Pith Number

pith:REFIMYVD

pith:2011:REFIMYVDMX5VYQMAZO3HPQOV4J

not attested not anchored not stored refs pending

Hyperbolically embedded virtually free subgroups of relatively hyperbolic groups

Saeko Yamagata, Shin-ichi Oguni, Yoshifumi Matsuda

arxiv:1109.2663 v3 · 2011-09-13 · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{REFIMYVDMX5VYQMAZO3HPQOV4J}

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	2026-05-18T03:55:12.282010Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

890a8662a365fb5c4180cbb677c1d5e257d8a10815f07aec8150ca9bf63bd25b

Aliases

arxiv: 1109.2663 · arxiv_version: 1109.2663v3 · doi: 10.48550/arxiv.1109.2663 · pith_short_12: REFIMYVDMX5V · pith_short_16: REFIMYVDMX5VYQMA · pith_short_8: REFIMYVD

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/REFIMYVDMX5VYQMAZO3HPQOV4J \
  | 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: 890a8662a365fb5c4180cbb677c1d5e257d8a10815f07aec8150ca9bf63bd25b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f5134ad0b049b2d60199c3aeb468fa9c0898bca136eb1306beec3f6471e35a05",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-09-13T02:04:29Z",
    "title_canon_sha256": "22f08d949d62645abbed67c03d6103c74c6a8365d74acb027521bd0de31f4589"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.2663",
    "kind": "arxiv",
    "version": 3
  }
}