Pith Number

pith:DYGK7HVY

pith:2009:DYGK7HVYVT7FZIJPNNNOVXMP26

not attested not anchored not stored refs pending

On Fixed Points of L\"{u}ders Operation

Liu Weihua, Wu Junde

arxiv:0906.1412 v6 · 2009-06-08 · 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{DYGK7HVYVT7FZIJPNNNOVXMP26}

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	2026-05-18T01:03:41.314146Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1e0caf9eb8acfe5ca12f6b5aeadd8fd7aa7f1178e2161da26e82cfaa4bd3e19e

Aliases

arxiv: 0906.1412 · arxiv_version: 0906.1412v6 · doi: 10.48550/arxiv.0906.1412 · pith_short_12: DYGK7HVYVT7F · pith_short_16: DYGK7HVYVT7FZIJP · pith_short_8: DYGK7HVY

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/DYGK7HVYVT7FZIJPNNNOVXMP26 \
  | 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: 1e0caf9eb8acfe5ca12f6b5aeadd8fd7aa7f1178e2161da26e82cfaa4bd3e19e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "951e34be218187444a7fb097335bddcab81469a9c10e4693db0dfb0e5fc30f7a",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2009-06-08T06:05:49Z",
    "title_canon_sha256": "6ab00c2bb7a1a2cd4f8aeaeea790dd684d22f0e042ed4f4166aa8591b14febc7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0906.1412",
    "kind": "arxiv",
    "version": 6
  }
}