Pith Number

pith:AKOQ46QD

pith:2013:AKOQ46QD6IK7ID6MP2DHGV3HHV

not attested not anchored not stored refs pending

Notes on relatively hyperbolic groups and relatively quasiconvex subgroups

Saeko Yamagata, Shin-ichi Oguni, Yoshifumi Matsuda

arxiv:1301.3201 v1 · 2013-01-15 · 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{AKOQ46QD6IK7ID6MP2DHGV3HHV}

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	2026-05-18T03:36:26.246572Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

029d0e7a03f215f40fcc7e867357673d78ccee2c5dcfa0ccb5849e98619946fc

Aliases

arxiv: 1301.3201 · arxiv_version: 1301.3201v1 · doi: 10.48550/arxiv.1301.3201 · pith_short_12: AKOQ46QD6IK7 · pith_short_16: AKOQ46QD6IK7ID6M · pith_short_8: AKOQ46QD

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/AKOQ46QD6IK7ID6MP2DHGV3HHV \
  | 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: 029d0e7a03f215f40fcc7e867357673d78ccee2c5dcfa0ccb5849e98619946fc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9734d36b4bdaa1021da410e093c38e8a7605ec804d79561c3e3748955adaf87a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-01-15T01:53:23Z",
    "title_canon_sha256": "b6ee8bab4f327530e666180e0b78b373adf90bac11a94ad6be44b3e72dc98e3f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.3201",
    "kind": "arxiv",
    "version": 1
  }
}