Pith Number

pith:R6ML3TUV

pith:2015:R6ML3TUVLHYQB53ZVBICAG5ZOL

not attested not anchored not stored refs pending

Lipschitz extensions of maps between Heisenberg groups

Pierre Pansu, Urs Lang, Zoltan Balogh

arxiv:1505.06093 v1 · 2015-05-22 · math.DG · math.GT · 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{R6ML3TUVLHYQB53ZVBICAG5ZOL}

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	2026-05-18T02:03:49.162050Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8f98bdce9559f100f779a850201bb972fe184b451cd446f053eed6ddbedfcdd6

Aliases

arxiv: 1505.06093 · arxiv_version: 1505.06093v1 · doi: 10.48550/arxiv.1505.06093 · pith_short_12: R6ML3TUVLHYQ · pith_short_16: R6ML3TUVLHYQB53Z · pith_short_8: R6ML3TUV

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/R6ML3TUVLHYQB53ZVBICAG5ZOL \
  | 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: 8f98bdce9559f100f779a850201bb972fe184b451cd446f053eed6ddbedfcdd6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6630dde3cff2517b1e7f0723098219bff05575ee94d191ef5ffa14f676f32d68",
    "cross_cats_sorted": [
      "math.GT",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-05-22T14:22:31Z",
    "title_canon_sha256": "1c136110a3740e6ed8b6dcde4dc65967480fb00da5161a9facbedacad7bf0977"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.06093",
    "kind": "arxiv",
    "version": 1
  }
}