Pith Number

pith:4KZL3QKI

pith:2015:4KZL3QKI5WFZSSTCOUMCKEZMYT

not attested not anchored not stored refs pending

Tilings of amenable groups

Dawid Huczek, Guohua Zhang, Tomasz Downarowicz

arxiv:1502.02413 v1 · 2015-02-09 · 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{4KZL3QKI5WFZSSTCOUMCKEZMYT}

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	2026-05-18T02:27:42.423702Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e2b2bdc148ed8b994a62751825132cc4f7e65ce571537eea8adb6f23e2762f35

Aliases

arxiv: 1502.02413 · arxiv_version: 1502.02413v1 · doi: 10.48550/arxiv.1502.02413 · pith_short_12: 4KZL3QKI5WFZ · pith_short_16: 4KZL3QKI5WFZSSTC · pith_short_8: 4KZL3QKI

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/4KZL3QKI5WFZSSTCOUMCKEZMYT \
  | 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: e2b2bdc148ed8b994a62751825132cc4f7e65ce571537eea8adb6f23e2762f35

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "43408e0ae8f5187e2f37e619e844643ec18a61257d4bba6c60a0dd3b3aac8e7d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-02-09T10:07:53Z",
    "title_canon_sha256": "f9b6f6104ae359a9eb1bc2673466e0541c869995185c30c5d029fe8c95907d8a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.02413",
    "kind": "arxiv",
    "version": 1
  }
}