Pith Number

pith:TMPPDP2X

pith:2018:TMPPDP2XDI3EVAC64PAJUVFUYL

not attested not anchored not stored refs pending

Equations in acylindrically hyperbolic groups and verbal closedness

Oleg Bogopolski

arxiv:1805.08071 v2 · 2018-05-18 · 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{TMPPDP2XDI3EVAC64PAJUVFUYL}

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	2026-05-17T23:50:59.682587Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9b1ef1bf571a364a805ee3c09a54b4c2e48c96c0619d56391c94b1a20a1c85cd

Aliases

arxiv: 1805.08071 · arxiv_version: 1805.08071v2 · doi: 10.48550/arxiv.1805.08071 · pith_short_12: TMPPDP2XDI3E · pith_short_16: TMPPDP2XDI3EVAC6 · pith_short_8: TMPPDP2X

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/TMPPDP2XDI3EVAC64PAJUVFUYL \
  | 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: 9b1ef1bf571a364a805ee3c09a54b4c2e48c96c0619d56391c94b1a20a1c85cd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "127c9ebef16493c298ba249889ecb5ac916ab715bd7c2e3a4bc9af5a1b68bc68",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2018-05-18T05:58:40Z",
    "title_canon_sha256": "47c69cb66d51d121e990143a39ae5e59dd557d30bcf3c724fcee3e3072bf44e2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1805.08071",
    "kind": "arxiv",
    "version": 2
  }
}