J. Scott Little
Independent Researcher, Columbus, Ohio, USA
Website Edition v1.0 — September 8, 2026
Independent research article · Not peer reviewed
Abstract
Higher gauge fields are normally reconstructed from a complete local descent diagram. This paper asks a narrower and more operational question: when only a declared subdiagram of local fields, overlaps, and coherences is retained, what does that selected information actually determine?
The paper defines the admitted witness reconstruction and its homotopy fiber. That fiber distinguishes three different failures: no globalization, more than one globalization, and gauge symmetry invisible to the retained witnesses. For abelian gerbes, a shifted mapping cone computes the relative defect. For nonabelian crossed modules, a filtered tower of coherent fillers replaces the unavailable additive cone. Four finite calculations show that a single missing higher coherence can obstruct globalization, a sparse dominated star can still reconstruct, transported coefficient action can obstruct even when the Postnikov class vanishes, and barycentric subdivision redistributes rather than removes a defect.
Conditional BRST/BV and Lorentzian Yang–Mills sections specify the additional differential, multiplicative, equation-bundle, and coherent-arrow data required for those interfaces. They do not construct a quantization or prove anomaly cancellation, a Yang–Mills mass gap, or confinement.
Main contribution
The standard machinery is higher-stack descent, homotopy limits, truncated cofinality, differential cocycles, crossed modules, local coefficients, and BV/BRST complexes. The paper's contribution is the relative reconstruction architecture for a declared witness subdiagram, together with explicit finite certificates that compute or falsify reconstruction.
The central object is
Its interpretation is direct:
- an empty fiber means the admitted local data do not globalize;
- multiple connected components mean globalization is ambiguous;
- higher homotopy groups record automorphisms invisible to the witnesses;
- a contractible fiber means the selected data reconstruct that global field uniquely up to coherent equivalence.
Four finite certificates
- Missing tetrahedron. Boundary data can satisfy every retained face condition yet fail the omitted tetrahedral coherence, producing a sharp
obstruction. - Dominated star. A sparse witness system obtained by deleting a dominated patch star can still reconstruct because an explicit chain contraction kills the relative defect.
- Transported action. For the split crossed module
, the Postnikov class vanishes while inversion transport yields the condition . The obstruction is transported action, not an associator. - Subdivision. Barycentric subdivision spreads the original defect over 24 refined tetrahedra, but their alternating product remains the single invariant obstruction.
Scope
This article does not claim invention of descent, homotopy fibers, mapping cones, standard obstruction theory, higher bundles, or BV/BRST. It does not make a global priority claim for every relative reconstruction formulation. The BV/BRST and Yang–Mills results are conditional interface theorems. No quantization, anomaly-cancellation, mass-gap, confinement, or Haag–Kastler realization claim is made.
Suggested citation
J. Scott Little, Admissible Witness Descent for Higher Gauge Fields, Website Edition v1.0, September 8, 2026.
© 2026 J. Scott Little. All rights reserved.
Definitions, results, and open questions in this paper
- Full descent diagram — definition
- Admitted witness system — definition
- Witness reconstruction object — definition
- Reconstruction fiber — definition
- Complete witness system — definition
- Truncated limit-initiality — definition
- Relative defect complex — definition
- Abelian globalization obstruction — definition
- Completion tower and filler space — definition
- Transported-action obstruction — definition
- Witnesswise-complete refinement — definition
- Reconstruction equivalence — definition
- Ward-compatible BV diagram — definition
- Yang–Mills equation-bundle descent — definition
- Truncated witness comparison — standard input applied — theorem
- Exact reconstruction sequence — derived theorem — theorem
- Comparison under witness enlargement — derived theorem — theorem
- Abelian realization bridge — standard input applied — theorem
- Abelian witness defect theorem — derived theorem — theorem
- Sharp tetrahedral defect — finite certificate — theorem
- Dominated-star reconstruction — finite certificate — theorem
- Filtered nonabelian reconstruction — derived theorem — theorem
- Transported action with trivial Postnikov class — finite certificate — theorem
- Refinement stability — derived theorem — theorem
- Aggregate subdivision defect — finite certificate — theorem
- Ward-compatible descent — conditional interface — theorem
- Ward hypercohomology audit — conditional interface — theorem
- Yang–Mills solution reconstruction — conditional interface — theorem
- Witness cardinality is not invariant — boundary theorem — theorem
- Universal finite cores need not exist — boundary theorem — theorem
- Connected fillers do not suffice — boundary theorem — theorem
- Open questions in admissible witness descent — open-problem