Pith Number

pith:6FDCJSGY

pith:2010:6FDCJSGYIOPK4BQ3SYCV2UNQQ4

not attested not anchored not stored refs pending

A Kronecker-Weyl theorem for subsets of abelian groups

Dikran Dikranjan, Dmitri Shakhmatov

arxiv:1012.4177 v1 · 2010-12-19 · math.GR · math.DS · math.GN · math.LO · 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{6FDCJSGYIOPK4BQ3SYCV2UNQQ4}

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	2026-05-18T04:27:56.335730Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f14624c8d8439eae061b96055d51b08725984171bceec51febd47cbaae26bcea

Aliases

arxiv: 1012.4177 · arxiv_version: 1012.4177v1 · doi: 10.48550/arxiv.1012.4177 · pith_short_12: 6FDCJSGYIOPK · pith_short_16: 6FDCJSGYIOPK4BQ3 · pith_short_8: 6FDCJSGY

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/6FDCJSGYIOPK4BQ3SYCV2UNQQ4 \
  | 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: f14624c8d8439eae061b96055d51b08725984171bceec51febd47cbaae26bcea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "de207970127b75cf4dde1bda2df02246d05fcb2ca92a82b2e9007c5b3d1189ec",
    "cross_cats_sorted": [
      "math.DS",
      "math.GN",
      "math.LO",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-12-19T16:00:25Z",
    "title_canon_sha256": "e39ce3cfcb78644fc3a680462682e79b34d2435981283e2bc67d9f5564bdbe00"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.4177",
    "kind": "arxiv",
    "version": 1
  }
}