Pith Number

pith:WUZXUGIU

pith:2018:WUZXUGIUT4QJ5OPZ2GUARXJRS2

not attested not anchored not stored refs pending

Composition Operators on Sobolev Spaces and Neumann Eigenvalues

A. Ukhlov, V. Gol'dshtein

arxiv:1801.10421 v1 · 2018-01-31 · 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{WUZXUGIUT4QJ5OPZ2GUARXJRS2}

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	2026-05-18T00:24:40.875869Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b5337a19149f209eb9f9d1a808dd31969449757f29f1ad33286340ecfb0abc5b

Aliases

arxiv: 1801.10421 · arxiv_version: 1801.10421v1 · doi: 10.48550/arxiv.1801.10421 · pith_short_12: WUZXUGIUT4QJ · pith_short_16: WUZXUGIUT4QJ5OPZ · pith_short_8: WUZXUGIU

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/WUZXUGIUT4QJ5OPZ2GUARXJRS2 \
  | 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: b5337a19149f209eb9f9d1a808dd31969449757f29f1ad33286340ecfb0abc5b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ffebecde74a6d4a6eceec1fb1d857f47508085884d69f4b89c252d73e9a43854",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-01-31T12:33:33Z",
    "title_canon_sha256": "3a8d54a27cabce1fc6fc9378be9da5dacc06a7ad4e798a4bf739247f6334d337"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1801.10421",
    "kind": "arxiv",
    "version": 1
  }
}