Gap-Free Rigidity + Robust Certificates (v19, chaos-facing hardening)

Folder layout
- rigidity_gapfree_global/
  - rigidity_gapfree_global_universality.tex  (main LaTeX entry point)
  - *.tex  (section inputs)
  - *.json / *_schema.json  (machine-readable artifact examples + JSON Schemas)

How to compile the PDF
- From inside rigidity_gapfree_global/:
  - latexmk -pdf rigidity_gapfree_global_universality.tex
    (or run pdflatex twice)
  - pdflatex -interaction=nonstopmode -halt-on-error rigidity_gapfree_global_universality.tex
  - pdflatex -interaction=nonstopmode -halt-on-error rigidity_gapfree_global_universality.tex

Artifact schemas (optional validation)
- All schemas are standard JSON Schema (draft 2020-12). Example validator usage:
  - python -m jsonschema -i global_universality_report_ThetaCan_certified.json global_universality_report_schema.json
  - python -m jsonschema -i global_universality_certificate_ThetaCan.json global_universality_certificate_schema.json
  - python -m jsonschema -i robust_certificate_example.json robust_certificate_schema.json
  - python -m jsonschema -i imprimitive_core_report_example.json imprimitive_core_report_schema.json
  - python -m jsonschema -i obstruction_witness_example.json obstruction_witness_schema.json
  - python -m jsonschema -i rate_pack_example.json rate_pack_schema.json
  - python -m jsonschema -i mather_sofic_model_example.json mather_sofic_model_schema.json
  - python -m jsonschema -i frontier_report_example.json frontier_report_schema.json
  - python -m jsonschema -i frontier_atlas_report_example.json frontier_atlas_report_schema.json
  - python -m jsonschema -i og2_inconsistency_witness_example.json og2_inconsistency_witness_schema.json
  - python -m jsonschema -i og3_cut_witness_example.json og3_cut_witness_schema.json
  - python -m jsonschema -i og3_nonreachability_certificate_example.json og3_nonreachability_certificate_schema.json

- Convenience validator script:
  - python tools/validate_artifacts.py

Core machine artifacts included
- Robust certificate schema + example
  - robust_certificate_schema.json
  - robust_certificate_example.json
- Imprimitive tight-core report schema + example (OG1 descriptor option)
  - imprimitive_core_report_schema.json
  - imprimitive_core_report_example.json
- Obstruction witness schema + example
  - obstruction_witness_schema.json
  - obstruction_witness_example.json
- OG2/OG3 specialized witness schemas + examples
  - og2_inconsistency_witness_schema.json
  - og2_inconsistency_witness_example.json
  - og3_cut_witness_schema.json
  - og3_cut_witness_example.json
  - og3_nonreachability_certificate_schema.json
  - og3_nonreachability_certificate_example.json
- Rate pack schema + example
  - rate_pack_schema.json
  - rate_pack_example.json
- Mather sofic extremal model schema + example
  - mather_sofic_model_schema.json
  - mather_sofic_model_example.json
- Frontier report / frontier atlas report schemas + examples
  - frontier_report_schema.json
  - frontier_report_example.json
  - frontier_atlas_report_schema.json
  - frontier_atlas_report_example.json
- Global universality report/certificate schemas + examples
  - global_universality_report_schema.json
  - global_universality_certificate_schema.json
  - global_universality_report_ThetaCan_certified.json
  - global_universality_report_ThetaCan_atlas.json
  - global_universality_certificate_ThetaCan.json

Chaos-theory bridge components integrated in the PDF
- chaos_vocabulary_bridge.tex
- related_work_chaos.tex
- open_problem_resolution_map.tex
- statistical_stability_analogue.tex
- rough_sensitive_dependence_analogue.tex
- algorithmic_complexity.tex
- switching_control_wedge.tex
- referee_map_and_checklist.tex
- minimality_sharpness_notes.tex (includes a minimizer-level OG4 sharpness proposition)


New in this pass
- Effective Mather/sofic extremal itinerary model + export schema: rigidity_gapfree_global/effective_mather_sofic.tex and rigidity_gapfree_global/mather_sofic_model_schema.json
- Added 0avoidance shift definition and RC1<->sofic nonemptiness proposition: rigidity_gapfree_global/syndetic_recurrence_tools.tex
- Pipeline correctness theorem (termination + soundness): rigidity_gapfree_global/pipeline_correctness.tex
- Doeblin-word search correctness lemma: added to rigidity_gapfree_global/doeblin_word_search.tex
- Conditional completeness: uniform contraction on the tight subshift forces a Doeblin block and excludes avoidance cycles: rigidity_gapfree_global/pipeline_conditional_completeness.tex
- Minimizer-level converse and closure: shift-uniform contraction forces a finite recurrence modulus (RC^\star_{\min}), and RC^\star_{\min} yields shift-uniform contraction with explicit palette-extracted constants: rigidity_gapfree_global/minimizer_level_recurrence_converse.tex
- Flagship theorem bullet + referee map updated to include the minimizer-level frontier sharpening explicitly: rigidity_gapfree_global/flagship_one_shot_theorem.tex and rigidity_gapfree_global/referee_map_and_checklist.tex

New in this pass (frontier report objects)
- Integrated the FrontierReport / FrontierAtlasReport export objects into the pipeline wording and audit checklist.
- Added schemas + examples + validator coverage:
  - rigidity_gapfree_global/frontier_report_schema.json, rigidity_gapfree_global/frontier_report_example.json
  - rigidity_gapfree_global/frontier_atlas_report_schema.json, rigidity_gapfree_global/frontier_atlas_report_example.json
