Pith Number

pith:IBWLIGTF

pith:2010:IBWLIGTFVM6KTYWHAIEPFESQFX

not attested not anchored not stored refs pending

Three commuting, unital, completely positive maps that have no minimal dilation

Michael Skeide, Orr Shalit

arxiv:1012.2111 v2 · 2010-12-09 · 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{IBWLIGTFVM6KTYWHAIEPFESQFX}

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	2026-05-18T04:16:22.707183Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

406cb41a65ab3ca9e2c70208f292502df3dd54c1576fe8b82971060b5b13738c

Aliases

arxiv: 1012.2111 · arxiv_version: 1012.2111v2 · doi: 10.48550/arxiv.1012.2111 · pith_short_12: IBWLIGTFVM6K · pith_short_16: IBWLIGTFVM6KTYWH · pith_short_8: IBWLIGTF

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/IBWLIGTFVM6KTYWHAIEPFESQFX \
  | 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: 406cb41a65ab3ca9e2c70208f292502df3dd54c1576fe8b82971060b5b13738c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a6ce2ba8fd5fb3d23c9c5ae83b2993ed633e768d49da3fa2a88e8d9cc01a3e05",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2010-12-09T20:58:45Z",
    "title_canon_sha256": "c4035e540c3cb81bc48438ca0d79ad72253eb9b83b36eaac6610d8fc35f51a80"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.2111",
    "kind": "arxiv",
    "version": 2
  }
}