Pith Number

pith:TTGHN3D5

pith:2003:TTGHN3D5FVBVV4RX44L6DOZWBY

not attested not anchored not stored refs pending

Product systems of graphs and the Toeplitz algebras of higher-rank graphs

Aidan Sims, Iain Raeburn

arxiv:math/0305371 v1 · 2003-05-27 · 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{TTGHN3D5FVBVV4RX44L6DOZWBY}

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	2026-05-18T01:05:28.856654Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9ccc76ec7d2d435af237e717e1bb360e1174469bbe0b7db89d40000edcc50a16

Aliases

arxiv: math/0305371 · arxiv_version: math/0305371v1 · doi: 10.48550/arxiv.math/0305371 · pith_short_12: TTGHN3D5FVBV · pith_short_16: TTGHN3D5FVBVV4RX · pith_short_8: TTGHN3D5

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/TTGHN3D5FVBVV4RX44L6DOZWBY \
  | 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: 9ccc76ec7d2d435af237e717e1bb360e1174469bbe0b7db89d40000edcc50a16

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "66929c3adf931c00483b12025058c15b328501d2309bc6f4f63756c0a25bb0fd",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.OA",
    "submitted_at": "2003-05-27T01:38:02Z",
    "title_canon_sha256": "92e7a1617c09b102c9dc85804511354d1ba36011cd35769ca4820e7f46e50aab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0305371",
    "kind": "arxiv",
    "version": 1
  }
}