Pith Number

pith:6CPCOP3M

pith:2019:6CPCOP3MOE3CCXODVMJX733VNB

not attested not anchored not stored refs pending

Counting closed geodesics in a compact rank one locally CAT(0) space

Russell Ricks

arxiv:1903.07635 v1 · 2019-03-18 · math.DS · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6CPCOP3MOE3CCXODVMJX733VNB}

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	2026-05-17T23:50:54.566909Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f09e273f6c7136215dc3ab137fef756867adcdaef1f095d8cf391eda5d71eb68

Aliases

arxiv: 1903.07635 · arxiv_version: 1903.07635v1 · doi: 10.48550/arxiv.1903.07635 · pith_short_12: 6CPCOP3MOE3C · pith_short_16: 6CPCOP3MOE3CCXOD · pith_short_8: 6CPCOP3M

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/6CPCOP3MOE3CCXODVMJX733VNB \
  | 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: f09e273f6c7136215dc3ab137fef756867adcdaef1f095d8cf391eda5d71eb68

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fdb56d7f0cec749cd5f5d428b6280d1bb17b4b0bd21aa14931ba474e362a5511",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2019-03-18T18:00:59Z",
    "title_canon_sha256": "486db1cb944d707c1e3810138be790e40814c06e69b74b5e45c9a0a1c83b0892"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1903.07635",
    "kind": "arxiv",
    "version": 1
  }
}