Pith Number

pith:MKWL4VQL

pith:2015:MKWL4VQLE2UZ7BLEFUVWKFNI3B

not attested not anchored not stored refs pending

A categorical perspective on the Atiyah-Segal completion theorem in $\mathrm{KK}$-theory

Yosuke Kubota, Yuki Arano

arxiv:1508.06815 v4 · 2015-08-27 · math.KT · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MKWL4VQLE2UZ7BLEFUVWKFNI3B}

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	2026-05-18T01:23:55.634631Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

62acbe560b26a99f85642d2b6515a8d873869da474dbac32671892a00abd26f6

Aliases

arxiv: 1508.06815 · arxiv_version: 1508.06815v4 · doi: 10.48550/arxiv.1508.06815 · pith_short_12: MKWL4VQLE2UZ · pith_short_16: MKWL4VQLE2UZ7BLE · pith_short_8: MKWL4VQL

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/MKWL4VQLE2UZ7BLEFUVWKFNI3B \
  | 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: 62acbe560b26a99f85642d2b6515a8d873869da474dbac32671892a00abd26f6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eaf989db20ea1c9fa4ca0d396a89326ab528299e2a9bb369694d0f4685795e61",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2015-08-27T11:46:12Z",
    "title_canon_sha256": "40cac8fefea19d812cb212ca1ab268461e601753af444b733d2b4677ef7b28d3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.06815",
    "kind": "arxiv",
    "version": 4
  }
}