Pith Number

pith:3PIUJB4Z

pith:2011:3PIUJB4ZNHGZZRQBBBHYNX3RSC

not attested not anchored not stored refs pending

On the number of ends of rank one locally symmetric spaces

Matthew Stover

arxiv:1112.4495 v2 · 2011-12-19 · math.GT · math.DG · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3PIUJB4ZNHGZZRQBBBHYNX3RSC}

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	2026-05-18T02:38:17.932378Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dbd144879969cd9cc601084f86df719095719e7e5255751a94d749e9d28e226e

Aliases

arxiv: 1112.4495 · arxiv_version: 1112.4495v2 · doi: 10.48550/arxiv.1112.4495 · pith_short_12: 3PIUJB4ZNHGZ · pith_short_16: 3PIUJB4ZNHGZZRQB · pith_short_8: 3PIUJB4Z

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/3PIUJB4ZNHGZZRQBBBHYNX3RSC \
  | 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: dbd144879969cd9cc601084f86df719095719e7e5255751a94d749e9d28e226e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "802422e1a83aca0f945ea36eb34a072b05a5fe4479b2d91925a884a38d100f8b",
    "cross_cats_sorted": [
      "math.DG",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-12-19T21:11:02Z",
    "title_canon_sha256": "556d18e4f89a1eeb165d3876c071a913e7bff98df9f7933c0678c6ca5030dd8b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.4495",
    "kind": "arxiv",
    "version": 2
  }
}