Pith Number

pith:XBIUZTSN

pith:2010:XBIUZTSNDSLTHP2OY5DVPTRMQ3

not attested not anchored not stored refs pending

Inclusion relations of hyperbolic type metric balls

Matti Vuorinen, Riku Kl\'en

arxiv:1005.3927 v2 · 2010-05-21 · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XBIUZTSNDSLTHP2OY5DVPTRMQ3}

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	2026-05-18T03:36:46.919352Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b8514cce4d1c9733bf4ec74757ce2c86c434308e8a21bf9b1d3dd2ae96f92bb0

Aliases

arxiv: 1005.3927 · arxiv_version: 1005.3927v2 · doi: 10.48550/arxiv.1005.3927 · pith_short_12: XBIUZTSNDSLT · pith_short_16: XBIUZTSNDSLTHP2O · pith_short_8: XBIUZTSN

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/XBIUZTSNDSLTHP2OY5DVPTRMQ3 \
  | 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: b8514cce4d1c9733bf4ec74757ce2c86c434308e8a21bf9b1d3dd2ae96f92bb0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f07988b657295d3081af7e45c03b6517ec48042a4f0b074ef8e42583530cf36f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2010-05-21T10:31:51Z",
    "title_canon_sha256": "841c7d115fd506ecd0d6cb46958123bee14123a4aaaab6ea5e87bfc6137a4149"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1005.3927",
    "kind": "arxiv",
    "version": 2
  }
}