Pith Number

pith:QCU2WQTN

pith:2014:QCU2WQTNTF4PMDT3PVU6OKAWFX

not attested not anchored not stored refs pending

Spectra of Schreier graphs of Grigorchuk's group and Schroedinger operators with aperiodic order

Daniel Lenz, Rostislav Grigorchuk, Tatiana Nagnibeda

arxiv:1412.6822 v5 · 2014-12-21 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QCU2WQTNTF4PMDT3PVU6OKAWFX}

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	2026-05-18T00:29:15.918692Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

80a9ab426d9978f60e7b7d69e728162dfdb790a4ab680b0dbbf1eaad55851019

Aliases

arxiv: 1412.6822 · arxiv_version: 1412.6822v5 · doi: 10.48550/arxiv.1412.6822 · pith_short_12: QCU2WQTNTF4P · pith_short_16: QCU2WQTNTF4PMDT3 · pith_short_8: QCU2WQTN

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/QCU2WQTNTF4PMDT3PVU6OKAWFX \
  | 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: 80a9ab426d9978f60e7b7d69e728162dfdb790a4ab680b0dbbf1eaad55851019

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "10f5dd70a646e76936197f4d777b1eb6677c27738f8ce65564cd5aec34d6c434",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-12-21T19:28:32Z",
    "title_canon_sha256": "5642af078a44ef49cdb35c9777646f21cb1e6af96bf2e84b537fdeec2edbecbc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.6822",
    "kind": "arxiv",
    "version": 5
  }
}