Pith Number

pith:ZH3DAHUJ

pith:2021:ZH3DAHUJZTKDTTI2L352F77JXH

not attested not anchored not stored refs pending

A new lower bound on the pebbling number of the grid

Jan Petr, Julien Portier, Szymon Stolarczyk

arxiv:2111.13173 v1 · 2021-11-25 · 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{ZH3DAHUJZTKDTTI2L352F77JXH}

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	2026-07-05T05:52:06.762893Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c9f6301e89ccd439cd1a5efba2ffe9b9d35ffcd78410fb7cfa2786ff617eff19

Aliases

arxiv: 2111.13173 · arxiv_version: 2111.13173v1 · doi: 10.48550/arxiv.2111.13173 · pith_short_12: ZH3DAHUJZTKD · pith_short_16: ZH3DAHUJZTKDTTI2 · pith_short_8: ZH3DAHUJ

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/ZH3DAHUJZTKDTTI2L352F77JXH \
  | 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: c9f6301e89ccd439cd1a5efba2ffe9b9d35ffcd78410fb7cfa2786ff617eff19

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b2284637faad5e5d9abd382ff943f37c634846615900714702d605c84aeec7a9",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2021-11-25T17:09:28Z",
    "title_canon_sha256": "994d617e167a0d8e5bbc267fae79a95af9e1deb01cc0cea9d49669781d6f79c3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2111.13173",
    "kind": "arxiv",
    "version": 1
  }
}