Pith Number

pith:2AZP2PX3

pith:2025:2AZP2PX32PI3VBP52DFQLRZP4Y

not attested not anchored not stored refs pending

The Sobolev space $W_2^{1/2}$: Simultaneous improvement of functions by a homeomorphism of the circle

Vladimir Lebedev

arxiv:2511.07840 v4 · 2025-11-11 · math.CA · 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{2AZP2PX32PI3VBP52DFQLRZP4Y}

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	2026-05-17T23:39:17.147038Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d032fd3efbd3d1ba85fdd0cb05c72fe60e4688228ab7c0faf84938d6cf3c8bde

Aliases

arxiv: 2511.07840 · arxiv_version: 2511.07840v4 · doi: 10.48550/arxiv.2511.07840 · pith_short_12: 2AZP2PX32PI3 · pith_short_16: 2AZP2PX32PI3VBP5 · pith_short_8: 2AZP2PX3

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/2AZP2PX32PI3VBP52DFQLRZP4Y \
  | 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: d032fd3efbd3d1ba85fdd0cb05c72fe60e4688228ab7c0faf84938d6cf3c8bde

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7578d882dfd50a9b3799a3a749ecfdbdee232bdfce6b075019f5bc573258da1b",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2025-11-11T05:18:06Z",
    "title_canon_sha256": "38616c1989767494221f30a2e70822de5103ef42660be3c987f6ba1c7e30ba3c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2511.07840",
    "kind": "arxiv",
    "version": 4
  }
}