Pith Number

pith:DZNP62XM

pith:2013:DZNP62XMJSPENYSC3MTMH2FBQ3

not attested not anchored not stored refs pending

The Lusin theorem and horizontal graphs in the Heisenberg group

Jacob Mirra, Piotr Hajlasz

arxiv:1306.6355 v1 · 2013-06-26 · math.FA · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DZNP62XMJSPENYSC3MTMH2FBQ3}

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	2026-05-18T03:19:45.015596Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1e5aff6aec4c9e46e242db26c3e8a186ff38e8aadeb7017290e216a1fec50a90

Aliases

arxiv: 1306.6355 · arxiv_version: 1306.6355v1 · doi: 10.48550/arxiv.1306.6355 · pith_short_12: DZNP62XMJSPE · pith_short_16: DZNP62XMJSPENYSC · pith_short_8: DZNP62XM

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/DZNP62XMJSPENYSC3MTMH2FBQ3 \
  | 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: 1e5aff6aec4c9e46e242db26c3e8a186ff38e8aadeb7017290e216a1fec50a90

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2c929ca9ccf59404c6a3599452cdd4b5e6dc2114bb9a50e1f233eccbc8427265",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-06-26T20:34:37Z",
    "title_canon_sha256": "bf88c2edc11af86c0d1b9290ad099ec61823bd5134e77f4aa396c465a38b323f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.6355",
    "kind": "arxiv",
    "version": 1
  }
}