Pith Number

pith:CW3HBTAK

pith:2011:CW3HBTAKGUN4RVBRJLNVOOXCSD

not attested not anchored not stored refs pending

Continuity of bilinear maps on direct sums of topological vector spaces

Helge Glockner

arxiv:1108.0169 v3 · 2011-07-31 · 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{CW3HBTAKGUN4RVBRJLNVOOXCSD}

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	2026-05-18T04:05:57.548355Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

15b670cc0a351bc8d4314adb573ae290dae833bd4ba0a9b9d3930b47f153b257

Aliases

arxiv: 1108.0169 · arxiv_version: 1108.0169v3 · doi: 10.48550/arxiv.1108.0169 · pith_short_12: CW3HBTAKGUN4 · pith_short_16: CW3HBTAKGUN4RVBR · pith_short_8: CW3HBTAK

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/CW3HBTAKGUN4RVBRJLNVOOXCSD \
  | 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: 15b670cc0a351bc8d4314adb573ae290dae833bd4ba0a9b9d3930b47f153b257

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "82b0235f70ce5267b9885d2a73355caf43e9bd33f0f4a35c37cdea412cd76c3e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-07-31T11:57:09Z",
    "title_canon_sha256": "7a93e78e3880b63f1843636804ae417ebe251e4e265f0c60fcf6e8402f647d56"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.0169",
    "kind": "arxiv",
    "version": 3
  }
}