Pith Number

pith:Q3HCPTB5

pith:2015:Q3HCPTB57CUXVASW26ZBPUUXTI

not attested not anchored not stored refs pending

A survey of Tur\'an problems for expansions

Dhruv Mubayi, Jacques Verstraete

arxiv:1505.08078 v1 · 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{Q3HCPTB57CUXVASW26ZBPUUXTI}

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	2026-05-18T01:59:59.778228Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

86ce27cc3df8a97a8256d7b217d2979a1d4b2d202d21e57d1e2387e3b7ac0967

Aliases

arxiv: 1505.08078 · arxiv_version: 1505.08078v1 · doi: 10.48550/arxiv.1505.08078 · pith_short_12: Q3HCPTB57CUX · pith_short_16: Q3HCPTB57CUXVASW · pith_short_8: Q3HCPTB5

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/Q3HCPTB57CUXVASW26ZBPUUXTI \
  | 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: 86ce27cc3df8a97a8256d7b217d2979a1d4b2d202d21e57d1e2387e3b7ac0967

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "89bf8f751985b12a10db04737af73d96cefc94ee951640d9bdeddf6f9d3bf46b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-05-29T15:00:52Z",
    "title_canon_sha256": "27269f1c1e883c2111d2b5645c9a7b29721563154c9170266ed8b391d4cd53fe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.08078",
    "kind": "arxiv",
    "version": 1
  }
}