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jasonlvolk/sigma-enron-demo

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App README

SIGMA: We Contained O(n^3)

The sheaf Laplacian on the Enron email network is 170,472 x 170,472. A dense eigensolve takes 14 hours. SIGMA decomposes it so no computation ever sees more than 500 vertices.

21 seconds. 641 MB. No GPU.

Part of the stack

SIGMA computes structural verification results. SATYA packages verification outcomes as Signed Verification Receipts.

—Try the SVR verifier: jasonlvolk/satya-svr-verifier
—Receipt conformance fixtures: jasonlvolk/svr-receipts-examples

Paper

This demo is part of the public evidence stack for:

Incremental Sheaf Cohomology on Cellular Complexes: O(1)-in-n Lazy Edit Processing under Bounded Local Geometry. arXiv:2606.04227 (https://arxiv.org/abs/2606.04227).

Enron Email Network Results (April 15, 2026)

—36,692 accounts, 183,831 relationships, power-law topology
—21 seconds (i9-13900H, 64GB RAM, no GPU)
—0.37 ms/vertex, 3,760 cells, nerve max dim 2
—4 seeds validated, identical partition structure
—Hub vertices at degree 1,141 (degree CV = 2.609)

O(n^3) Containment

The O(n^3) eigensolve is factored into n/500 independent bounded subproblems. Each takes 0.37 ms. Total cost: O(n).

The cube didn't disappear. It got imprisoned inside a constant.

Scale Validation

Vertices	Topology	Cells	ms/vertex	Peak RAM
21,309	Power-law (Enron)	3,760	0.37	641 MB
50,000	Geometric	1,180	0.52	1.7 GB
100,000	Power-law (BA)	7,028	0.60	1.3 GB
100,000	Geometric	2,552	0.51	3.2 GB
250,000	Geometric	5,987	0.94	7.5 GB
1,000,000	Geometric	23,123	0.85	28.3 GB

47x growth in vertices. Cost per entity: flat. Zero crashes at all scales.

Decomposition Pipeline

1.Hub extraction (degree > mean + 2*std)
2.Hub neighbor freeze (70.3% frozen)
3.Connected component detection (1,209 after hub removal)
4.BFS balanced partitioning (giant component -> 2,534 chunks)
5.K-doubling cap (dim > 1,600 -> immediate fallback)
6.Clean split (no boundary duplication, nerve dim capped at 2)