Pith Number

pith:TCCEUEZM

pith:2016:TCCEUEZMBBWNOJJKT4BUADQT7G

not attested not anchored not stored refs pending

Branching Systems and General Cuntz-Krieger Uniqueness Theorem for Ultragraph C*-algebras

Daniel Gon\c{c}alves, Danilo Royer, Hui Li

arxiv:1601.07005 v1 · 2016-01-26 · 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{TCCEUEZMBBWNOJJKT4BUADQT7G}

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	2026-05-18T01:21:59.327556Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

98844a132c086cd7252a9f03400e13f995898fb65ce00a48c2ee855165e2957a

Aliases

arxiv: 1601.07005 · arxiv_version: 1601.07005v1 · doi: 10.48550/arxiv.1601.07005 · pith_short_12: TCCEUEZMBBWN · pith_short_16: TCCEUEZMBBWNOJJK · pith_short_8: TCCEUEZM

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/TCCEUEZMBBWNOJJKT4BUADQT7G \
  | 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: 98844a132c086cd7252a9f03400e13f995898fb65ce00a48c2ee855165e2957a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "090c20db164e613bdab4dbceb0ddd630b7b23cacf814483fc2ed53f6f20f9347",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2016-01-26T13:11:43Z",
    "title_canon_sha256": "4b77b69fb81f35fcbee7b0ec192ec8ccbd642e443e36fe5981406d79365a3809"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.07005",
    "kind": "arxiv",
    "version": 1
  }
}