Pith Number

pith:QQVIHZUG

pith:2014:QQVIHZUGOPPSMVP2NSQBYE4QJX

not attested not anchored not stored refs pending

Mixing properties and the chromatic number of Ramanujan complexes

Alexander Lubotzky, Konstantin Golubev, Shai Evra

arxiv:1407.7700 v2 · 2014-07-29 · math.CO · math.GR · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QQVIHZUGOPPSMVP2NSQBYE4QJX}

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	2026-05-17T23:44:33.327686Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

842a83e68673df2655fa6ca01c13904df0ae4b64794b0a0fa9c054ca27643329

Aliases

arxiv: 1407.7700 · arxiv_version: 1407.7700v2 · doi: 10.48550/arxiv.1407.7700 · pith_short_12: QQVIHZUGOPPS · pith_short_16: QQVIHZUGOPPSMVP2 · pith_short_8: QQVIHZUG

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/QQVIHZUGOPPSMVP2NSQBYE4QJX \
  | 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: 842a83e68673df2655fa6ca01c13904df0ae4b64794b0a0fa9c054ca27643329

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "70e5d110230a79c8d28481b1d24afed69e862904367ae91c1a9c6177c425b01a",
    "cross_cats_sorted": [
      "math.GR",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-07-29T11:42:50Z",
    "title_canon_sha256": "2b76bca187969604e51c81fa11959ae03a2ff6a66b9cd751439fc09083be9620"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1407.7700",
    "kind": "arxiv",
    "version": 2
  }
}