Pith Number

pith:PFZM3SK7

pith:2009:PFZM3SK7MCHOCCHJS2UXJ2NERW

not attested not anchored not stored refs pending

Gradient estimates for the subelliptic heat kernel on H-type groups

Nathaniel Eldredge

arxiv:0904.1781 v2 · 2009-04-11 · math.AP · math.DG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PFZM3SK7MCHOCCHJS2UXJ2NERW}

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	2026-05-18T02:49:03.567975Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7972cdc95f608ee108e996a974e9a48d899ffff37ed04d391e7469d41e5ce068

Aliases

arxiv: 0904.1781 · arxiv_version: 0904.1781v2 · doi: 10.48550/arxiv.0904.1781 · pith_short_12: PFZM3SK7MCHO · pith_short_16: PFZM3SK7MCHOCCHJ · pith_short_8: PFZM3SK7

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/PFZM3SK7MCHOCCHJS2UXJ2NERW \
  | 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: 7972cdc95f608ee108e996a974e9a48d899ffff37ed04d391e7469d41e5ce068

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b4e5413ef2a73026990ed2b2cfa63330319240959b3dbc65ea13ce76c6c82fd8",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2009-04-11T07:06:05Z",
    "title_canon_sha256": "fb53333bfbd496b4caed52b865de2e8dae36636bc513de43d27a497b12d392dc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0904.1781",
    "kind": "arxiv",
    "version": 2
  }
}