Pith Number

pith:33MOTMUF

pith:2020:33MOTMUFAKAOKWMYWXBS5QG2RB

not attested not anchored not stored refs pending

Analogues of Katona's and Milner's Theorems for two families

Peter Frankl, Willie Wong H.W

arxiv:2006.12602 v2 · 2020-06-22 · 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{33MOTMUFAKAOKWMYWXBS5QG2RB}

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	2026-07-05T02:28:49.876680Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ded8e9b2850280e55998b5c32ec0da884f9cf5d9bc8ebd6a51aa5aab8006b79c

Aliases

arxiv: 2006.12602 · arxiv_version: 2006.12602v2 · doi: 10.48550/arxiv.2006.12602 · pith_short_12: 33MOTMUFAKAO · pith_short_16: 33MOTMUFAKAOKWMY · pith_short_8: 33MOTMUF

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/33MOTMUFAKAOKWMYWXBS5QG2RB \
  | 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: ded8e9b2850280e55998b5c32ec0da884f9cf5d9bc8ebd6a51aa5aab8006b79c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4c305f36fdda40a1aca39914d890a03f6a7dfa99432ccfa0ae2531a04deddf00",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2020-06-22T20:33:51Z",
    "title_canon_sha256": "8dc43ceb0dc7045bbb149f5e4b1264d27b25b12ced6f7ae1c30d0646bc473784"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2006.12602",
    "kind": "arxiv",
    "version": 2
  }
}