Pith Number

pith:IVHSXQBI

pith:2015:IVHSXQBIFDYI3JHGHYH5PWS7ZP

not attested not anchored not stored refs pending

Harnack inequality for hypoelliptic second order partial differential operators

Alessia E. Kogoj, Sergio Polidoro

arxiv:1509.05245 v1 · 2015-09-17 · 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{IVHSXQBIFDYI3JHGHYH5PWS7ZP}

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	2026-05-18T01:32:49.511747Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

454f2bc02828f08da4e63e0fd7da5fcbd80e01feac3d7d33f39b1f94366ee228

Aliases

arxiv: 1509.05245 · arxiv_version: 1509.05245v1 · doi: 10.48550/arxiv.1509.05245 · pith_short_12: IVHSXQBIFDYI · pith_short_16: IVHSXQBIFDYI3JHG · pith_short_8: IVHSXQBI

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/IVHSXQBIFDYI3JHGHYH5PWS7ZP \
  | 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: 454f2bc02828f08da4e63e0fd7da5fcbd80e01feac3d7d33f39b1f94366ee228

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "458e5c2195c5751e753750e5c6ee973a4bb07997298aab361c92b66075f6637f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-09-17T13:18:08Z",
    "title_canon_sha256": "4584b249bdec419fe158307c11800796c0cdad275b0c887679ffceacc6821bd1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.05245",
    "kind": "arxiv",
    "version": 1
  }
}