Pith Number

pith:4VUS4DOP

pith:2025:4VUS4DOPSYJQVDC667RX6YXL3E

not attested not anchored not stored refs pending

An Ohsawa-Takegoshi-type $L^2$ extension for upper semi-continuous $L^2$-optimal functions

Zhuo Liu

arxiv:2506.22834 v1 · 2025-06-28 · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4VUS4DOPSYJQVDC667RX6YXL3E}

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	2026-07-05T11:28:46.190326Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5692e0dcf96130a8c5ef7e37f62ebd920f5e82e2e96f0e7e8cc6fdf805da280

Aliases

arxiv: 2506.22834 · arxiv_version: 2506.22834v1 · doi: 10.48550/arxiv.2506.22834 · pith_short_12: 4VUS4DOPSYJQ · pith_short_16: 4VUS4DOPSYJQVDC6 · pith_short_8: 4VUS4DOP

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/4VUS4DOPSYJQVDC667RX6YXL3E \
  | 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: e5692e0dcf96130a8c5ef7e37f62ebd920f5e82e2e96f0e7e8cc6fdf805da280

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1c2e7becc1ec2cf6c1cca3b921843d413aacfcbb5483fe20015bcc1376a5a49b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2025-06-28T10:31:44Z",
    "title_canon_sha256": "30503313b650ff26d31987e986c723443d020b033215d2eeda0b4b1bc274b6c9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.22834",
    "kind": "arxiv",
    "version": 1
  }
}