Pith Number

pith:MN3TGV5Q

pith:2010:MN3TGV5QOHF75HVFOPE2KACJAP

not attested not anchored not stored refs pending

Presentations and Tietze transformations of C*-algebras

Will Grilliette

arxiv:1012.1275 v3 · 2010-12-06 · 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{MN3TGV5QOHF75HVFOPE2KACJAP}

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	2026-05-18T00:43:10.062644Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

63773357b071cbfe9ea573c9a5004903c717197b0598380fa5e8aae39922f3db

Aliases

arxiv: 1012.1275 · arxiv_version: 1012.1275v3 · doi: 10.48550/arxiv.1012.1275 · pith_short_12: MN3TGV5QOHF7 · pith_short_16: MN3TGV5QOHF75HVF · pith_short_8: MN3TGV5Q

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/MN3TGV5QOHF75HVFOPE2KACJAP \
  | 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: 63773357b071cbfe9ea573c9a5004903c717197b0598380fa5e8aae39922f3db

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "084003dcc6b89ad0e87876c0e2e149652981f0ecca925f4529a4d41d649b3ef4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2010-12-06T18:38:33Z",
    "title_canon_sha256": "3063eb431dfa7dae84f2391b70c8b7faedca0de6425252397205675a9df42236"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.1275",
    "kind": "arxiv",
    "version": 3
  }
}