Pith Number

pith:T5NA4BP4

pith:2015:T5NA4BP4PI3XADNYCBJS7SGO3B

not attested not anchored not stored refs pending

On acylindrical hyperbolicity of groups with positive first $\ell^2$-Betti number

D. Osin

arxiv:1501.03066 v2 · 2015-01-13 · math.GR · math.GT · math.OA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{T5NA4BP4PI3XADNYCBJS7SGO3B}

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	2026-05-18T00:15:59.736135Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9f5a0e05fc7a37700db810532fc8ced86804e2d566a5d30ba8e7b459a46ea76a

Aliases

arxiv: 1501.03066 · arxiv_version: 1501.03066v2 · doi: 10.48550/arxiv.1501.03066 · pith_short_12: T5NA4BP4PI3X · pith_short_16: T5NA4BP4PI3XADNY · pith_short_8: T5NA4BP4

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/T5NA4BP4PI3XADNYCBJS7SGO3B \
  | 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: 9f5a0e05fc7a37700db810532fc8ced86804e2d566a5d30ba8e7b459a46ea76a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c608c84e0163d139ee9f3c591deab52aa42313422d00f8934e63346e7fe10b4c",
    "cross_cats_sorted": [
      "math.GT",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-01-13T16:37:32Z",
    "title_canon_sha256": "f773e26ceabc19f05249c4f81c434cd04dc8b4a46eecc78e397af7b63459d6c4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.03066",
    "kind": "arxiv",
    "version": 2
  }
}