Pith Number

pith:V4HLYNOM

pith:2016:V4HLYNOMM3RBBNUYRGPZ7NVFGQ

not attested not anchored not stored refs pending

Boundedness and closedness of linear relations

Guixin Xu, Guojing Ren, Yuming Shi

arxiv:1604.07979 v1 · 2016-04-27 · 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{V4HLYNOMM3RBBNUYRGPZ7NVFGQ}

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	2026-05-18T01:16:08.485261Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

af0ebc35cc66e210b698899f9fb6a5343b85ed4aa6e15c144146720367f64450

Aliases

arxiv: 1604.07979 · arxiv_version: 1604.07979v1 · doi: 10.48550/arxiv.1604.07979 · pith_short_12: V4HLYNOMM3RB · pith_short_16: V4HLYNOMM3RBBNUY · pith_short_8: V4HLYNOM

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/V4HLYNOMM3RBBNUYRGPZ7NVFGQ \
  | 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: af0ebc35cc66e210b698899f9fb6a5343b85ed4aa6e15c144146720367f64450

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "00651b76f39d6af83e8a3f0c1a690907a3336179e0dedf28e7894296e4352b13",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-04-27T08:49:36Z",
    "title_canon_sha256": "ee2e53eadca6954c8e275b03b196ed659d4180072fd654b9046cf943c781266e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.07979",
    "kind": "arxiv",
    "version": 1
  }
}