Pith Number

pith:MMHHWYGG

pith:2020:MMHHWYGGQATF4IUWS27ESOLDIH

not attested not anchored not stored refs pending

Stationary measures and orbit closures of uniformly expanding random dynamical systems on surfaces

Ping Ngai Chung

arxiv:2006.03166 v3 · 2020-06-04 · math.DS · 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{MMHHWYGGQATF4IUWS27ESOLDIH}

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.

Cited by

1 paper in Pith

Continuity properties of partial entropy

Receipt and verification

First computed	2026-07-05T01:09:07.631398Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

630e7b60c680265e229696be49396341f18be9228b1e7147eb9a244f7013e865

Aliases

arxiv: 2006.03166 · arxiv_version: 2006.03166v3 · doi: 10.48550/arxiv.2006.03166 · pith_short_12: MMHHWYGGQATF · pith_short_16: MMHHWYGGQATF4IUW · pith_short_8: MMHHWYGG

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/MMHHWYGGQATF4IUWS27ESOLDIH \
  | 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: 630e7b60c680265e229696be49396341f18be9228b1e7147eb9a244f7013e865

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bb7e442d020345208fb5da0a6748b4c67f63bb5ff19b70663ec1728f4537ebfa",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2020-06-04T23:08:49Z",
    "title_canon_sha256": "ff01a6bac7683cd54d20b781d17fde0706d13974b1c4c28752d697248e374a25"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2006.03166",
    "kind": "arxiv",
    "version": 3
  }
}