Pith Number

pith:3D6P5IA5

pith:2017:3D6P5IA53S4OPD7CG5VTPMYNYT

not attested not anchored not stored refs pending

A robust version of Freiman's $3k-4$ Theorem and applications

Max Wenqiang Xu, Xuancheng Shao

arxiv:1711.11060 v3 · 2017-11-29 · math.NT · 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{3D6P5IA53S4OPD7CG5VTPMYNYT}

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	2026-07-05T00:44:35.554817Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d8fcfea01ddcb8e78fe2376b37b30dc4f5019defa88bd2114b3e7faf55058f34

Aliases

arxiv: 1711.11060 · arxiv_version: 1711.11060v3 · doi: 10.48550/arxiv.1711.11060 · pith_short_12: 3D6P5IA53S4O · pith_short_16: 3D6P5IA53S4OPD7C · pith_short_8: 3D6P5IA5

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/3D6P5IA53S4OPD7CG5VTPMYNYT \
  | 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: d8fcfea01ddcb8e78fe2376b37b30dc4f5019defa88bd2114b3e7faf55058f34

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9536e68629d386c0a189c198100793d42d48b2fc65c7614a5b23152501632296",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2017-11-29T19:09:34Z",
    "title_canon_sha256": "00055f2036ee78fc3614049495a85696d501b5d3deed8c20a815ff3ab10e5923"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1711.11060",
    "kind": "arxiv",
    "version": 3
  }
}