Pith Number

pith:UKC7VHYJ

pith:2007:UKC7VHYJM7MTRHYKXPOUP6J4HC

not attested not anchored not stored refs pending

Bundles of C*-algebras and the KK(X;-,-)-bifunctor

Ezio Vasselli

arxiv:0711.3568 v1 · 2007-11-22 · 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{UKC7VHYJM7MTRHYKXPOUP6J4HC}

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	2026-05-18T04:08:05.382127Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a285fa9f0967d9389f0abbdd47f93c38a86b3e0a7622b77f86c89e905fdc8d8e

Aliases

arxiv: 0711.3568 · arxiv_version: 0711.3568v1 · doi: 10.48550/arxiv.0711.3568 · pith_short_12: UKC7VHYJM7MT · pith_short_16: UKC7VHYJM7MTRHYK · pith_short_8: UKC7VHYJ

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/UKC7VHYJM7MTRHYKXPOUP6J4HC \
  | 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: a285fa9f0967d9389f0abbdd47f93c38a86b3e0a7622b77f86c89e905fdc8d8e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "857be9a383221491f323aefcc894b0f57e0c8c1614179f35b9c366066a3f0fae",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "",
    "primary_cat": "math.KT",
    "submitted_at": "2007-11-22T13:30:52Z",
    "title_canon_sha256": "b00e22181fbeab9a1d0143ad01006adf179066f0660f0b7aea5ffd4ec6eb6510"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0711.3568",
    "kind": "arxiv",
    "version": 1
  }
}