Pith Number

pith:YBU6XPEQ

pith:2013:YBU6XPEQO77GCEK3ZT64HGPXHT

not attested not anchored not stored refs pending

Lower bounds on the norms of extension operators for Lipschitz domains

Vladimir Lotoreichik

arxiv:1306.1524 v1 · 2013-06-06 · math.SP · math.AP · 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{YBU6XPEQO77GCEK3ZT64HGPXHT}

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	2026-05-18T03:21:33.951717Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c069ebbc9077fe61115bccfdc399f73cdc198939ee9e7e5f819619206ca5f28c

Aliases

arxiv: 1306.1524 · arxiv_version: 1306.1524v1 · doi: 10.48550/arxiv.1306.1524 · pith_short_12: YBU6XPEQO77G · pith_short_16: YBU6XPEQO77GCEK3 · pith_short_8: YBU6XPEQ

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/YBU6XPEQO77GCEK3ZT64HGPXHT \
  | 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: c069ebbc9077fe61115bccfdc399f73cdc198939ee9e7e5f819619206ca5f28c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "12a5b45390fd81da810fc8c96d046da08c1e903e1f9938bb44cd36247e14e14d",
    "cross_cats_sorted": [
      "math.AP",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2013-06-06T19:50:58Z",
    "title_canon_sha256": "b02adf49c7d6417cafc4244cf759a73ba31155a2bb9d26710a68d046ac22055f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.1524",
    "kind": "arxiv",
    "version": 1
  }
}