Pith Number

pith:PN4X2TVA

pith:2010:PN4X2TVAJQ22USP24SI6IFRD3G

not attested not anchored not stored refs pending

Projections and relative hyperbolicity

Alessandro Sisto

arxiv:1010.4552 v4 · 2010-10-21 · math.MG · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PN4X2TVAJQ22USP24SI6IFRD3G}

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	2026-05-18T03:58:48.818359Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b797d4ea04c35aa49fae491e41623d99c02e77fec4d4424b697d99f0f8e9f22

Aliases

arxiv: 1010.4552 · arxiv_version: 1010.4552v4 · doi: 10.48550/arxiv.1010.4552 · pith_short_12: PN4X2TVAJQ22 · pith_short_16: PN4X2TVAJQ22USP2 · pith_short_8: PN4X2TVA

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/PN4X2TVAJQ22USP24SI6IFRD3G \
  | 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: 7b797d4ea04c35aa49fae491e41623d99c02e77fec4d4424b697d99f0f8e9f22

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "73498cba3f68114242c4da9097c3a1bfa1269b82fd4fe1120520c42104fd5f3d",
    "cross_cats_sorted": [
      "math.GR",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2010-10-21T18:39:16Z",
    "title_canon_sha256": "5b4968ae93d5cae68b7bcf9e5d6f6ba8e813f35e80eae86a3ed21e02ea00c5ac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.4552",
    "kind": "arxiv",
    "version": 4
  }
}