Pith Number

pith:ZXXOOIAS

pith:2019:ZXXOOIAS5D6D5UMMTQ24OFOWZB

not attested not anchored not stored refs pending

Caps and progression-free sets in $\mathbb{Z}_m^n$

Christian Elsholtz, P\'eter P\'al Pach

arxiv:1903.08266 v1 · 2019-03-19 · math.CO · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZXXOOIAS5D6D5UMMTQ24OFOWZB}

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	2026-05-17T23:50:49.855457Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cdeee72012e8fc3ed18c9c35c715d6c84f6b648aaa482dd636f1e71e5ac961b5

Aliases

arxiv: 1903.08266 · arxiv_version: 1903.08266v1 · doi: 10.48550/arxiv.1903.08266 · pith_short_12: ZXXOOIAS5D6D · pith_short_16: ZXXOOIAS5D6D5UMM · pith_short_8: ZXXOOIAS

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/ZXXOOIAS5D6D5UMMTQ24OFOWZB \
  | 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: cdeee72012e8fc3ed18c9c35c715d6c84f6b648aaa482dd636f1e71e5ac961b5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a9ee1bf652762e5fd41df55ff90b6e076bd4a5ee704e1d57a7953101bffb438",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-03-19T21:43:33Z",
    "title_canon_sha256": "f23d0f1d36a6903b630235c9fbb48a5815e934a794f94b70ca339808f152d19c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1903.08266",
    "kind": "arxiv",
    "version": 1
  }
}