Pith Number

pith:RZ5WT4GP

pith:2017:RZ5WT4GPDCLLL3IBSSCV5KHAZP

not attested not anchored not stored refs pending

Surface group amalgams that (don't) act on 3-manifolds

Emily Stark, G. Christopher Hruska, Hung Cong Tran

arxiv:1705.01361 v2 · 2017-05-03 · 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{RZ5WT4GPDCLLL3IBSSCV5KHAZP}

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	2026-05-18T00:06:41.916501Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8e7b69f0cf1896b5ed0194855ea8e0cbcd1992bec00533c8bdc5bdc0ad41d80a

Aliases

arxiv: 1705.01361 · arxiv_version: 1705.01361v2 · doi: 10.48550/arxiv.1705.01361 · pith_short_12: RZ5WT4GPDCLL · pith_short_16: RZ5WT4GPDCLLL3IB · pith_short_8: RZ5WT4GP

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/RZ5WT4GPDCLLL3IBSSCV5KHAZP \
  | 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: 8e7b69f0cf1896b5ed0194855ea8e0cbcd1992bec00533c8bdc5bdc0ad41d80a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "01015f7a84d028aab678da569193c5abc1491933be954891e77b84184421092d",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2017-05-03T11:13:56Z",
    "title_canon_sha256": "dac218106f3da9814bb2020f262036524270d78f1132bf4d0f500331c158f31d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.01361",
    "kind": "arxiv",
    "version": 2
  }
}