PCVDM XiGraph

Assembly-first graph engine built around the existing xi_step kernel.

Built rule

xi_step remains the atomic Phase Calculus loop. Every active node is an XiState and the native hot path runs:

for each node:
    xi_step(node.state)
    if carry_event:
        try 2D edge carry resolution first
        if unresolved:
            trigger 3D node carry / node birth

This implements the hierarchy:

1D carry: bit-level carry inside xi_step
2D carry: monodromy edge creation / reinforcement
3D carry: new debt-hosting node birth when edge resolution fails

Build

make all
make test
make run

Default run artifacts are written to run_artifacts/.

Main files

asm/xi_full_engine_kernel.S        original Xi loop, reused unchanged
asm/xi_graph_tick.S                assembly graph hot loop; calls xi_step per node
src/domain/xi_state.h              XiState layout matching the assembly offsets
src/domain/xigraph_types.h         graph/domain data types
src/application/xigraph_engine.c   edge-first carry hierarchy and node birth logic
src/presentation/xigraph_runner.c  CLI runner
tests/application/test_xigraph.c   acceptance tests
verification/xigraph_sympy_audit.py
verification/XiGraphCarryHierarchy.lean
notebooks/xigraph_verification.ipynb

Runner

build/xigraph_runner [initial_nodes=4] [ticks=512] [node_capacity=128] [edge_capacity=2048] [timeline_csv] [summary_json] [snapshot_csv]

Examples:

build/xigraph_runner 4 512 128 2048 run_artifacts/xigraph_timeline.csv run_artifacts/xigraph_summary.json run_artifacts/xigraph_node_snapshot.csv
build/xigraph_runner 1 256 64 512 run_artifacts/xigraph_birth_timeline.csv run_artifacts/xigraph_birth_summary.json run_artifacts/xigraph_birth_node_snapshot.csv

Verification status

• C/ASM build: compiled with -O3 -Wall -Wextra -Werror.
• C tests: passing.
• SymPy audit: passing and emits verification/xigraph_sympy_audit_report.json.
• Jupyter notebook: executed.
• Lean companion file: included; not executed in this container because Lean is not installed.