Pith Number

pith:QT3NFFZ2

pith:2011:QT3NFFZ24W45ZLXKOIUGLOWADR

not attested not anchored not stored refs pending

On the lack of density of Lipschitz mappings in Sobolev spaces with Heisenberg target

Anton Lukyanenko, Jeremy Tyson, Noel DeJarnette, Piotr Hajlasz

arxiv:1109.4641 v3 · 2011-09-21 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QT3NFFZ24W45ZLXKOIUGLOWADR}

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	2026-05-18T02:50:52.182491Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

84f6d2973ae5b9dcaeea722865bac01c43a4c50168f6fb9add1c87c165c62187

Aliases

arxiv: 1109.4641 · arxiv_version: 1109.4641v3 · doi: 10.48550/arxiv.1109.4641 · pith_short_12: QT3NFFZ24W45 · pith_short_16: QT3NFFZ24W45ZLXK · pith_short_8: QT3NFFZ2

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/QT3NFFZ24W45ZLXKOIUGLOWADR \
  | 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: 84f6d2973ae5b9dcaeea722865bac01c43a4c50168f6fb9add1c87c165c62187

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fc61b97eb18c4844ba402511cd730d60d809a10bdc01dbc2586953deb88515b7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-09-21T20:02:23Z",
    "title_canon_sha256": "cfad1f248593ee79cd20829cccd7d640a6f76654823cb44827befb3ef2106911"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.4641",
    "kind": "arxiv",
    "version": 3
  }
}