Pith Number

pith:E6IMYE35

pith:2018:E6IMYE35LRQ4TN6V5F5JDZBKLH

not attested not anchored not stored refs pending

A $C^m$ Whitney Extension Theorem for Horizontal Curves in the Heisenberg Group

Andrea Pinamonti, Gareth Speight, Scott Zimmerman

arxiv:1807.07936 v1 · 2018-07-20 · 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{E6IMYE35LRQ4TN6V5F5JDZBKLH}

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	2026-05-18T00:10:15.270814Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2790cc137d5c61c9b7d5e97a91e42a59d55410ed9ea7c57f1ac9cb3f0860a6ed

Aliases

arxiv: 1807.07936 · arxiv_version: 1807.07936v1 · doi: 10.48550/arxiv.1807.07936 · pith_short_12: E6IMYE35LRQ4 · pith_short_16: E6IMYE35LRQ4TN6V · pith_short_8: E6IMYE35

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/E6IMYE35LRQ4TN6V5F5JDZBKLH \
  | 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: 2790cc137d5c61c9b7d5e97a91e42a59d55410ed9ea7c57f1ac9cb3f0860a6ed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e055d15b8b00486272f4a7878b2dfdc9a6ab067143e308c13830db407740a8ce",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2018-07-20T16:52:36Z",
    "title_canon_sha256": "723e13ccf01e94b7877b3e51ebc58bc5dc9566e5f4f832a2ec2aa71b67878801"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.07936",
    "kind": "arxiv",
    "version": 1
  }
}