RH Archimedean Kernel Rigidity

Archimedean Kernel Coercivity Lemma (AKCL) framework for a rigidity-based reduction of the Riemann Hypothesis.

AKCL index

• docs/rigidity/rh/INDEX.md

Start Here

• QUICKSTART.md
• docs/SETUP_GUIDE.md
• docs/rigidity/rh/INDEX.md

What this repository is

• a focused AKCL executable artifact surface;
• a status-locked repository for the Archimedean coercivity line;
• a verification-first repository with a canonical truth suite.

Conditional note

This repository is conditional. The Archimedean kernel coercivity program remains conditional on the remaining coercivity-plus-defect control certificate.

Current status

• repository scope: active executable artifact and status surface;
• theorem status: conditional, with the remaining coercivity-plus-defect certificate isolated in-repo;
• canonical truth lock: make akcl-truth.

Core files

• docs/rigidity/rh/archimedean_kernel_coercivity.md
• docs/rigidity/rh/COERCIVITY_GAP_NOTE_2026_04.md
• docs/rigidity/rh/INDEX.md
• src/kernel/compute_kernel.py
• tests/test_energy_nonnegative.py

Quick verification

make akcl-truth

Contribution paths

• onboarding and documentation improvements;
• truth-suite and regression hardening;
• repository-surface clarifications;
• explicitly justified semantic changes only.

See CONTRIBUTING.md.

AKCL truth suite

Run the repository truth suite with:

make akcl-truth
This is the canonical local verification entry point for the AKCL status surface.

## External status

This repository is governed by [`docs/status/EXTERNAL_STATUS_LOCK.md`](docs/status/EXTERNAL_STATUS_LOCK.md). Build success, CI success, dashboards, ledgers, axioms, admits, `sorry`, or placeholder witnesses do not constitute theorem-level closure.