Pith Number

pith:OO2BU33H

pith:2015:OO2BU33HQTM4AET66QGPVT2VAJ

not attested not anchored not stored refs pending

The Whitney Extension Theorem for $C^1$, horizontal curves in the Heisenberg group

Scott Zimmerman

arxiv:1507.02240 v3 · 2015-07-08 · 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{OO2BU33HQTM4AET66QGPVT2VAJ}

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	2026-05-18T01:00:12.775179Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

73b41a6f6784d9c0127ef40cfacf55024d9f111f3fdd0747d2441ca39228f845

Aliases

arxiv: 1507.02240 · arxiv_version: 1507.02240v3 · doi: 10.48550/arxiv.1507.02240 · pith_short_12: OO2BU33HQTM4 · pith_short_16: OO2BU33HQTM4AET6 · pith_short_8: OO2BU33H

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/OO2BU33HQTM4AET66QGPVT2VAJ \
  | 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: 73b41a6f6784d9c0127ef40cfacf55024d9f111f3fdd0747d2441ca39228f845

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a4d0339ce0c9f5df7af52fd0407242a5b2faf6914fba0b6682a4c4e43a7d45e2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2015-07-08T17:58:42Z",
    "title_canon_sha256": "add5d874a92375cf9a0e969823176fbd669cbb0881b7ffb144a06523a3b31ccc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.02240",
    "kind": "arxiv",
    "version": 3
  }
}