Pith Number

pith:OYZ4P3JL

pith:2015:OYZ4P3JLLBMLYDMKYJGKBJCTRE

not attested not anchored not stored refs pending

Regularity for Subelliptic PDE Through Uniform Estimates in Multi-Scale Geometries

Giovanna Citti, Luca Capogna

arxiv:1504.04762 v1 · 2015-04-18 · 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{OYZ4P3JLLBMLYDMKYJGKBJCTRE}

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	2026-05-18T02:18:24.830882Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7633c7ed2b5858bc0d8ac24ca0a453890a15dd4d256bab5d01685b8f6715f73f

Aliases

arxiv: 1504.04762 · arxiv_version: 1504.04762v1 · doi: 10.48550/arxiv.1504.04762 · pith_short_12: OYZ4P3JLLBML · pith_short_16: OYZ4P3JLLBMLYDMK · pith_short_8: OYZ4P3JL

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/OYZ4P3JLLBMLYDMKYJGKBJCTRE \
  | 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: 7633c7ed2b5858bc0d8ac24ca0a453890a15dd4d256bab5d01685b8f6715f73f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "12df4e5a7bca640e46e69952bcfead66888884a7856ed2d0143674450804881e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-04-18T21:09:55Z",
    "title_canon_sha256": "88144fb006781cd2b07bac58c63ab7ceb7b2187e2a11e84d465dba467a1a384e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.04762",
    "kind": "arxiv",
    "version": 1
  }
}