Pith Number

pith:43PXYYPU

pith:2017:43PXYYPURGP6G4AO7PTISWZBUQ

not attested not anchored not stored refs pending

Unavoidable subprojections in union-closed set systems of infinite breadth

Hung Le Pham, Mahya Ghandehari, Yemon Choi

arxiv:1702.06266 v6 · 2017-02-21 · math.CO · math.FA · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{43PXYYPURGP6G4AO7PTISWZBUQ}

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	2026-07-05T02:26:43.890994Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e6df7c61f4899fe3700efbe6895b21a418dc97fdc0f3244a6b00c68778ccaade

Aliases

arxiv: 1702.06266 · arxiv_version: 1702.06266v6 · doi: 10.48550/arxiv.1702.06266 · pith_short_12: 43PXYYPURGP6 · pith_short_16: 43PXYYPURGP6G4AO · pith_short_8: 43PXYYPU

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/43PXYYPURGP6G4AO7PTISWZBUQ \
  | 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: e6df7c61f4899fe3700efbe6895b21a418dc97fdc0f3244a6b00c68778ccaade

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f51ebf9ed3d8d0a8564f5f0d2dab33dce8610e2729bd4d9acd1e3a7943506c48",
    "cross_cats_sorted": [
      "math.FA",
      "math.GR"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-02-21T05:08:37Z",
    "title_canon_sha256": "b3af804df2fc3fe1ba9abcb03fa6cb8dbcd056160feca8537e0d99fcfa78e3e4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1702.06266",
    "kind": "arxiv",
    "version": 6
  }
}