Pith Number

pith:BZEEQABQ

pith:2024:BZEEQABQNUVPHTKFJS3MFBGYNK

not attested not anchored not stored refs pending

Constructions of minimally $t$-tough regular graphs

Chengli Li, Feng Liu, Kun Cheng

arxiv:2412.12659 v1 · 2024-12-17 · 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{BZEEQABQNUVPHTKFJS3MFBGYNK}

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	2026-07-05T09:50:18.716396Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0e484800306d2af3cd454cb6c284d86a9642273382dcca2965e752489543f1e9

Aliases

arxiv: 2412.12659 · arxiv_version: 2412.12659v1 · doi: 10.48550/arxiv.2412.12659 · pith_short_12: BZEEQABQNUVP · pith_short_16: BZEEQABQNUVPHTKF · pith_short_8: BZEEQABQ

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/BZEEQABQNUVPHTKFJS3MFBGYNK \
  | 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: 0e484800306d2af3cd454cb6c284d86a9642273382dcca2965e752489543f1e9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1bdc36eb517df306a01b958594bc5e4b1be2f37617f6497098281501f6313e27",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2024-12-17T08:27:47Z",
    "title_canon_sha256": "20a5a4c054fdee3c0a1872c19232204002a896206e4649e5bf65c46bc72ec7d3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.12659",
    "kind": "arxiv",
    "version": 1
  }
}