Pith Number

pith:ECC7J54W

pith:2013:ECC7J54WN2X7WN3QQ5F2N4QMFB

not attested not anchored not stored refs pending

A note on zero sets of fractional sobolev functions with negative power of integrability

Armin Schikorra

arxiv:1307.5236 v1 · 2013-07-19 · 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{ECC7J54WN2X7WN3QQ5F2N4QMFB}

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	2026-05-18T03:18:05.368648Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2085f4f7966eaffb3770874ba6f20c2874d123209ded7db5de8fc753e1fe786c

Aliases

arxiv: 1307.5236 · arxiv_version: 1307.5236v1 · doi: 10.48550/arxiv.1307.5236 · pith_short_12: ECC7J54WN2X7 · pith_short_16: ECC7J54WN2X7WN3Q · pith_short_8: ECC7J54W

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/ECC7J54WN2X7WN3QQ5F2N4QMFB \
  | 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: 2085f4f7966eaffb3770874ba6f20c2874d123209ded7db5de8fc753e1fe786c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ea09bc00e87f0e436dc29aecc036cf5b081aa5e410736b1ee4c210f9e24a6cec",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-07-19T14:40:01Z",
    "title_canon_sha256": "7063ae6fbce5bf6dda4668ef0586a85240464041068ac3a9a8a132313b326075"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.5236",
    "kind": "arxiv",
    "version": 1
  }
}