Pith Number

pith:BYV7F3J7

pith:2020:BYV7F3J7MHQAFBXKZXIAF5VEAV

not attested not anchored not stored refs pending

Kim--Vu's sandwich conjecture is true for $d \gg \log^4 n$

Brendan McKay, Mikhail Isaev, Pu Gao

arxiv:2011.09449 v5 · 2020-11-18 · 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{BYV7F3J7MHQAFBXKZXIAF5VEAV}

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.

Cited by

1 paper in Pith

Diameter Thresholds of Random Cayley Graphs

Receipt and verification

First computed	2026-07-05T11:02:57.439507Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0e2bf2ed3f61e00286eacdd002f6a4057b86a100260c87c4cd5c06ed443c9867

Aliases

arxiv: 2011.09449 · arxiv_version: 2011.09449v5 · doi: 10.48550/arxiv.2011.09449 · pith_short_12: BYV7F3J7MHQA · pith_short_16: BYV7F3J7MHQAFBXK · pith_short_8: BYV7F3J7

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/BYV7F3J7MHQAFBXKZXIAF5VEAV \
  | 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: 0e2bf2ed3f61e00286eacdd002f6a4057b86a100260c87c4cd5c06ed443c9867

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "49e6616c671abf91cfa84bb9d1fa8486fbe6df7826a1c699b82a922bacf3f177",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2020-11-18T18:26:00Z",
    "title_canon_sha256": "20c83f3b34e40455966e27f9fc066ddaf7b09f3e9d06efdc428950dc4764ce94"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2011.09449",
    "kind": "arxiv",
    "version": 5
  }
}