Gauge section updates and research notes

18 October 2026 — second expansion

Version 2.0 expands the section from 47 to 70 gauge pages. It adds eighteen advanced technical articles, three interactive explorers, six concrete collaboration briefs on a new research-project page, and a question-led map to the rest of SMONAD. The reading paths, worked exercises, glossary, frequently asked questions, research status and reference connections have been extended accordingly.

The new explorers calculate shared-reference completion, rank-two projector curvature at a fixed spectrum, and a positive coefficient on a nonzero vacuum-punctured low space. Each includes readable default results, equations, presets, input validation, accessible numerical tables and JSON/CSV exports. The original seven explorers remain available, and the singlet explorer now also covers the full two-angle SU(3) diagonal family with a center-element preset.

Six companion gauge posts are now included in the research blog. All twelve source PDFs are preserved unchanged. Page citations identify version 2.0; the RSS feed, sitemap and search metadata include the expanded public page list.

18 October 2026: an expanded gauge research section

This revision expands the existing gauge guides in place and retains their public addresses. The complete section now includes forty-seven pages: the main index, reading paths, thirty-one technical articles, seven interactive explorers, worked exercises, a research-status ledger, collaboration invitations, glossary, FAQ, reference library and this update page.

The source library brings together twelve supplied manuscripts totaling 466 PDF pages. Their copies are unchanged and accompanied by version notes. The original filename and SHA-256 hash for each copy are recorded in the source manifest.

New explanations follow the chain from completed records and predictive sufficiency through carrier reconstruction, exact loop response, protected spectral geometry, matter consistency, regulated vacuum dynamics and the remaining continuum targets. Formula notes keep transport signs, projection identities and the exact Hessian normalization consistent.

Seven calculations to inspect and export

• Transport explorer: local frames, invariant loop traces and distinct interference readouts.
• Singlet explorer: exact finite-model energy, weak-hopping approximation and excitation gap.
• Auxiliary-cycle explorer: charged and neutral spectra, twist dependence and softening.
• Feshbach explorer: exact two-block eigenvalues and the corrected vacuum-window cancellation.
• Symmetry explorer: retained tensors, stabilizer dimensions and global quotient descent.
• Anomaly explorer: one-generation charge sums and consistency checks under changed inputs.
• Projection explorer: finite-loop survival, geometric phase and convergence.

The default examples remain readable without JavaScript. Interactive downloads include the chosen model inputs and units, making it possible to reproduce a reported value.

Companion research-blog articles

• Why gauge transport remembers a history — the path from future interference to a sufficient record.
• From an exact loop energy to a physical coupling — what the solved model fixes and what matching must add.
• Why an auxiliary gap is not yet a physical mass gap — a calculation-led account of the vacuum and uniformity questions.
• Research questions for a gauge-theory collaboration — focused invitations for physics, mathematics and philosophy.

These posts offer shorter entrances to the technical material. Their links lead back to the derivations and original sources.

Read the source sequence by its purpose

The early three- and four-page sketches introduce the proposed temporal origin of gauge structure. Later spectral manuscripts add protected eigenspaces and a proposed geometric framework. The sevenfold and temporal-completion manuscripts expose the carrier, determinant and dynamics assumptions, while the focused completed-record paper sharpens the operational statements and reference-resource limits.

The lattice sequence similarly separates exact fixed-regulator constructions from the vacuum-aware reduction and the complete continuum programme. The supplied orientation manuscript is an expanded skeleton with placeholders; its role is documented accordingly. The reference library gives the exact version note for every file. A later focused theorem should be read at its stated scope rather than used to retroactively validate every earlier claim.

Follow new work and report corrections

Subscribe to the gauge RSS feed for the section’s current article revisions. The research-blog feed follows blog posts, and the email updates page provides the site’s subscription route. The section sitemap lists canonical gauge pages for discovery.

For a correction, identify the article, the passage or equation, and the source version. Explain the mathematical change and which conclusion depends on it. For a new contribution, see the collaboration page. Current contact and social-account details are maintained on the main contact page.