Pith Number

pith:6SRJ22YY

pith:2021:6SRJ22YYMBAQDBKTOY6LY6JYUT

not attested not anchored not stored refs pending

A short proof of Kneser's theorem via transversals

Luis Montejano

arxiv:2109.06989 v1 · 2021-09-14 · 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{6SRJ22YYMBAQDBKTOY6LY6JYUT}

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	2026-07-05T03:14:37.840576Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f4a29d6b186041018553763cbc7938a4c4c9c8c5550e98d53ea32b8554214aed

Aliases

arxiv: 2109.06989 · arxiv_version: 2109.06989v1 · doi: 10.48550/arxiv.2109.06989 · pith_short_12: 6SRJ22YYMBAQ · pith_short_16: 6SRJ22YYMBAQDBKT · pith_short_8: 6SRJ22YY

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/6SRJ22YYMBAQDBKTOY6LY6JYUT \
  | 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: f4a29d6b186041018553763cbc7938a4c4c9c8c5550e98d53ea32b8554214aed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bbce6accd3ffbc1cfdcbf6246db8c8e21cb8780f3e317ceb6c9985e3893f313b",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2021-09-14T22:09:29Z",
    "title_canon_sha256": "5943afb0944f84615ae83ee083c34fdcbd3af4b3de43525038618c6387d39226"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2109.06989",
    "kind": "arxiv",
    "version": 1
  }
}