Pith Number

pith:DKD62QFF

pith:2015:DKD62QFFRN5MI4LCWTJPH2V7T3

not attested not anchored not stored refs pending

Prime ends in the Heisenberg group $\mathbb{H}_{1}$ and the boundary behavior of quasiconformal mappings

Ben Warhurst, Tomasz Adamowicz

arxiv:1512.09165 v1 · 2015-12-30 · 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{DKD62QFFRN5MI4LCWTJPH2V7T3}

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	2026-05-18T01:23:33.139529Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1a87ed40a58b7ac47162b4d2f3eabf9efe9e681a4a1d1ca8bed94bb03d85e375

Aliases

arxiv: 1512.09165 · arxiv_version: 1512.09165v1 · doi: 10.48550/arxiv.1512.09165 · pith_short_12: DKD62QFFRN5M · pith_short_16: DKD62QFFRN5MI4LC · pith_short_8: DKD62QFF

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/DKD62QFFRN5MI4LCWTJPH2V7T3 \
  | 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: 1a87ed40a58b7ac47162b4d2f3eabf9efe9e681a4a1d1ca8bed94bb03d85e375

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "767c86df368d9a1fb77ef113459422a2c73696cecbaed9f4d101e6f5cc26e48a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2015-12-30T22:04:45Z",
    "title_canon_sha256": "144449213657583f72d9e06dcef90a62370b48afa8c22f23f0ab297c4c7dc88e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.09165",
    "kind": "arxiv",
    "version": 1
  }
}