Pith Number

pith:T3RE6R2L

pith:2009:T3RE6R2LYAWD4YUGG6M7KXLHTU

not attested not anchored not stored refs pending

Closed geodesics in Alexandrov spaces of curvature bounded from above

Longzhi Lin

arxiv:0909.4981 v3 · 2009-09-28 · math.DG · math.GT · 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{T3RE6R2LYAWD4YUGG6M7KXLHTU}

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	2026-05-18T00:13:14.288959Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9ee24f474bc02c3e62863799f55d679d33771bfaa36d7247ef4f15afbc56848b

Aliases

arxiv: 0909.4981 · arxiv_version: 0909.4981v3 · doi: 10.48550/arxiv.0909.4981 · pith_short_12: T3RE6R2LYAWD · pith_short_16: T3RE6R2LYAWD4YUG · pith_short_8: T3RE6R2L

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/T3RE6R2LYAWD4YUGG6M7KXLHTU \
  | 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: 9ee24f474bc02c3e62863799f55d679d33771bfaa36d7247ef4f15afbc56848b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "368688b3638e140012e74825e88d1779731e56b2175c330573c2371516c1ae18",
    "cross_cats_sorted": [
      "math.GT",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2009-09-28T07:43:36Z",
    "title_canon_sha256": "0c93b47ed05f6b2d93248284a57e4c304000a352e7da82868dfbbd39bf9ba9cb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.4981",
    "kind": "arxiv",
    "version": 3
  }
}