Pith Number

pith:UY5MXBWJ

pith:2018:UY5MXBWJIGKJCXDOGAFYG3RZ54

not attested not anchored not stored refs pending

Fractional DP-Colorings of Sparse Graphs

Alexandr Kostochka, Anton Bernshteyn, Xuding Zhu

arxiv:1801.07307 v2 · 2018-01-22 · 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{UY5MXBWJIGKJCXDOGAFYG3RZ54}

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	2026-05-17T23:44:32.778552Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a63acb86c94194915c6e300b836e39ef0327bb3e1b7c9739056a7af2442d0bd7

Aliases

arxiv: 1801.07307 · arxiv_version: 1801.07307v2 · doi: 10.48550/arxiv.1801.07307 · pith_short_12: UY5MXBWJIGKJ · pith_short_16: UY5MXBWJIGKJCXDO · pith_short_8: UY5MXBWJ

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/UY5MXBWJIGKJCXDOGAFYG3RZ54 \
  | 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: a63acb86c94194915c6e300b836e39ef0327bb3e1b7c9739056a7af2442d0bd7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d53b34adb41615103e93fd130e39a0b74ae099d2fa044a3aba6258fc46588d8d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-01-22T20:29:48Z",
    "title_canon_sha256": "1cc7fc6e1d34ccbf5c0bc33f3eed2ad2eb19c4407c0857ea4637f0c3857fc893"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1801.07307",
    "kind": "arxiv",
    "version": 2
  }
}