Pith Number

pith:5BO3UD5N

pith:2009:5BO3UD5NJSX33MK7BWQJEZ2L5W

not attested not anchored not stored refs pending

Expansive homeomorphisms of the plane

Jorge Groisman

arxiv:0906.4596 v1 · 2009-06-25 · 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{5BO3UD5NJSX33MK7BWQJEZ2L5W}

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	2026-05-18T04:39:16.925079Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e85dba0fad4cafbdb15f0da092674bed8b343a016ed381bf2c6c433dfca522b8

Aliases

arxiv: 0906.4596 · arxiv_version: 0906.4596v1 · doi: 10.48550/arxiv.0906.4596 · pith_short_12: 5BO3UD5NJSX3 · pith_short_16: 5BO3UD5NJSX33MK7 · pith_short_8: 5BO3UD5N

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/5BO3UD5NJSX33MK7BWQJEZ2L5W \
  | 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: e85dba0fad4cafbdb15f0da092674bed8b343a016ed381bf2c6c433dfca522b8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5460ccdb07242c5598f001eff4a12ea04e0b8ef9db1d7a29ec302ffd5520d2d2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2009-06-25T03:28:14Z",
    "title_canon_sha256": "18d90c842f59a38e6d3b3dfc21ed6b77fff6ca98c4ce2c2217d62d2df47e647c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0906.4596",
    "kind": "arxiv",
    "version": 1
  }
}