Paper XII: Patching Support, Hecke Packets, and Conditional Automorphic Completion
How does deformation support lead to Hecke occupancy, and which inputs make arithmetic completion possible?
The paper develops algebraic support descent, finite Hecke packet decompositions, and conditional completion criteria. It distinguishes a point being supported from the additional arithmetic data needed for automorphy.
Assumptions and limits. Support results retain their finiteness and Noetherian assumptions where stated. Arithmetic completion requires explicit occupancy, comparison, and classicality inputs; universal companion existence is not proved.
Completion: Reading edition complete · Lean: Inherited / related evidence · Confidence: Historical formal evidence
Before you start
Suggested background: Vectors, matrices, linear maps, kernels and images, and reading a statement with hypotheses. Consult the selected paper for any additional algebra or analysis it uses.
Recorded results and limits: 49 revised claims map to 291 production targets in historical evidence. Original wording remains 41 complete, seven partial, one unchecked. Arithmetic and automorphic inputs remain explicit.
Remaining work: Replay the pinned amended contract and preserve the original-versus-amended concordance. Do not promote missing arithmetic premises.
The background advice is an editorial starting point. The work itself states its prerequisites and hypotheses.
Reading routes · Glossary · Claim links · Download this work
Worked examples for this work
These introductory calculations lead into this work’s subject. The source and evidence links below retain the work’s recorded scope.
Read
- Read online: complete monograph, reading map and revision scope
- Visual guide: all 27 HTML plates and 23 drawings
- Edition README
- Read PDF
- Visual guide (PDF)
Back to work navigation · Worked examples
Written proofs
Read the written arguments in the PDF. The manuscript source remains available below.
Find the statement number or section in the reading files, then read its assumptions and argument. A claim map may cover only part of the written result.
Find this work among other written proofs
Back to work navigation · Worked examples
Lean
Start with the edition guide and the build instructions below. Check the correspondence records to see which written claims the Lean declarations cover. Source links lead to .lean files. PDF guides explain the formalization.
- Historical formal replay instructions (September 2026)
- Current reader-build instructions (no Lean execution)
- Lean guide (PDF)
- Paper XII production modules
- Reused Paper X modules
Find this work among other Lean projects
Back to work navigation · Worked examples
Code
These links include code, examples, checks, or build tools. Read the edition guide for setup instructions and what each command does. All software is beta and work in progress.
Find this work among other code projects
Back to work navigation · Worked examples
Evidence
- Completion, Lean coverage, confidence, and cited evidence
- Source-file receipt (identity and availability)
- All files in this source edition
The evidence records describe the reviews and runs completed for this edition.
Back to work navigation · Worked examples