Pith Number

pith:U3FGTW3U

pith:2026:U3FGTW3UXTJCSPBXSM3OQZGJ6J

not attested not anchored not stored refs pending

The sharp diagonal spectral correlation inequality on the discrete cube

Fan Chang, Hong Liu, Miao Liu

arxiv:2606.32024 v1 · 2026-06-30 · math.CO · math.FA · 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{U3FGTW3UXTJCSPBXSM3OQZGJ6J}

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	2026-07-01T02:17:47.576682Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a6ca69db74bcd2293c379336e864c9f26acaf4a4e212f6d9c9f4351119c316cd

Aliases

arxiv: 2606.32024 · arxiv_version: 2606.32024v1 · doi: 10.48550/arxiv.2606.32024 · pith_short_12: U3FGTW3UXTJC · pith_short_16: U3FGTW3UXTJCSPBX · pith_short_8: U3FGTW3U

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/U3FGTW3UXTJCSPBXSM3OQZGJ6J \
  | 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: a6ca69db74bcd2293c379336e864c9f26acaf4a4e212f6d9c9f4351119c316cd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f9f3ce39fca10dc4923fc36af6deb4eea469e9f9cc8a75e0d6d983ca5e51424b",
    "cross_cats_sorted": [
      "math.FA",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-30T17:52:59Z",
    "title_canon_sha256": "38007b92bc50339f9b7522cce85e3d52036ae48b8caf2151501008dc14e90e19"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.32024",
    "kind": "arxiv",
    "version": 1
  }
}