Pith Number

pith:UFR67YYE

pith:2010:UFR67YYEUT4256JUGMEDAT4OLK

not attested not anchored not stored refs pending

Solving linear equations over finitely generated abelian groups

Ren\'e Hartung

arxiv:1007.2477 v1 · 2010-07-15 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UFR67YYEUT4256JUGMEDAT4OLK}

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	2026-07-04T17:31:50.317607Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a163efe304a4f9aef9343308304f8e5a9c54ac068303462a5ec4e50bf5bd3c2f

Aliases

arxiv: 1007.2477 · arxiv_version: 1007.2477v1 · doi: 10.48550/arxiv.1007.2477 · pith_short_12: UFR67YYEUT42 · pith_short_16: UFR67YYEUT4256JU · pith_short_8: UFR67YYE

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/UFR67YYEUT4256JUGMEDAT4OLK \
  | 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: a163efe304a4f9aef9343308304f8e5a9c54ac068303462a5ec4e50bf5bd3c2f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "682b0f46b6c3833a9e1dcba4927b5bb858be1a9129c7da68ddf16ce17e8db98d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-07-15T05:17:01Z",
    "title_canon_sha256": "5c816db4c02b2d7730c1fe1946a2dc31730b7c3a35eaf62b4036663f9a789582"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.2477",
    "kind": "arxiv",
    "version": 1
  }
}