Pith Number

pith:ERDJGBSQ

pith:2009:ERDJGBSQP5OPSY5UQ6Z4PBEL6L

not attested not anchored not stored refs pending

Local extremality of the Calabi-Croke sphere for the length of the shortest closed geodesic

Stephane Sabourau

arxiv:0907.2223 v1 · 2009-07-13 · 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{ERDJGBSQP5OPSY5UQ6Z4PBEL6L}

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	2026-05-18T02:58:02.968163Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

24469306507f5cf963b487b3c7848bf2c7af42038925fedeb77ee5262ab0eecd

Aliases

arxiv: 0907.2223 · arxiv_version: 0907.2223v1 · doi: 10.48550/arxiv.0907.2223 · pith_short_12: ERDJGBSQP5OP · pith_short_16: ERDJGBSQP5OPSY5U · pith_short_8: ERDJGBSQ

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/ERDJGBSQP5OPSY5UQ6Z4PBEL6L \
  | 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: 24469306507f5cf963b487b3c7848bf2c7af42038925fedeb77ee5262ab0eecd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eb78e2def1be4931c1beadc9d9c8d4ca74a9bbebf2b188b5fcc8c9e6ad6afe27",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2009-07-13T18:24:36Z",
    "title_canon_sha256": "6304d3e41582a656bc00226e4cac0cc53bcab6bc54649c56b0d2d2f69ae6b8a4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.2223",
    "kind": "arxiv",
    "version": 1
  }
}