Pith Number

pith:PBQ4HUKQ

pith:2010:PBQ4HUKQQZBERM7DKTUQKGR5G2

not attested not anchored not stored refs pending

Homotopes of Symmetric Spaces I. Construction by Algebras with Two Involutions

Pierre Bieliavsky (IRMP), Wolfgang Bertram (IECN)

arxiv:1011.2923 v2 · 2010-11-12 · 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{PBQ4HUKQQZBERM7DKTUQKGR5G2}

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	2026-05-18T04:01:00.000721Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7861c3d150864248b3e354e9051a3d36b3c808b088cde37c6f03ec070d48b468

Aliases

arxiv: 1011.2923 · arxiv_version: 1011.2923v2 · doi: 10.48550/arxiv.1011.2923 · pith_short_12: PBQ4HUKQQZBE · pith_short_16: PBQ4HUKQQZBERM7D · pith_short_8: PBQ4HUKQ

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/PBQ4HUKQQZBERM7DKTUQKGR5G2 \
  | 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: 7861c3d150864248b3e354e9051a3d36b3c808b088cde37c6f03ec070d48b468

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a55aa6477d3f394811014916a98fd6bba5af32e18073912542c198998c28038e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2010-11-12T14:44:33Z",
    "title_canon_sha256": "d4403bf2f60cfd2b0d7a5cb2c923a591268a7652227f4696fe33ae5bfae42f2c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.2923",
    "kind": "arxiv",
    "version": 2
  }
}