Pith Number

pith:MGUPYDK3

pith:2016:MGUPYDK3FZFBEXAKXWUULCH3HS

not attested not anchored not stored refs pending

Mapping theorems for Sobolev-spaces of vector-valued functions

Marcel Kreuter, Wolfgang Arendt

arxiv:1611.06161 v1 · 2016-11-18 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MGUPYDK3FZFBEXAKXWUULCH3HS}

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	2026-05-18T00:26:08.533140Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61a8fc0d5b2e4a125c0abda94588fb3c9f0045233e6a4a2b76b9ece3e3fbe4ad

Aliases

arxiv: 1611.06161 · arxiv_version: 1611.06161v1 · doi: 10.48550/arxiv.1611.06161 · pith_short_12: MGUPYDK3FZFB · pith_short_16: MGUPYDK3FZFBEXAK · pith_short_8: MGUPYDK3

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/MGUPYDK3FZFBEXAKXWUULCH3HS \
  | 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: 61a8fc0d5b2e4a125c0abda94588fb3c9f0045233e6a4a2b76b9ece3e3fbe4ad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a220ca1d9d1bbf52abd9af633e0e9499b7a4bd1e0d434fff4cb7e2a01726795a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-11-18T17:10:06Z",
    "title_canon_sha256": "174f9ca4919850064781f3f314fd50bc3c854794c97b55b11b9261c4e26bfdd6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.06161",
    "kind": "arxiv",
    "version": 1
  }
}