Pith Number

pith:ROIKZI5Q

pith:2015:ROIKZI5QT2LAEYSXWJGIY7NOQH

not attested not anchored not stored refs pending

Beltrami equations with coefficient in the fractional Sobolev space $W^{\theta, \frac2{\theta}}$

Albert Clop, Antonio Luis Bais\'on, Joan Orobitg

arxiv:1507.05799 v1 · 2015-07-21 · math.CV · 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{ROIKZI5QT2LAEYSXWJGIY7NOQH}

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	2026-05-18T01:36:32.429098Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8b90aca3b09e96026257b24c8c7dae81ed75deb037f361e5b3a161c91cb9b7a5

Aliases

arxiv: 1507.05799 · arxiv_version: 1507.05799v1 · doi: 10.48550/arxiv.1507.05799 · pith_short_12: ROIKZI5QT2LA · pith_short_16: ROIKZI5QT2LAEYSX · pith_short_8: ROIKZI5Q

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/ROIKZI5QT2LAEYSXWJGIY7NOQH \
  | 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: 8b90aca3b09e96026257b24c8c7dae81ed75deb037f361e5b3a161c91cb9b7a5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0f97aec1b6a3ad6e90658b7909830411f2ef9f2ca402ac8973e16e97b6cdb071",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2015-07-21T12:09:19Z",
    "title_canon_sha256": "1a9bf406cb7f005af564cfec0e0ac941f542e260ca01c9bb1f4a8fd3df0dbea7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.05799",
    "kind": "arxiv",
    "version": 1
  }
}