Pith Number

pith:GQYP7T3D

pith:2010:GQYP7T3DRUX5EGFACKWERW7O2T

not attested not anchored not stored refs pending

A Harnack inequality and H\"older continuity for weak solutions to parabolic operators involving H\"ormander vector fields

Garrett Rea

arxiv:1010.1554 v1 · 2010-10-07 · 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{GQYP7T3DRUX5EGFACKWERW7O2T}

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	2026-05-18T04:39:40.231613Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3430ffcf638d2fd218a012ac48dbeed4fcb14996463cc53dc3fab11464711f51

Aliases

arxiv: 1010.1554 · arxiv_version: 1010.1554v1 · doi: 10.48550/arxiv.1010.1554 · pith_short_12: GQYP7T3DRUX5 · pith_short_16: GQYP7T3DRUX5EGFA · pith_short_8: GQYP7T3D

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/GQYP7T3DRUX5EGFACKWERW7O2T \
  | 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: 3430ffcf638d2fd218a012ac48dbeed4fcb14996463cc53dc3fab11464711f51

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "df3403eea28c51e66459a2a52ce905f0ab03893f6de577079a11ae4952bf9dab",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-10-07T21:46:44Z",
    "title_canon_sha256": "466d992f9f5638dda0f1c3d1e52db9aab9877a8ec5968df4cac15b7ff7eddf3b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.1554",
    "kind": "arxiv",
    "version": 1
  }
}