Pith Number

pith:VT5QOY2O

pith:2015:VT5QOY2OI4ZVZHDWCJDH2N6I2B

not attested not anchored not stored refs pending

Hypoelliptic heat kernel on nilpotent Lie groups

Malva Asaad, Maria Gordina

arxiv:1505.03928 v2 · 2015-05-15 · math.DG · math.AP · math.PR · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VT5QOY2OI4ZVZHDWCJDH2N6I2B}

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	2026-05-18T01:21:23.073771Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

acfb07634e47335c9c7612467d37c8d04487a1cd26c55a6210bb37bba3395941

Aliases

arxiv: 1505.03928 · arxiv_version: 1505.03928v2 · doi: 10.48550/arxiv.1505.03928 · pith_short_12: VT5QOY2OI4ZV · pith_short_16: VT5QOY2OI4ZVZHDW · pith_short_8: VT5QOY2O

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/VT5QOY2OI4ZVZHDWCJDH2N6I2B \
  | 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: acfb07634e47335c9c7612467d37c8d04487a1cd26c55a6210bb37bba3395941

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fade77230b0b1a921d1f9cb1baec84503dcde48d70b690c049023442f0c95742",
    "cross_cats_sorted": [
      "math.AP",
      "math.PR",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-05-15T00:44:39Z",
    "title_canon_sha256": "19aab05843c2656b7e7afdd9302fa6cfd37075511625143d65187e98a090e7f1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.03928",
    "kind": "arxiv",
    "version": 2
  }
}