Data dictionary

The census files in results/ are JSON or gzipped JSON files. The canonical SHA-256 hashes for those files live in the repository README.md, and CI checks the census files against that table.

Survivor JSON schema

Each per-order file records metadata for one census order and a list of survivor graphs. The exact audit metadata may vary by file, but survivor entries are intended to be self-contained enough to rebuild the graph.

Top-level fields:

Field	Meaning
order	Number of vertices n.
delta_max	Maximum degree, equal to 3 for this census.
min_degree_bound	Minimum-degree bound used by geng (2).
generated_biconnected	Count of 2-connected candidates generated by geng.
pruned_by_filters	Count removed by the F1/F2 pruning filters.
class1_or_noncritical	Count removed as class 1 or non-critical.
total_critical	Count of edge-chromatic critical candidates before the overfull test.
overfull_count	Count removed as trivial (containing a 3-overfull subgraph).
survivor_count	Number of nontrivial survivors in the file.
survivors	Array of survivor graph records.
runtime_seconds	Wall-clock generation time for the order.

Survivor-record fields:

Field	Meaning
status	Record status, "survivor" for nontrivial survivors.
graph6	Compact graph6 encoding of the unlabeled graph.
edges	Edge list using integer vertex labels; the most direct field for rebuilding the graph.
degree_sequence	Sorted (descending) multiset of vertex degrees.
delta_max	Maximum degree of the survivor (3).
delta_min	Minimum degree of the survivor (2).
alpha	Independence number.
alpha_ratio	Independence ratio alpha / n.
overfull_subsets	Witnessing overfull subsets (empty for nontrivial survivors).

graph6 encoding

graph6 is a compact ASCII format for simple undirected graphs, widely used by nauty and NetworkX. It is convenient for deduplicating, comparing, and transferring graphs. When both edges and graph6 are present, the edge list is the most direct reconstruction path for scripts, while graph6 is useful for interoperability with graph-census tools.

Loading a survivor with Python

import json, networkx as nx
data = json.load(open("results/order_13_delta_3.json"))
record = data["survivors"][0]
G = nx.Graph(record["edges"])

For .json.gz files, open the file with Python's gzip.open(..., "rt") before passing it to json.load.

Hashes and CI

Do not copy SHA-256 values from the README into downstream documents. The README's census-file table is the single source of truth, and continuous integration checks those hashes on every push.