Pith Number

pith:FTWRRKAM

pith:2021:FTWRRKAMMTUBY2RBSFMMMTYPZM

not attested not anchored not stored refs pending

Best possible bounds on the number of distinct differences in intersecting families

Andrey Kupavskii, Peter Frankl, Sergei Kiselev

arxiv:2106.05355 v2 · 2021-06-09 · math.CO · cs.DM

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FTWRRKAMMTUBY2RBSFMMMTYPZM}

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	2026-07-05T04:47:38.890370Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2ced18a80c64e81c6a219158c64f0fcb126e66be2cbf35483ff920fea283a5d0

Aliases

arxiv: 2106.05355 · arxiv_version: 2106.05355v2 · doi: 10.48550/arxiv.2106.05355 · pith_short_12: FTWRRKAMMTUB · pith_short_16: FTWRRKAMMTUBY2RB · pith_short_8: FTWRRKAM

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/FTWRRKAMMTUBY2RBSFMMMTYPZM \
  | 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: 2ced18a80c64e81c6a219158c64f0fcb126e66be2cbf35483ff920fea283a5d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1f0aba5c4bd540a4212798c5b0fc650012f39033a4273f9ddc66a06bac0f5740",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2021-06-09T19:42:11Z",
    "title_canon_sha256": "2ceb42d2a65879229b929c0b8480c05bf89a6ec67bfdc3d698486df4fb30d995"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2106.05355",
    "kind": "arxiv",
    "version": 2
  }
}