Pith Number

pith:XJNRXXPL

pith:2009:XJNRXXPLWZQUYKRMXW76QHRCLV

not attested not anchored not stored refs pending

Positive Entropy Invariant Measures on the Space of Lattices with Escape of Mass

Shirali Kadyrov

arxiv:0912.0487 v3 · 2009-12-02 · 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{XJNRXXPLWZQUYKRMXW76QHRCLV}

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	2026-05-18T04:41:05.194776Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba5b1bddebb6614c2a2cbdbfe81e225d4536b421d812620d89735822ed16ca22

Aliases

arxiv: 0912.0487 · arxiv_version: 0912.0487v3 · doi: 10.48550/arxiv.0912.0487 · pith_short_12: XJNRXXPLWZQU · pith_short_16: XJNRXXPLWZQUYKRM · pith_short_8: XJNRXXPL

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/XJNRXXPLWZQUYKRMXW76QHRCLV \
  | 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: ba5b1bddebb6614c2a2cbdbfe81e225d4536b421d812620d89735822ed16ca22

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "faa0f0c21da86da49ba7909d34808312133207cd4a04781a004334ab1e5cb2ce",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2009-12-02T18:30:09Z",
    "title_canon_sha256": "e839813890dbae5dc3af8d7f18d88e1e0d9e4c6cbefb5e1c7e6fde95764f2668"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.0487",
    "kind": "arxiv",
    "version": 3
  }
}