Pith Number

pith:X4GUZZ3A

pith:2011:X4GUZZ3AW5QB3B2FCQFSIBYZL2

not attested not anchored not stored refs pending

Spheres with more than 7 vector fields: all the fault of Spin(9)

Maurizio Parton, Paolo Piccinni

arxiv:1107.0462 v2 · 2011-07-03 · math.DG · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X4GUZZ3AW5QB3B2FCQFSIBYZL2}

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	2026-05-18T03:56:45.170407Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf0d4ce760b7601d8745140b2407195eb2d445a0e75c993c07c9daa29070305f

Aliases

arxiv: 1107.0462 · arxiv_version: 1107.0462v2 · doi: 10.48550/arxiv.1107.0462 · pith_short_12: X4GUZZ3AW5QB · pith_short_16: X4GUZZ3AW5QB3B2F · pith_short_8: X4GUZZ3A

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/X4GUZZ3AW5QB3B2FCQFSIBYZL2 \
  | 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: bf0d4ce760b7601d8745140b2407195eb2d445a0e75c993c07c9daa29070305f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3243e1759d50f6d1e960f1f7e1b8332b81624490bf273c03cbc9059ea33a1c41",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-07-03T14:06:39Z",
    "title_canon_sha256": "15f7237502f8f3f5157885c4dae81609b88633bac783eab32a661979c2ad1fc4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.0462",
    "kind": "arxiv",
    "version": 2
  }
}