Pith Number

pith:67MQFUAJ

pith:2015:67MQFUAJNAOXLZCAXITIQA4RVA

not attested not anchored not stored refs pending

Asymptotic formulae for s-numbers of a Sobolev embedding and a Volterra type operator

David E. Edmunds, Jan Lang

arxiv:1504.02515 v1 · 2015-04-09 · 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{67MQFUAJNAOXLZCAXITIQA4RVA}

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	2026-05-18T02:19:07.453128Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7d902d009681d75e440ba26880391a8196792cabc84fef10248d267edd56089

Aliases

arxiv: 1504.02515 · arxiv_version: 1504.02515v1 · doi: 10.48550/arxiv.1504.02515 · pith_short_12: 67MQFUAJNAOX · pith_short_16: 67MQFUAJNAOXLZCA · pith_short_8: 67MQFUAJ

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/67MQFUAJNAOXLZCAXITIQA4RVA \
  | 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: f7d902d009681d75e440ba26880391a8196792cabc84fef10248d267edd56089

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "907838a32ac46755cd7a41d03e0790855beecefba431c9805b14663da351578d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-04-09T22:57:28Z",
    "title_canon_sha256": "d41a850c1c45efee0d67fca211d099edd466a3b58e631d51801becac7f72665a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.02515",
    "kind": "arxiv",
    "version": 1
  }
}