Pith Number

pith:HE2P7RGZ

pith:2016:HE2P7RGZRBPIQAXFSXUH3ZZ7YR

not attested not anchored not stored refs pending

Heat kernel asymptotics on sub-Riemannian manifolds with symmetries and applications to the bi-Heisenberg group

Davide Barilari, Robert W. Neel, Ugo Boscain

arxiv:1606.01159 v1 · 2016-06-03 · math.AP · math.DG · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HE2P7RGZRBPIQAXFSXUH3ZZ7YR}

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	2026-05-18T01:12:59.199262Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3934ffc4d9885e8802e595e87de73fc46418ab45798d6dd128c7816c39d87085

Aliases

arxiv: 1606.01159 · arxiv_version: 1606.01159v1 · doi: 10.48550/arxiv.1606.01159 · pith_short_12: HE2P7RGZRBPI · pith_short_16: HE2P7RGZRBPIQAXF · pith_short_8: HE2P7RGZ

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/HE2P7RGZRBPIQAXFSXUH3ZZ7YR \
  | 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: 3934ffc4d9885e8802e595e87de73fc46418ab45798d6dd128c7816c39d87085

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6264e6e0a66a2804e6828d3e061ef28bfd12da32c729e12cee90d73a67d6ed5f",
    "cross_cats_sorted": [
      "math.DG",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-06-03T16:05:03Z",
    "title_canon_sha256": "9c381fe7c2de8522b50952dee8d41be4bbb9e37d3d00abf7f2ab7afe7a898423"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.01159",
    "kind": "arxiv",
    "version": 1
  }
}