Pith Number

pith:7H5XYSQG

pith:2021:7H5XYSQG5TZ2AQEDOO5S7ASL3B

not attested not anchored not stored refs pending

On the small measure expansion phenomenon in connected noncompact nonabelian groups

Chieu-Minh Tran, Jinpeng An, Ruixiang Zhang, Yifan Jing

arxiv:2111.05236 v1 · 2021-11-09 · math.GR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7H5XYSQG5TZ2AQEDOO5S7ASL3B}

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.

Cited by

1 paper in Pith

Measure doubling in unimodular locally compact groups and quotients

Receipt and verification

First computed	2026-07-05T03:30:22.837245Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f9fb7c4a06ecf3a0408373bb2f824bd84f56d8f14895896b39a0c664022547f1

Aliases

arxiv: 2111.05236 · arxiv_version: 2111.05236v1 · doi: 10.48550/arxiv.2111.05236 · pith_short_12: 7H5XYSQG5TZ2 · pith_short_16: 7H5XYSQG5TZ2AQED · pith_short_8: 7H5XYSQG

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/7H5XYSQG5TZ2AQEDOO5S7ASL3B \
  | 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: f9fb7c4a06ecf3a0408373bb2f824bd84f56d8f14895896b39a0c664022547f1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7a5d532e4e58c482e18c11bf7704b0bac5cbefee4c248c769e7eb2dcff9d2cbf",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2021-11-09T16:16:01Z",
    "title_canon_sha256": "0045ca3ceebe52da076cd299b8ca14e374b22e86154f0ad1fd5d2f62012e11b4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2111.05236",
    "kind": "arxiv",
    "version": 1
  }
}