Pith Number

pith:4JW3YGF7

pith:2011:4JW3YGF7YFLGJGN2ZRIJRINDCB

not attested not anchored not stored refs pending

Tur\`an numbers of Multiple Paths and Equibipartite Trees

Nathan Kettle, Neal Bushaw

arxiv:1106.5904 v2 · 2011-06-29 · 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{4JW3YGF7YFLGJGN2ZRIJRINDCB}

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	2026-05-18T03:57:26.897376Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e26dbc18bfc1566499bacc5098a1a31073506141a65946c4ed2efec8db056176

Aliases

arxiv: 1106.5904 · arxiv_version: 1106.5904v2 · doi: 10.48550/arxiv.1106.5904 · pith_short_12: 4JW3YGF7YFLG · pith_short_16: 4JW3YGF7YFLGJGN2 · pith_short_8: 4JW3YGF7

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/4JW3YGF7YFLGJGN2ZRIJRINDCB \
  | 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: e26dbc18bfc1566499bacc5098a1a31073506141a65946c4ed2efec8db056176

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "586ae27fc01ffd495c10441ea88486d51086263445e59ef7b6d7d4e346fbe72a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-06-29T10:57:56Z",
    "title_canon_sha256": "78b20b3602863ca2a3f771cf513e33f165e5a1df5d2e8c394378092def9c6e9c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.5904",
    "kind": "arxiv",
    "version": 2
  }
}