Pith Number

pith:ULLRAONJ

pith:2021:ULLRAONJ5RVZGP4UDWFBQ446VQ

not attested not anchored not stored refs pending

Property (QT) for 3-manifold groups

Hoang Thanh Nguyen, Suzhen Han, Wenyuan Yang

arxiv:2108.03361 v4 · 2021-08-07 · math.GT · 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{ULLRAONJ5RVZGP4UDWFBQ446VQ}

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.

Cited by

1 paper in Pith

Stable cylinders and fine structures for hyperbolic groups and curve graphs

Receipt and verification

First computed	2026-07-05T10:28:08.961033Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a2d71039a9ec6b933f941d8a18739eac07f99407785fc084a134b850cecf60d1

Aliases

arxiv: 2108.03361 · arxiv_version: 2108.03361v4 · doi: 10.48550/arxiv.2108.03361 · pith_short_12: ULLRAONJ5RVZ · pith_short_16: ULLRAONJ5RVZGP4U · pith_short_8: ULLRAONJ

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/ULLRAONJ5RVZGP4UDWFBQ446VQ \
  | 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: a2d71039a9ec6b933f941d8a18739eac07f99407785fc084a134b850cecf60d1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "84ac0a9d159ac92e1d290c781f8adbd60e2ece81c953ed46e8852425f8ebebd4",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2021-08-07T04:04:26Z",
    "title_canon_sha256": "9710624aebafbf5e4968ca9ee48fa0b31fd9c3288036d78c5ff8705a5d0caac8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2108.03361",
    "kind": "arxiv",
    "version": 4
  }
}