Pith Number

pith:TOKSI2I6

pith:2015:TOKSI2I6KISMTVJLF4EDC2ZFIW

not attested not anchored not stored refs pending

Transitivity degrees of countable groups and acylindrical hyperbolicity

D. Osin, M. Hull

arxiv:1501.04182 v1 · 2015-01-17 · 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{TOKSI2I6KISMTVJLF4EDC2ZFIW}

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	2026-05-18T02:29:09.830936Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9b9524691e5224c9d52b2f08316b2545bd08a3815fe4f8996b25fc7f139b28f8

Aliases

arxiv: 1501.04182 · arxiv_version: 1501.04182v1 · doi: 10.48550/arxiv.1501.04182 · pith_short_12: TOKSI2I6KISM · pith_short_16: TOKSI2I6KISMTVJL · pith_short_8: TOKSI2I6

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/TOKSI2I6KISMTVJLF4EDC2ZFIW \
  | 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: 9b9524691e5224c9d52b2f08316b2545bd08a3815fe4f8996b25fc7f139b28f8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "adf344cbe3e7baf62fe32085166d70827a22a6d955519a929cc09d439162ae2f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-01-17T09:43:55Z",
    "title_canon_sha256": "7146cd2e39d60e9d830a06ba1dd160e8cccd7b1e4016e1768a1a956273d829ea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.04182",
    "kind": "arxiv",
    "version": 1
  }
}