Pith Number

pith:ZD3X3EAC

pith:2012:ZD3X3EAC6UA3QP3CNSQDRU5WGZ

not attested not anchored not stored refs pending

Remarks on minimal sets and conjectures of Cassels, Swinnerton-Dyer, and Margulis

Barak Weiss, Jinpeng An

arxiv:1212.0216 v2 · 2012-12-02 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZD3X3EAC6UA3QP3CNSQDRU5WGZ}

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	2026-05-18T03:05:18.743498Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c8f77d9002f501b83f626ca038d3b63668f88b32177ee046018aea8a6bda72c3

Aliases

arxiv: 1212.0216 · arxiv_version: 1212.0216v2 · doi: 10.48550/arxiv.1212.0216 · pith_short_12: ZD3X3EAC6UA3 · pith_short_16: ZD3X3EAC6UA3QP3C · pith_short_8: ZD3X3EAC

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/ZD3X3EAC6UA3QP3CNSQDRU5WGZ \
  | 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: c8f77d9002f501b83f626ca038d3b63668f88b32177ee046018aea8a6bda72c3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3dfef77a4d18512fdb034f767091bdc28374a9aeb77d526ccf938f117c6380bf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-12-02T15:09:34Z",
    "title_canon_sha256": "8454b7f923a3fc6b90bc5ea49eedf2bfcca02137c9b22fdce32bab7c2bd5039b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.0216",
    "kind": "arxiv",
    "version": 2
  }
}