Pith Number

pith:V2VTIH6Q

pith:2015:V2VTIH6QJQ7THD26JHU7LX7VR3

not attested not anchored not stored refs pending

Operator space and operator system analogs of Kirchberg's nuclear embedding theorem

Martino Lupini

arxiv:1502.05966 v2 · 2015-02-20 · math.OA · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{V2VTIH6QJQ7THD26JHU7LX7VR3}

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	2026-05-18T01:15:36.317777Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aeab341fd04c3f338f5e49e9f5dff58ec6531c0f780c0c5f72f8b54e12b2972b

Aliases

arxiv: 1502.05966 · arxiv_version: 1502.05966v2 · doi: 10.48550/arxiv.1502.05966 · pith_short_12: V2VTIH6QJQ7T · pith_short_16: V2VTIH6QJQ7THD26 · pith_short_8: V2VTIH6Q

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/V2VTIH6QJQ7THD26JHU7LX7VR3 \
  | 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: aeab341fd04c3f338f5e49e9f5dff58ec6531c0f780c0c5f72f8b54e12b2972b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1d02de2e95d2c5827c75b6894b3170918717d4aa027ef21f889f6c2987012e50",
    "cross_cats_sorted": [
      "math.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2015-02-20T18:36:53Z",
    "title_canon_sha256": "4aa480d722d435a3f97cc86322b50b5edb3a9990be983a2d0ac6c3709de4d0d4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.05966",
    "kind": "arxiv",
    "version": 2
  }
}