Pith Number

pith:WCBDZVS6

pith:2016:WCBDZVS6DBUSXVJZNTYZJLKCZ3

not attested not anchored not stored refs pending

Clique Minors in Double-critical Graphs

Martin Rolek, Zi-Xia Song

arxiv:1603.06964 v2 · 2016-03-22 · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WCBDZVS6DBUSXVJZNTYZJLKCZ3}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T00:32:51.273203Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b0823cd65e18692bd5396cf194ad42cee446e53dc8209f5b07bc131f72aa4bdf

Aliases

arxiv: 1603.06964 · arxiv_version: 1603.06964v2 · doi: 10.48550/arxiv.1603.06964 · pith_short_12: WCBDZVS6DBUS · pith_short_16: WCBDZVS6DBUSXVJZ · pith_short_8: WCBDZVS6

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/WCBDZVS6DBUSXVJZNTYZJLKCZ3 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: b0823cd65e18692bd5396cf194ad42cee446e53dc8209f5b07bc131f72aa4bdf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5d6bb0e2e63a369efd31f8a0ff8079e2b1b122aee53f8dd808b10943229944e3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-03-22T20:18:01Z",
    "title_canon_sha256": "b7d1fbe49bb4d38767a5b1df7f5c4cc9b8bb0e6df40737257aa9f61cab1d6cc5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.06964",
    "kind": "arxiv",
    "version": 2
  }
}