Pith Number

pith:X5SIMP5X

pith:2011:X5SIMP5XTRR5AWES2Q5B27ZDX2

not attested not anchored not stored refs pending

Tur\'an numbers for $K_{s,t}$-free graphs: topological obstructions and algebraic constructions

Boris Bukh, Pavle Blagojevi\'c, Roman Karasev

arxiv:1108.5254 v3 · 2011-08-26 · math.CO · math.AG · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X5SIMP5XTRR5AWES2Q5B27ZDX2}

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	2026-05-18T03:01:54.711225Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf64863fb79c63d05892d43a1d7f23be8d1747f78ce3c62af958feead45de7e1

Aliases

arxiv: 1108.5254 · arxiv_version: 1108.5254v3 · doi: 10.48550/arxiv.1108.5254 · pith_short_12: X5SIMP5XTRR5 · pith_short_16: X5SIMP5XTRR5AWES · pith_short_8: X5SIMP5X

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/X5SIMP5XTRR5AWES2Q5B27ZDX2 \
  | 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: bf64863fb79c63d05892d43a1d7f23be8d1747f78ce3c62af958feead45de7e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2123834e823476088edfebac6b3b76d85d4aab9286bf50547841ab3aa5e4660e",
    "cross_cats_sorted": [
      "math.AG",
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-08-26T08:14:56Z",
    "title_canon_sha256": "9d018449cfd8b4b91499e78eaaa2f200b44b6478f4502f3568d9b14d08a1d4e5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.5254",
    "kind": "arxiv",
    "version": 3
  }
}