Pith Number

pith:GB5WSYVG

pith:2015:GB5WSYVGKHGJEPBJRCWSTPLWHP

not attested not anchored not stored refs pending

Sobolev spaces, fine gradients and quasicontinuity on quasiopen sets

Anders Bj\"orn, Jana Bj\"orn, Visa Latvala

arxiv:1504.08205 v1 · 2015-04-30 · 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{GB5WSYVGKHGJEPBJRCWSTPLWHP}

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	2026-05-18T00:51:01.576779Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

307b6962a651cc923c2988ad29bd763bea4d15c7ad54924d38af99828bbfc858

Aliases

arxiv: 1504.08205 · arxiv_version: 1504.08205v1 · doi: 10.48550/arxiv.1504.08205 · pith_short_12: GB5WSYVGKHGJ · pith_short_16: GB5WSYVGKHGJEPBJ · pith_short_8: GB5WSYVG

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/GB5WSYVGKHGJEPBJRCWSTPLWHP \
  | 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: 307b6962a651cc923c2988ad29bd763bea4d15c7ad54924d38af99828bbfc858

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3fbe933d6e9c720b38c41dcd24d4b7828a89fc2f9a938e0787cffaca36f06d71",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-04-30T13:01:16Z",
    "title_canon_sha256": "e5bd453ec0ecd43f3843ed12f3b2eb845dabfcb505aff3dd98ce10f6eb6c09f7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.08205",
    "kind": "arxiv",
    "version": 1
  }
}