Pith Number

pith:45YQK2Z5

pith:2014:45YQK2Z53SGWBRPYC2H4EKOEBD

not attested not anchored not stored refs pending

Besicovitch Covering Property for homogeneous distances in the Heisenberg groups

Enrico Le Donne, Severine Rigot

arxiv:1406.1484 v2 · 2014-06-05 · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{45YQK2Z53SGWBRPYC2H4EKOEBD}

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	2026-05-18T02:48:18.922974Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e771056b3ddc8d60c5f8168fc229c408e8b73add8ed0d5d256489d29ff3b3ff7

Aliases

arxiv: 1406.1484 · arxiv_version: 1406.1484v2 · doi: 10.48550/arxiv.1406.1484 · pith_short_12: 45YQK2Z53SGW · pith_short_16: 45YQK2Z53SGWBRPY · pith_short_8: 45YQK2Z5

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/45YQK2Z53SGWBRPYC2H4EKOEBD \
  | 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: e771056b3ddc8d60c5f8168fc229c408e8b73add8ed0d5d256489d29ff3b3ff7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ae6fffb218fb221fce26eace4172f819b0859d3e5bbafa58c16747a6dec00f9c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2014-06-05T19:12:09Z",
    "title_canon_sha256": "07dbaebfc630cc675fb40af0f2816b2d0de50a98abfc853e012118244a1a19a6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1406.1484",
    "kind": "arxiv",
    "version": 2
  }
}