Pith Number

pith:JQSDXZGH

pith:2014:JQSDXZGHA2JRS7MKAPGSRQDIJ2

not attested not anchored not stored refs pending

Lusin Approximation and Horizontal Curves in Carnot Groups

Gareth Speight

arxiv:1412.2531 v4 · 2014-12-08 · 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{JQSDXZGHA2JRS7MKAPGSRQDIJ2}

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	2026-05-18T01:26:02.955493Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4c243be4c70693197d8a03cd28c0684eb0834d2a6c353645caaebd9aa4e99bca

Aliases

arxiv: 1412.2531 · arxiv_version: 1412.2531v4 · doi: 10.48550/arxiv.1412.2531 · pith_short_12: JQSDXZGHA2JR · pith_short_16: JQSDXZGHA2JRS7MK · pith_short_8: JQSDXZGH

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/JQSDXZGHA2JRS7MKAPGSRQDIJ2 \
  | 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: 4c243be4c70693197d8a03cd28c0684eb0834d2a6c353645caaebd9aa4e99bca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "49b3a1d1e226481bebbded3c3b8a670473d4e208dad7d8534a7edc8d26bc5620",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2014-12-08T12:09:59Z",
    "title_canon_sha256": "3e0c7bd49ea7ebe6633cb28e4d3c9b75e49f2d5bb18d660ba3d624e9b61731de"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.2531",
    "kind": "arxiv",
    "version": 4
  }
}