Pith Number

pith:PQQS6HTO

pith:2013:PQQS6HTOQS6PMPVT6XZB4KCUKP

not attested not anchored not stored refs pending

Sobolev homeomorphisms and Brennan's conjecture

Alexander Ukhlov, Vladimir Gol'dshtein

arxiv:1309.1940 v1 · 2013-09-08 · 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{PQQS6HTOQS6PMPVT6XZB4KCUKP}

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	2026-05-18T03:13:56.941817Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7c212f1e6e84bcf63eb3f5f21e285453ef7611c5ce0302a565f52a9d6b288ab4

Aliases

arxiv: 1309.1940 · arxiv_version: 1309.1940v1 · doi: 10.48550/arxiv.1309.1940 · pith_short_12: PQQS6HTOQS6P · pith_short_16: PQQS6HTOQS6PMPVT · pith_short_8: PQQS6HTO

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/PQQS6HTOQS6PMPVT6XZB4KCUKP \
  | 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: 7c212f1e6e84bcf63eb3f5f21e285453ef7611c5ce0302a565f52a9d6b288ab4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a34593279e504b3b1ac9f7f12b8df1e13803beb145cc161773fe4e99bcfa94ba",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-09-08T08:37:32Z",
    "title_canon_sha256": "d6c0f15daa9a8fc369ae0142d86eb5691d0607f9399adead25ee2248a7bdc2e6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.1940",
    "kind": "arxiv",
    "version": 1
  }
}