Pith Number

pith:VAQGT5YE

pith:2017:VAQGT5YE73SREASLE4YVRTBG2Y

not attested not anchored not stored refs pending

Negligibility of parabolic elements in relatively hyperbolic groups

Motiejus Valiunas

arxiv:1708.02223 v2 · 2017-08-07 · 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{VAQGT5YE73SREASLE4YVRTBG2Y}

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	2026-05-18T00:38:20.292228Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a82069f704fee512024b273158cc26d605133cd0155b44a6d4d1daa0cb6ba663

Aliases

arxiv: 1708.02223 · arxiv_version: 1708.02223v2 · doi: 10.48550/arxiv.1708.02223 · pith_short_12: VAQGT5YE73SR · pith_short_16: VAQGT5YE73SREASL · pith_short_8: VAQGT5YE

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/VAQGT5YE73SREASLE4YVRTBG2Y \
  | 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: a82069f704fee512024b273158cc26d605133cd0155b44a6d4d1daa0cb6ba663

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "15a1909fe30992f4ff081fbf326c17311f548c91d11ba21a8bc498a5547b79dd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2017-08-07T17:43:25Z",
    "title_canon_sha256": "8de21a7b2be8ff1ad2808948f3e3e1eb448c399b4955945b05b853fa19848894"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1708.02223",
    "kind": "arxiv",
    "version": 2
  }
}