Pith Number

pith:46LADX2B

pith:2016:46LADX2BDEVCO4UET2WK2BDDXU

not attested not anchored not stored refs pending

A density problem for Sobolev spaces on Gromov hyperbolic domains

Pekka Koskela, Tapio Rajala, Yi Ru-Ya Zhang

arxiv:1605.08260 v1 · 2016-05-26 · 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{46LADX2BDEVCO4UET2WK2BDDXU}

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	2026-05-18T01:13:32.099192Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e79601df41192a2772849eacad0463bd3f32705b86fcf96bbca2c0d9c768ae01

Aliases

arxiv: 1605.08260 · arxiv_version: 1605.08260v1 · doi: 10.48550/arxiv.1605.08260 · pith_short_12: 46LADX2BDEVC · pith_short_16: 46LADX2BDEVCO4UE · pith_short_8: 46LADX2B

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/46LADX2BDEVCO4UET2WK2BDDXU \
  | 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: e79601df41192a2772849eacad0463bd3f32705b86fcf96bbca2c0d9c768ae01

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "03ff13bec7289168bd435e7658b196d09b1ab1ae35f8b0410281c86b42609859",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-05-26T13:13:39Z",
    "title_canon_sha256": "1190c1736cb055a629ba01ee085204461d88e1945b8f827ec655e7196e59a36d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.08260",
    "kind": "arxiv",
    "version": 1
  }
}