the historical witness. The QAM/MML/MMA store-array material is an infrastructure layer. It provides a guarded object-store, instruction, execution, snapshot, clone, rollback, scrub, mirror, stripe, and parity/residual vocabulary for future formal development. It does not by itself close any open problem. File roles Recommended Zenodo upload files: QuantumSphaeraCompanionᵥ3₃4₀ₐctivecore. pdfGoverning current proof line and reader-facing active core. QuantumSphaeraCompanionᵥ3₃4₀ₕistoricalwitness. pdfPreserved historical witness / Part II proof memory. QuantumSphaeraCompanionᵥ3₃4₀ᵣeleasebundle. zipComplete release archive containing PDFs, TeX sources, manifest, audit report, checksums, Zenodo description, and GitHub release notes. Supporting files included in the bundle: QuantumSphaeraCompanionᵥ3₃4₀ₐctivecore. tex QuantumSphaeraCompanionᵥ3₃4₀ₕistoricalwitness. tex QuantumSphaeraCompanionᵥ3₃4₀ₘanifest. txt QuantumSphaeraCompanionᵥ3₃4₀ₐuditᵣeport. txt QuantumSphaeraCompanionᵥ3₃4₀checksumsₛha256. txt QuantumSphaeraCompanionᵥ3₃4₀githubᵣeleaseₙotes. md QuantumSphaeraCompanionᵥ3₃4₀ᵦenododescription. md Build and audit summary Active Core: 628 pages 1786 source labels 0 duplicate labels 0 undefined references 0 undefined citations 0 overfull vbox warnings 46 overfull hbox warnings Historical Witness: 248 pages 156 source labels 0 duplicate labels 0 undefined references 0 undefined citations 0 overfull vbox warnings 11 overfull hbox warnings Selected rendered-page overlap review: Active Core pages 1–12, 20–30, and 624–628 reviewed. Historical Witness pages 1–10 and 244–248 reviewed. No visible text-on-text overlap was observed in the reviewed pages. Recommended citation note For the current release, cite the version DOI: 10. 5281/zenodo. 19746821 For the evolving concept record, cite the concept DOI: 10. 5281/zenodo. 19210728

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