Pith Number

pith:VX75TPBU

pith:2007:VX75TPBUXVYXZAN75Z2UV2X4C2

not attested not anchored not stored refs pending

Subelliptic Bourgain-Brezis Estimates on Groups

Jean Van Schaftingen, Sagun Chanillo

arxiv:0712.3730 v2 · 2007-12-21 · math.AP · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VX75TPBUXVYXZAN75Z2UV2X4C2}

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	2026-05-18T00:07:44.243627Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

adffd9bc34bd717c81bfee754aeafc16b746ddce1fbb3d5b1e041a0c38b28edc

Aliases

arxiv: 0712.3730 · arxiv_version: 0712.3730v2 · doi: 10.48550/arxiv.0712.3730 · pith_short_12: VX75TPBUXVYX · pith_short_16: VX75TPBUXVYXZAN7 · pith_short_8: VX75TPBU

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/VX75TPBUXVYXZAN75Z2UV2X4C2 \
  | 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: adffd9bc34bd717c81bfee754aeafc16b746ddce1fbb3d5b1e041a0c38b28edc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0d58e618f2ae7dce53be4c814a8386a6611b70c68090173b356fc03e79352997",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "",
    "primary_cat": "math.AP",
    "submitted_at": "2007-12-21T16:04:21Z",
    "title_canon_sha256": "0bd7e10a1675d2fb211245a88e8f6e2abb811bab84aff69c413636493183174d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0712.3730",
    "kind": "arxiv",
    "version": 2
  }
}