Pith Number

pith:VNOPSMVT

pith:2009:VNOPSMVTTQCHZC4PDPQLQOL7BZ

not attested not anchored not stored refs pending

On invariant sets in Lagrangian graphs

Lei Zhao, Xiaojun Cui

arxiv:0911.5720 v3 · 2009-11-30 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VNOPSMVTTQCHZC4PDPQLQOL7BZ}

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	2026-05-18T02:10:35.433138Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab5cf932b39c047c8b8f1be0b8397f0e53d4d9f7ef9e7c2d711e2713404f34c0

Aliases

arxiv: 0911.5720 · arxiv_version: 0911.5720v3 · doi: 10.48550/arxiv.0911.5720 · pith_short_12: VNOPSMVTTQCH · pith_short_16: VNOPSMVTTQCHZC4P · pith_short_8: VNOPSMVT

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/VNOPSMVTTQCHZC4PDPQLQOL7BZ \
  | 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: ab5cf932b39c047c8b8f1be0b8397f0e53d4d9f7ef9e7c2d711e2713404f34c0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "82d80ef3e480e62bdc0011614f0f388529053ae95df592a1fe3ad0fa8b451ec5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2009-11-30T19:47:53Z",
    "title_canon_sha256": "bff650f7cff62ed2a50b804a1b5344961abcdff845e5dc01406534d0a6f8db18"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.5720",
    "kind": "arxiv",
    "version": 3
  }
}