Pith Number

pith:X2NVNAGZ

pith:2008:X2NVNAGZCVT73PLHUNDKL2OZV3

not attested not anchored not stored refs pending

Hopf images and inner faithful representations

Julien Bichon, Teodor Banica

arxiv:0807.3827 v2 · 2008-07-24 · math.QA · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X2NVNAGZCVT73PLHUNDKL2OZV3}

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	2026-05-18T04:41:44.225788Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be9b5680d91567fdbd67a346a5e9d9aed003b6a432880efd294b374b28259239

Aliases

arxiv: 0807.3827 · arxiv_version: 0807.3827v2 · doi: 10.48550/arxiv.0807.3827 · pith_short_12: X2NVNAGZCVT7 · pith_short_16: X2NVNAGZCVT73PLH · pith_short_8: X2NVNAGZ

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/X2NVNAGZCVT73PLHUNDKL2OZV3 \
  | 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: be9b5680d91567fdbd67a346a5e9d9aed003b6a432880efd294b374b28259239

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8551247c68549811acff5c7aa54a4db474967c73e9ece03bd9af218b53d258a9",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2008-07-24T09:25:23Z",
    "title_canon_sha256": "284a28b9c721187967b8489d0f44317fb26acb2dba80c266cd9c9c84cb8736c9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0807.3827",
    "kind": "arxiv",
    "version": 2
  }
}