Pith Number

pith:FKBFLXWE

pith:2019:FKBFLXWE56M4IYOPB6ANYW6LJ3

not attested not anchored not stored refs pending

Vertical versus horizontal Sobolev spaces

Katrin F\"assler, Tuomas Orponen

arxiv:1905.13630 v1 · 2019-05-31 · math.CA · math.FA · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FKBFLXWE56M4IYOPB6ANYW6LJ3}

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	2026-05-17T23:44:34.379957Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2a8255dec4ef99c461cf0f80dc5bcb4efa22a85346d4ac5f4879d7c996731500

Aliases

arxiv: 1905.13630 · arxiv_version: 1905.13630v1 · doi: 10.48550/arxiv.1905.13630 · pith_short_12: FKBFLXWE56M4 · pith_short_16: FKBFLXWE56M4IYOP · pith_short_8: FKBFLXWE

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/FKBFLXWE56M4IYOPB6ANYW6LJ3 \
  | 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: 2a8255dec4ef99c461cf0f80dc5bcb4efa22a85346d4ac5f4879d7c996731500

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8d73e027705ebbb641083b123c810ab451ba6654f2022e3760d4c45571aafff3",
    "cross_cats_sorted": [
      "math.FA",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2019-05-31T14:18:08Z",
    "title_canon_sha256": "016544c059ca18abb3628dc998adfcd5747114893b0b92a3553b818dd42dd669"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1905.13630",
    "kind": "arxiv",
    "version": 1
  }
}