Pith Number

pith:QESYOPRF

pith:2010:QESYOPRFNDJPUMG2KBOUDQSIQH

not attested not anchored not stored refs pending

Relative Ends, l^2 Invariants and Property (T)

Aditi Kar, Graham A. Niblo

arxiv:1003.2370 v2 · 2010-03-11 · 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{QESYOPRFNDJPUMG2KBOUDQSIQH}

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	2026-05-18T04:28:09.888283Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8125873e2568d2fa30da505d41c24881c9847062503108f891fc6ce8593a9c22

Aliases

arxiv: 1003.2370 · arxiv_version: 1003.2370v2 · doi: 10.48550/arxiv.1003.2370 · pith_short_12: QESYOPRFNDJP · pith_short_16: QESYOPRFNDJPUMG2 · pith_short_8: QESYOPRF

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/QESYOPRFNDJPUMG2KBOUDQSIQH \
  | 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: 8125873e2568d2fa30da505d41c24881c9847062503108f891fc6ce8593a9c22

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dfe1f948e30f1f027a2dcf3d6e1cc39be82babb12fcca1967fd4e8508cb4df9a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-03-11T17:47:40Z",
    "title_canon_sha256": "da740b671d8f4bba864eb003f4aefbd8eaa2bcbe13d260c14a9803c90e4a6ae5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1003.2370",
    "kind": "arxiv",
    "version": 2
  }
}