Pith Number

pith:EURPNE4K

pith:2010:EURPNE4KYXM75K2NLKHDUGN443

not attested not anchored not stored refs pending

Patterson-Sullivan distributions for symmetric spaces of the noncompact type

Michael Schroeder

arxiv:1012.1113 v1 · 2010-12-06 · 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{EURPNE4KYXM75K2NLKHDUGN443}

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	2026-05-18T04:34:01.794528Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2522f6938ac5d9feab4d5a8e3a19bce6ff9fe38e9e050c70b2a12e22f9e84c3e

Aliases

arxiv: 1012.1113 · arxiv_version: 1012.1113v1 · doi: 10.48550/arxiv.1012.1113 · pith_short_12: EURPNE4KYXM7 · pith_short_16: EURPNE4KYXM75K2N · pith_short_8: EURPNE4K

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/EURPNE4KYXM75K2NLKHDUGN443 \
  | 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: 2522f6938ac5d9feab4d5a8e3a19bce6ff9fe38e9e050c70b2a12e22f9e84c3e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d388c557507e9a16cee95a16b11e0bc32efe2b33970a9724af291efb8853c5ba",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-12-06T10:11:45Z",
    "title_canon_sha256": "bee2bc39da85cb4b184f238442905b65266f3f418be78f3f270a4df35889ef24"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.1113",
    "kind": "arxiv",
    "version": 1
  }
}