Pith Number

pith:KQPRTENO

pith:2020:KQPRTENOHK3LZIUPNX5PKNDGTW

not attested not anchored not stored refs pending

Sandwiching biregular random graphs

Andrzej Ruci\'nski, Christian Reiher, Matas \v{S}ileikis, Tereza Klimo\v{s}ov\'a

arxiv:2010.15751 v3 · 2020-10-29 · math.CO · 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{KQPRTENOHK3LZIUPNX5PKNDGTW}

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	2026-07-05T03:19:02.254842Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

541f1991ae3ab6bca28f6dfaf534669dba4affe288b9be3f5c054580973aa73a

Aliases

arxiv: 2010.15751 · arxiv_version: 2010.15751v3 · doi: 10.48550/arxiv.2010.15751 · pith_short_12: KQPRTENOHK3L · pith_short_16: KQPRTENOHK3LZIUP · pith_short_8: KQPRTENO

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/KQPRTENOHK3LZIUPNX5PKNDGTW \
  | 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: 541f1991ae3ab6bca28f6dfaf534669dba4affe288b9be3f5c054580973aa73a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b4e4f86c8238206f0fe2389053185e4f0bace28ccaf2af0f7324366110d02b7d",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2020-10-29T16:58:24Z",
    "title_canon_sha256": "1f9ada193d64f1d8bd8ffc66607cfe1e0aef41f01731b9c00a492c0b7c2bcc96"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2010.15751",
    "kind": "arxiv",
    "version": 3
  }
}