Pith Number

pith:JWJP7SZC

pith:2010:JWJP7SZCNJGYSKLDTTK45QJQZV

not attested not anchored not stored refs pending

A Topological Degree Counting for some Liouville Systems of Mean Field Equations

Chang-shou Lin, Lei Zhang

arxiv:1009.0259 v1 · 2010-09-01 · math.AP · 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{JWJP7SZCNJGYSKLDTTK45QJQZV}

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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	2026-05-18T04:41:35.282137Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4d92ffcb226a4d8929639cd5cec130cd61ea9b8ebd40514c1c65b77b9cfdea75

Aliases

arxiv: 1009.0259 · arxiv_version: 1009.0259v1 · doi: 10.48550/arxiv.1009.0259 · pith_short_12: JWJP7SZCNJGY · pith_short_16: JWJP7SZCNJGYSKLD · pith_short_8: JWJP7SZC

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/JWJP7SZCNJGYSKLDTTK45QJQZV \
  | 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: 4d92ffcb226a4d8929639cd5cec130cd61ea9b8ebd40514c1c65b77b9cfdea75

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d9d63e862dd6b3f8f0f0b4194d460a601702730cb804a61a52732dfea71ec856",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-09-01T19:50:01Z",
    "title_canon_sha256": "96248fab8c8b460fe4f1778a42189f00cf91271374358d203e41512015ce81a0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.0259",
    "kind": "arxiv",
    "version": 1
  }
}