Pith Number

pith:Y3NPR7SR

pith:2026:Y3NPR7SRBAXMOJMSELHLRH3TT2

not attested not anchored not stored refs pending

The volume of tubes in Lie groups

Andreas Bernig, Dmitry Faifman, Jan Kotrbat\'y

arxiv:2606.17747 v1 · 2026-06-16 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Y3NPR7SRBAXMOJMSELHLRH3TT2}

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	2026-06-19T16:10:40.379518Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c6daf8fe51082ec7259222ceb89f739ea3fe2f492d464b1b5f9b0a6269747249

Aliases

arxiv: 2606.17747 · arxiv_version: 2606.17747v1 · doi: 10.48550/arxiv.2606.17747 · pith_short_12: Y3NPR7SRBAXM · pith_short_16: Y3NPR7SRBAXMOJMS · pith_short_8: Y3NPR7SR

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/Y3NPR7SRBAXMOJMSELHLRH3TT2 \
  | 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: c6daf8fe51082ec7259222ceb89f739ea3fe2f492d464b1b5f9b0a6269747249

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b532452c0b5ef341e81fddb88e37e3fb365f5afcfc66e36c7f9501d772e00ceb",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-06-16T10:07:08Z",
    "title_canon_sha256": "a34841765b52d0ba7c8006dcc764bf750dda09929341eb130cf21ca039c920a7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.17747",
    "kind": "arxiv",
    "version": 1
  }
}