Pith Number

pith:TUM2HA3X

pith:2009:TUM2HA3XZMF7AOTWH7VBMADCLV

not attested not anchored not stored refs pending

Double Affine Bundles

Janusz Grabowski, Mikolaj Rotkiewicz, Pawel Urbanski

arxiv:0904.2095 v2 · 2009-04-14 · math.DG · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TUM2HA3XZMF7AOTWH7VBMADCLV}

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	2026-05-18T04:08:04.213606Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9d19a38377cb0bf03a763fea1600625d6d435d48651f657dddd52e25a4945445

Aliases

arxiv: 0904.2095 · arxiv_version: 0904.2095v2 · doi: 10.48550/arxiv.0904.2095 · pith_short_12: TUM2HA3XZMF7 · pith_short_16: TUM2HA3XZMF7AOTW · pith_short_8: TUM2HA3X

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/TUM2HA3XZMF7AOTWH7VBMADCLV \
  | 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: 9d19a38377cb0bf03a763fea1600625d6d435d48651f657dddd52e25a4945445

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bd76e6f589eaa65b199a61a10cb54a3719f0a66016b400dd4d3cf662210a5bc4",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2009-04-14T11:13:22Z",
    "title_canon_sha256": "3bdd9d089b7ca8137a7e6addc8bed124100cd5b9fe0b5c2c01a6cd8c6b707958"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0904.2095",
    "kind": "arxiv",
    "version": 2
  }
}