Pith Number

pith:ZF2JUXBX

pith:2009:ZF2JUXBXY2DUIZ7WPIKS24PEJC

not attested not anchored not stored refs pending

Ancient solutions of Ricci flow on spheres and generalized Hopf fibrations

Ioannis Bakas, Lei Ni, Shengli Kong

arxiv:0906.0589 v2 · 2009-06-02 · math.DG · hep-th · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZF2JUXBXY2DUIZ7WPIKS24PEJC}

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	2026-05-18T04:27:02.792786Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c9749a5c37c6874467f67a152d71e44897f01b9d4b027fa87defaf36561e57e8

Aliases

arxiv: 0906.0589 · arxiv_version: 0906.0589v2 · doi: 10.48550/arxiv.0906.0589 · pith_short_12: ZF2JUXBXY2DU · pith_short_16: ZF2JUXBXY2DUIZ7W · pith_short_8: ZF2JUXBX

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/ZF2JUXBXY2DUIZ7WPIKS24PEJC \
  | 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: c9749a5c37c6874467f67a152d71e44897f01b9d4b027fa87defaf36561e57e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2b7c95483aa352ad65764334a7c8200b06e738adb01791fda943ca0d90336b8c",
    "cross_cats_sorted": [
      "hep-th",
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2009-06-02T20:13:25Z",
    "title_canon_sha256": "992ef06af54129a1b1618537a6cb46110bd94a3726e59250faa2237903eacb89"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0906.0589",
    "kind": "arxiv",
    "version": 2
  }
}