Pith Number

pith:TVFQMBM5

pith:2019:TVFQMBM5ZIUD6EGHVQPI6Z6DAO

not attested not anchored not stored refs pending

A $C^m$ Lusin Approximation Theorem for Horizontal Curves in the Heisenberg Group

Andrea Pinamonti, Gareth Speight, Marco Capolli

arxiv:1908.07624 v2 · 2019-08-20 · math.MG · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TVFQMBM5ZIUD6EGHVQPI6Z6DAO}

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	2026-07-05T03:44:49.032335Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9d4b06059dca283f10c7ac1e8f67c303b3d1b53e27976a8c2941117be9cb5dcd

Aliases

arxiv: 1908.07624 · arxiv_version: 1908.07624v2 · doi: 10.48550/arxiv.1908.07624 · pith_short_12: TVFQMBM5ZIUD · pith_short_16: TVFQMBM5ZIUD6EGH · pith_short_8: TVFQMBM5

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/TVFQMBM5ZIUD6EGHVQPI6Z6DAO \
  | 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: 9d4b06059dca283f10c7ac1e8f67c303b3d1b53e27976a8c2941117be9cb5dcd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "246f712be4e8477b6d63bc73288aaa64398cfcd32b7e3982321f4aea1d38a380",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2019-08-20T21:57:20Z",
    "title_canon_sha256": "9ca665d8da4be85e1ef6e9d3b7205912bb8f6fdf5423a622e8e8a71b7e88b654"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.07624",
    "kind": "arxiv",
    "version": 2
  }
}