Pith Number

pith:FRRJD6YR

pith:2026:FRRJD6YR7NKFV3UQD5C7OW64NT

not attested not anchored not stored refs pending

On the Packing Coloring Gap of Graphs

Batoul Tarhini, Didem G\"oz\"upek

arxiv:2605.16680 v1 · 2026-05-15 · 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{FRRJD6YR7NKFV3UQD5C7OW64NT}

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	2026-05-20T00:02:36.249088Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2c6291fb11fb545aee901f45f75bdc6cf54ee106c1b4c99d70063279b4ce8928

Aliases

arxiv: 2605.16680 · arxiv_version: 2605.16680v1 · doi: 10.48550/arxiv.2605.16680 · pith_short_12: FRRJD6YR7NKF · pith_short_16: FRRJD6YR7NKFV3UQ · pith_short_8: FRRJD6YR

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/FRRJD6YR7NKFV3UQD5C7OW64NT \
  | 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: 2c6291fb11fb545aee901f45f75bdc6cf54ee106c1b4c99d70063279b4ce8928

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4aa0e9252beba66a99d122f0de19bd02452fa8fbd48f3055e8349eb570815221",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-15T22:34:39Z",
    "title_canon_sha256": "66608c97382599d8d5267484d2422d603a09924c99f4496b5a814600a8c3641c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16680",
    "kind": "arxiv",
    "version": 1
  }
}