Pith Number

pith:F2G5I5CR

pith:2018:F2G5I5CRZYV4TQEMMIZQ64SKEK

not attested not anchored not stored refs pending

Density problems for second order Sobolev spaces and cut-off functions on manifolds with unbounded geometry

Debora Impera, Giona Veronelli, Michele Rimoldi

arxiv:1810.02578 v2 · 2018-10-05 · math.DG · 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{F2G5I5CRZYV4TQEMMIZQ64SKEK}

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	2026-05-17T23:52:15.463893Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2e8dd47451ce2bc9c08c62330f724a228bf8ea3d9600fcc32bf97a1017eb5428

Aliases

arxiv: 1810.02578 · arxiv_version: 1810.02578v2 · doi: 10.48550/arxiv.1810.02578 · pith_short_12: F2G5I5CRZYV4 · pith_short_16: F2G5I5CRZYV4TQEM · pith_short_8: F2G5I5CR

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/F2G5I5CRZYV4TQEMMIZQ64SKEK \
  | 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: 2e8dd47451ce2bc9c08c62330f724a228bf8ea3d9600fcc32bf97a1017eb5428

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1b7deb393edaa524cb5579156a85eb3ab7b35ac95486ba835e2c1335eb117948",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2018-10-05T09:13:15Z",
    "title_canon_sha256": "0f101d08546624a22d5c93deeb8e41bf7141981fc970082299a294f0d9a35d86"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1810.02578",
    "kind": "arxiv",
    "version": 2
  }
}