Pith Number

pith:CZZWQXNC

pith:2005:CZZWQXNCULZVRYIBT3NSFGFGWQ

not attested not anchored not stored refs pending

A product of trees as universal space for hyperbolic groups

Sergei Buyalo, Viktor Schroeder

arxiv:math/0509355 v1 · 2005-09-15 · math.GR · 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{CZZWQXNCULZVRYIBT3NSFGFGWQ}

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.

Cited by

1 paper in Pith

Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces

Receipt and verification

First computed	2026-07-04T14:40:23.147679Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1673685da2a2f358e1019edb2298a6b435c63f8db274dbc1b98eeb0ae2912dd0

Aliases

arxiv: math/0509355 · arxiv_version: math/0509355v1 · doi: 10.48550/arxiv.math/0509355 · pith_short_12: CZZWQXNCULZV · pith_short_16: CZZWQXNCULZVRYIB · pith_short_8: CZZWQXNC

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/CZZWQXNCULZVRYIBT3NSFGFGWQ \
  | 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: 1673685da2a2f358e1019edb2298a6b435c63f8db274dbc1b98eeb0ae2912dd0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "91fdce8303a51273880b95e45f3857b509cab7370590bbb3627dd71ac4096ece",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2005-09-15T16:25:14Z",
    "title_canon_sha256": "fe1ee8c75464408579158e9586cc706e4010b3b86d2701571f487b2d4cc955ec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0509355",
    "kind": "arxiv",
    "version": 1
  }
}