Pith Number

pith:CI2TNQ43

pith:2013:CI2TNQ4324AGQDN7EZCPP6IRNC

not attested not anchored not stored refs pending

Frequency of Sobolev dimension distortion of horizontal subgroups of Heisenberg groups

Jeremy T. Tyson, Kevin Wildrick, Zolt\'an M. Balogh

arxiv:1303.7094 v1 · 2013-03-28 · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CI2TNQ4324AGQDN7EZCPP6IRNC}

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	2026-05-18T03:29:38.260388Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

123536c39bd700680dbf2644f7f911689aabaca75edda0446f8d4a80c49865ab

Aliases

arxiv: 1303.7094 · arxiv_version: 1303.7094v1 · doi: 10.48550/arxiv.1303.7094 · pith_short_12: CI2TNQ4324AG · pith_short_16: CI2TNQ4324AGQDN7 · pith_short_8: CI2TNQ43

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/CI2TNQ4324AGQDN7EZCPP6IRNC \
  | 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: 123536c39bd700680dbf2644f7f911689aabaca75edda0446f8d4a80c49865ab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0265eecaadcc4c4d0d0eedaf5bd71defcbc94d0662583a3d7000215bfe876921",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2013-03-28T11:02:54Z",
    "title_canon_sha256": "678b9d451e2016948b99a008887fe0d620393bf5d0d31cff4d38a7a8099be2fd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.7094",
    "kind": "arxiv",
    "version": 1
  }
}