Pith Number

pith:5U4XKHCM

pith:2009:5U4XKHCMI33FS4U4BRFQYMQASX

not attested not anchored not stored refs pending

Large scale geometry of negatively curved $\R^n \rtimes \R$

Xiangdong Xie

arxiv:1001.0147 v1 · 2009-12-31 · math.GR · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5U4XKHCMI33FS4U4BRFQYMQASX}

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	2026-05-18T02:38:18.659020Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed39751c4c46f659729c0c4b0c320095f6fd5c72c261a723c232c59768bed4e7

Aliases

arxiv: 1001.0147 · arxiv_version: 1001.0147v1 · doi: 10.48550/arxiv.1001.0147 · pith_short_12: 5U4XKHCMI33F · pith_short_16: 5U4XKHCMI33FS4U4 · pith_short_8: 5U4XKHCM

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/5U4XKHCMI33FS4U4BRFQYMQASX \
  | 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: ed39751c4c46f659729c0c4b0c320095f6fd5c72c261a723c232c59768bed4e7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b0c898c6fcf50692aee4e895cece0354e35ffae704cf4cf75bf2af7147985b22",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-12-31T16:23:59Z",
    "title_canon_sha256": "d82ce799a37a3ae9c5bebc960895ad8240091f921cd493735d0212d07f2fd84a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.0147",
    "kind": "arxiv",
    "version": 1
  }
}