Pith Number

pith:F7OFJOTM

pith:2026:F7OFJOTMSKBSMAE63BFBK56GJY

not attested not anchored not stored refs pending

On the Smallest Eigenvalues and Quantum Chromatic Numbers of Hamming Graphs and Generalizations

Jack H. Koolen, Xiande Zhang, Yu Ning

arxiv:2605.28402 v1 · 2026-05-27 · 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{F7OFJOTMSKBSMAE63BFBK56GJY}

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	2026-05-28T01:05:17.177837Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2fdc54ba6c928326009ed84a1577c64e0e2dbf13e8f7fe5baf9339b95fe0abf5

Aliases

arxiv: 2605.28402 · arxiv_version: 2605.28402v1 · doi: 10.48550/arxiv.2605.28402 · pith_short_12: F7OFJOTMSKBS · pith_short_16: F7OFJOTMSKBSMAE6 · pith_short_8: F7OFJOTM

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/F7OFJOTMSKBSMAE63BFBK56GJY \
  | 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: 2fdc54ba6c928326009ed84a1577c64e0e2dbf13e8f7fe5baf9339b95fe0abf5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "882862baf66d5d85f17e0b80dd79b1f1178fcd49c074b802dd32a88004bc7dfc",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-27T12:38:30Z",
    "title_canon_sha256": "a8d7ebfd99ac6916d5b75a04252b5e5fd5ef62b5da2da9d8225319be05984d40"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.28402",
    "kind": "arxiv",
    "version": 1
  }
}