Pith Number

pith:QOY34HJI

pith:2010:QOY34HJINBOWGMZ5BUDXNEJKCY

not attested not anchored not stored refs pending

The Geometry of the Osculating Nilpotent Group Structures of the Heisenberg Calculus

Erik van Erp, Pierre Julg

arxiv:1007.4759 v2 · 2010-07-27 · math.AP · 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{QOY34HJINBOWGMZ5BUDXNEJKCY}

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	2026-05-18T02:31:27.809654Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

83b1be1d28685d63333d0d0776912a16207c65f495b86e49e69344a27e6f8ea4

Aliases

arxiv: 1007.4759 · arxiv_version: 1007.4759v2 · doi: 10.48550/arxiv.1007.4759 · pith_short_12: QOY34HJINBOW · pith_short_16: QOY34HJINBOWGMZ5 · pith_short_8: QOY34HJI

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/QOY34HJINBOWGMZ5BUDXNEJKCY \
  | 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: 83b1be1d28685d63333d0d0776912a16207c65f495b86e49e69344a27e6f8ea4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b04daf17bfb1f2d9182ac13a0b141acf38e451347e8051ecbe5143d216d197f8",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-07-27T15:45:44Z",
    "title_canon_sha256": "ce49f8ec56c93028eedd42119a4f1101216db3fc9606382494e1436f98c9f9fd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.4759",
    "kind": "arxiv",
    "version": 2
  }
}