Pith Number

pith:TSWYJZRJ

pith:2026:TSWYJZRJKHQFLSUC6ZG5KPI44X

not attested not anchored not stored refs pending

Spectral Sidorenko inequalities and edge-spectral supersaturation

Hong Liu, Shengtong Zhang, Wilson Lin, Yongtao Li

arxiv:2605.26614 v1 · 2026-05-26 · 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{TSWYJZRJKHQFLSUC6ZG5KPI44X}

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	2026-05-27T01:06:02.223873Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9cad84e62951e055ca82f64dd53d1ce5f27b318f56a085d9c41e7010aa23ee3f

Aliases

arxiv: 2605.26614 · arxiv_version: 2605.26614v1 · doi: 10.48550/arxiv.2605.26614 · pith_short_12: TSWYJZRJKHQF · pith_short_16: TSWYJZRJKHQFLSUC · pith_short_8: TSWYJZRJ

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/TSWYJZRJKHQFLSUC6ZG5KPI44X \
  | 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: 9cad84e62951e055ca82f64dd53d1ce5f27b318f56a085d9c41e7010aa23ee3f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4e061d46365ba3bfd691bab8b4d35ad8e6fd9f748573a2d988db3943ba925753",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-26T06:51:18Z",
    "title_canon_sha256": "6da7e1b0751538f6ae7b1860051a121d7b13d1b6511d4a747b69c66cd5ccd951"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.26614",
    "kind": "arxiv",
    "version": 1
  }
}