Pith Number

pith:LWAXJHFZ

pith:2015:LWAXJHFZYVIBXNFIIKNK4OJ5YC

not attested not anchored not stored refs pending

Positive independence densities of finite rank countable hypergraphs are achieved by finite hypergraphs

B\'ela Bollob\'as, Karen Gunderson, Paul Balister

arxiv:1505.08044 v2 · 2015-05-29 · 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{LWAXJHFZYVIBXNFIIKNK4OJ5YC}

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	2026-05-18T01:16:50.432821Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5d81749cb9c5501bb4a8429aae393dc082a057e4e8d9b9fe5a1107960a6d9ec3

Aliases

arxiv: 1505.08044 · arxiv_version: 1505.08044v2 · doi: 10.48550/arxiv.1505.08044 · pith_short_12: LWAXJHFZYVIB · pith_short_16: LWAXJHFZYVIBXNFI · pith_short_8: LWAXJHFZ

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/LWAXJHFZYVIBXNFIIKNK4OJ5YC \
  | 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: 5d81749cb9c5501bb4a8429aae393dc082a057e4e8d9b9fe5a1107960a6d9ec3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "31e41e5795ea637f6b515f0dc9b0889f9251c97310fec8c7f22f6af5978bf6e1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-05-29T13:49:01Z",
    "title_canon_sha256": "c3cd66c9a74455f349e9040636886261dba36916e134c19c7ce099d0d6af18f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.08044",
    "kind": "arxiv",
    "version": 2
  }
}