Pith Number

pith:KLU277NO

pith:2015:KLU277NO5A7ZYDWFH2RTVMY67C

not attested not anchored not stored refs pending

Direct sums and products in topological groups and vector spaces

Dikran Dikranjan, Dmitri Shakhmatov, Jan Sp\v{e}v\'ak

arxiv:1508.00667 v1 · 2015-08-04 · math.GN · math.FA · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KLU277NO5A7ZYDWFH2RTVMY67C}

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	2026-05-18T01:18:18.339951Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

52e9affdaee83f9c0ec53ea33ab31ef895e7051fe53e713c957a072282798784

Aliases

arxiv: 1508.00667 · arxiv_version: 1508.00667v1 · doi: 10.48550/arxiv.1508.00667 · pith_short_12: KLU277NO5A7Z · pith_short_16: KLU277NO5A7ZYDWF · pith_short_8: KLU277NO

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/KLU277NO5A7ZYDWFH2RTVMY67C \
  | 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: 52e9affdaee83f9c0ec53ea33ab31ef895e7051fe53e713c957a072282798784

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b2e71d57db0dd051f839612ba93dd862516daa5fbdd040f828a3aa8128f69484",
    "cross_cats_sorted": [
      "math.FA",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GN",
    "submitted_at": "2015-08-04T05:57:10Z",
    "title_canon_sha256": "4a70499b4ad49c5d15dd93677d238e45ca46689961e167e13f3337f440aeb62e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.00667",
    "kind": "arxiv",
    "version": 1
  }
}