Pith Number

pith:4KZ2U6WN

pith:2013:4KZ2U6WNOC7GTE3UW2L3ZPC3JF

not attested not anchored not stored refs pending

Variations on the Sum-Product Problem

Brendan Murphy, Ilya D. Shkredov, Oliver Roche-Newton

arxiv:1312.6438 v2 · 2013-12-22 · 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{4KZ2U6WNOC7GTE3UW2L3ZPC3JF}

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	2026-05-18T03:02:58.847975Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e2b3aa7acd70be699374b697bcbc5b495ddf99f3b611d3642c84ef2534b6363c

Aliases

arxiv: 1312.6438 · arxiv_version: 1312.6438v2 · doi: 10.48550/arxiv.1312.6438 · pith_short_12: 4KZ2U6WNOC7G · pith_short_16: 4KZ2U6WNOC7GTE3U · pith_short_8: 4KZ2U6WN

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/4KZ2U6WNOC7GTE3UW2L3ZPC3JF \
  | 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: e2b3aa7acd70be699374b697bcbc5b495ddf99f3b611d3642c84ef2534b6363c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f3b77652b0e3bab57915c0c3e35f7274dc5e380f65d9eeb073dd51517c597445",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-12-22T22:46:58Z",
    "title_canon_sha256": "32c1fb50937c917d439a97f4d9ebc7e141e40c793324839d0e746d192b8c616a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.6438",
    "kind": "arxiv",
    "version": 2
  }
}