Pith Number

pith:5QYWQEXP

pith:2019:5QYWQEXP6AIEUS6ZTNGHQ5SX6R

not attested not anchored not stored refs pending

Vector Colorings of Random, Ramanujan, and Large-Girth Irregular Graphs

Jess Banks, Luca Trevisan

arxiv:1907.02539 v1 · 2019-07-04 · cs.CC · cs.SI · math.CO · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5QYWQEXP6AIEUS6ZTNGHQ5SX6R}

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	2026-05-17T23:41:24.078002Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ec316812eff0104a4bd99b4c787657f459fe1dd15abb2e92af07c1cb013a5218

Aliases

arxiv: 1907.02539 · arxiv_version: 1907.02539v1 · doi: 10.48550/arxiv.1907.02539 · pith_short_12: 5QYWQEXP6AIE · pith_short_16: 5QYWQEXP6AIEUS6Z · pith_short_8: 5QYWQEXP

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/5QYWQEXP6AIEUS6ZTNGHQ5SX6R \
  | 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: ec316812eff0104a4bd99b4c787657f459fe1dd15abb2e92af07c1cb013a5218

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "44769cbf3c057be8f99ed7a4fc830529776b9f670ceb3375a281b283c38e6cc1",
    "cross_cats_sorted": [
      "cs.SI",
      "math.CO",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2019-07-04T18:00:04Z",
    "title_canon_sha256": "8da98e61ef69e0a7726a55fc1b1f838a20f9faaf285191637127ca52f76bf2df"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.02539",
    "kind": "arxiv",
    "version": 1
  }
}