Pith Number

pith:MKGOMKKK

pith:2015:MKGOMKKKBK2BCARJUVSZVCRTSQ

not attested not anchored not stored refs pending

Layouts of Expander Graphs

Anastasios Sidiropoulos, David R. Wood, Vida Dujmovi\'c

arxiv:1501.05020 v3 · 2015-01-20 · math.CO · cs.CG · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MKGOMKKKBK2BCARJUVSZVCRTSQ}

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	2026-05-18T01:21:13.574577Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

628ce6294a0ab4110229a5659a8a3394163d0326c430a65f12ee49ba6aa08e97

Aliases

arxiv: 1501.05020 · arxiv_version: 1501.05020v3 · doi: 10.48550/arxiv.1501.05020 · pith_short_12: MKGOMKKKBK2B · pith_short_16: MKGOMKKKBK2BCARJ · pith_short_8: MKGOMKKK

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/MKGOMKKKBK2BCARJUVSZVCRTSQ \
  | 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: 628ce6294a0ab4110229a5659a8a3394163d0326c430a65f12ee49ba6aa08e97

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "61eb24df3d02b1eafea0dcecf4b7ce7d58bc194b3049573a31084aaf8a044514",
    "cross_cats_sorted": [
      "cs.CG",
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-01-20T23:33:56Z",
    "title_canon_sha256": "b52258d9cdbbc6b3a744149518e15e28da58e533237fad884b1d37788523be06"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.05020",
    "kind": "arxiv",
    "version": 3
  }
}