Pith Number

pith:YV2JEMGQ

pith:2014:YV2JEMGQ2HUKE26BQBIA5BD3NR

not attested not anchored not stored refs pending

Optimal geometric estimates for fractional Sobolev capacities

Jie Xiao

arxiv:1404.2245 v1 · 2014-04-08 · math.DG · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YV2JEMGQ2HUKE26BQBIA5BD3NR}

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	2026-05-18T02:54:38.213523Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c5749230d0d1e8a26bc180500e847b6c4b10615f89198f7e2cacae0e86aef2ac

Aliases

arxiv: 1404.2245 · arxiv_version: 1404.2245v1 · doi: 10.48550/arxiv.1404.2245 · pith_short_12: YV2JEMGQ2HUK · pith_short_16: YV2JEMGQ2HUKE26B · pith_short_8: YV2JEMGQ

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/YV2JEMGQ2HUKE26BQBIA5BD3NR \
  | 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: c5749230d0d1e8a26bc180500e847b6c4b10615f89198f7e2cacae0e86aef2ac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a8c9f05e226cbc54872f2b58a891147d858de28f46b37ad741ca64e2687242b3",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2014-04-08T18:44:00Z",
    "title_canon_sha256": "df346ee5600e16c18a3e14aa27a32db7e4e1537b783211cccb512afe8131b25f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1404.2245",
    "kind": "arxiv",
    "version": 1
  }
}