Geometric Langlands via Hecke-Eigensheaf Persistence

Canonical Lane (defined term): the manifold-constrained local-to-global correspondence super-architecture (GEO1-GEO8)

Canonical Lane super-repo for a flagship umbrella problem in representation theory and algebraic geometry: proving persistence of admissible Hecke eigensheaves and spectral correspondences through a multi-lane geometric-Langlands architecture.

Main Manuscript

• paper/GEOMETRIC_LANGLANDS_PREPRINT.md
• paper/CANONICAL_ROUTING_INDEX.md

Super-Repo Role

This repository is not one isolated geometric Langlands instance. It coordinates an admissible correspondence lattice whose native routed families are:

1. geometric Satake and spherical Hecke transport,
2. Hecke eigensheaf generation,
3. spectral-side coherence on local systems,
4. categorical duality and sheaf-theoretic transfer,
5. local-global stitching across the declared stack-level packets.

The runtime surface certifies closure of the declared super-lane, not just one local geometric example.

Structure

• paper/

  • GEOMETRIC_LANGLANDS_PREPRINT.md
  • CANONICAL_ROUTING_INDEX.md
  • EXTRACTION_SPEC.md

• notes/

  • EG1_public.md
  • EG2_public.md
  • EG3_public.md
  • EG4_public.md
  • IDENTIFICATION_BRIDGE.md

• repro/

  • REPRO_PACK.md
  • THIRD_PARTY_RERUN_PROTOCOL.md
  • run_repro.sh
  • repro_manifest.json
  • certificate_baseline.json

• scripts/

  • geo_closure_guard.py
  • extract_constants.py
  • promote_constants.py
  • update_manifest.py
  • release_gate.py
  • README.md

• artifacts/

  • constants_extraction_inputs.json
  • constants_extracted.json
  • constants_registry.json
  • stitch_constants.json
  • promotion_report.json

Local Reproducibility Command

bash repro/run_repro.sh

This writes repro/certificate_runtime.json.

How To Read This Professionally

1. Super-lane theorem chain first: read paper/GEOMETRIC_LANGLANDS_PREPRINT.md.
2. Correspondence-lattice routing second: audit paper/CANONICAL_ROUTING_INDEX.md and the note layer.
3. Constants provenance third: audit paper/EXTRACTION_SPEC.md, artifacts/constants_extraction_inputs.json, artifacts/constants_extracted.json, and artifacts/promotion_report.json.
4. Pipeline fourth: run bash repro/run_repro.sh to audit hashes, provenance, and gates; it is reproducibility infrastructure, not theorem generation.

Release modes:

• normalized: status=normalized_placeholder allowed when explicitly labeled.
• fully_extracted: requires status=derived_numeric for all required constants and stitch keys.

Current GEO runner policy:

• repro/run_repro.sh extracts, promotes, runs scripts/geo_closure_guard.py, updates repro/repro_manifest.json, and enforces fully_extracted release-gate mode.

Routing Rule (inclusion discipline)

Every claim-bearing item must be routed through all three layers:

1. main preprint section/appendix,
2. mirror note under notes/,
3. artifact key consumed by scripts/geo_closure_guard.py.

Routing map: paper/CANONICAL_ROUTING_INDEX.md

Citation

• Metadata: CITATION.cff
• Manuscript target: paper/GEOMETRIC_LANGLANDS_PREPRINT.md

Authorship

• Program author: HautevilleHouse
• Canonical attribution source: CITATION.cff