Pith Number

pith:KSK2DKIV

pith:2011:KSK2DKIVJPQZHSUU52TDSPEUQQ

not attested not anchored not stored refs pending

Lens rigidity with trapped geodesics in two dimensions

Christopher B. Croke, Pilar Herreros

arxiv:1108.4938 v1 · 2011-08-24 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KSK2DKIVJPQZHSUU52TDSPEUQQ}

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	2026-05-18T04:14:45.767427Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5495a1a9154be193ca94eea6393c9484058dab6f9ab97aa5e3be966db9d93d36

Aliases

arxiv: 1108.4938 · arxiv_version: 1108.4938v1 · doi: 10.48550/arxiv.1108.4938 · pith_short_12: KSK2DKIVJPQZ · pith_short_16: KSK2DKIVJPQZHSUU · pith_short_8: KSK2DKIV

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/KSK2DKIVJPQZHSUU52TDSPEUQQ \
  | 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: 5495a1a9154be193ca94eea6393c9484058dab6f9ab97aa5e3be966db9d93d36

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d7464773f51f7e6558b87a37439e1e9f92ff703581ceb68a3342a13f53987851",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-08-24T20:13:50Z",
    "title_canon_sha256": "cf97997f71b758a20d988a9c28ecd0b2bca7ad78d87f2828d1c4b6143abc73fb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.4938",
    "kind": "arxiv",
    "version": 1
  }
}