Pith Number

pith:UKPCYK4Q

pith:2016:UKPCYK4QPR5I4VJCMC3LCFDD7M

not attested not anchored not stored refs pending

A Note on the Alon-Kleitman Argument for Sum-free Subset Theorem

Lihua Liu, Zhengjun Cao

arxiv:1606.07823 v2 · 2016-06-23 · math.CO · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UKPCYK4QPR5I4VJCMC3LCFDD7M}

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	2026-05-18T00:44:37.102946Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a29e2c2b907c7a8e552260b6b11463fb2fe5b065e661d4a08c52f3d79df4c855

Aliases

arxiv: 1606.07823 · arxiv_version: 1606.07823v2 · doi: 10.48550/arxiv.1606.07823 · pith_short_12: UKPCYK4QPR5I · pith_short_16: UKPCYK4QPR5I4VJC · pith_short_8: UKPCYK4Q

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/UKPCYK4QPR5I4VJCMC3LCFDD7M \
  | 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: a29e2c2b907c7a8e552260b6b11463fb2fe5b065e661d4a08c52f3d79df4c855

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "90db11b12ba7e1503a791b8764fee59c375f492e191574d15281dfe3261a3ead",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-06-23T02:04:02Z",
    "title_canon_sha256": "2718e427d71ad88e65175dd36a385c385e5c7e10ea93ed74ba2f71a95dc3a263"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.07823",
    "kind": "arxiv",
    "version": 2
  }
}