Pith Number

pith:HVDV2I2M

pith:2012:HVDV2I2MQV3XMGRVR5RT72GTFV

not attested not anchored not stored refs pending

Singularities of the divergence of continuous vector fields and uniform Hausdorff estimates

Augusto C. Ponce

arxiv:1206.0624 v2 · 2012-06-04 · math.AP · 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{HVDV2I2MQV3XMGRVR5RT72GTFV}

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	2026-05-18T02:48:24.801862Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3d475d234c8577761a358f633fe8d32d6a7b97916528842eba6dfb6702198f0e

Aliases

arxiv: 1206.0624 · arxiv_version: 1206.0624v2 · doi: 10.48550/arxiv.1206.0624 · pith_short_12: HVDV2I2MQV3X · pith_short_16: HVDV2I2MQV3XMGRV · pith_short_8: HVDV2I2M

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/HVDV2I2MQV3XMGRVR5RT72GTFV \
  | 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: 3d475d234c8577761a358f633fe8d32d6a7b97916528842eba6dfb6702198f0e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "582aad8dd44c601dddf74452ca7f7a3ff6834ca5b73e817ffdc764bad45d3fbc",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-06-04T13:54:28Z",
    "title_canon_sha256": "3b078670e55fd018372fbe1c4ba987ac57c3dfa39039da5ca1aa5ba6335bd86a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.0624",
    "kind": "arxiv",
    "version": 2
  }
}