Pith Number

pith:SDLF42CQ

pith:2015:SDLF42CQLAZJG57YO4IZVMGNVY

not attested not anchored not stored refs pending

A concrete approach to diagonal short time asymptotics of heat kernels associated with sub-Laplacian on CR manifolds

Hiroki Kondo

arxiv:1511.09338 v1 · 2015-11-30 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SDLF42CQLAZJG57YO4IZVMGNVY}

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	2026-05-18T01:25:40.519163Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

90d65e685058329377f877119ab0cdae1113cb5dfa54f880126d8d6ce6014752

Aliases

arxiv: 1511.09338 · arxiv_version: 1511.09338v1 · doi: 10.48550/arxiv.1511.09338 · pith_short_12: SDLF42CQLAZJ · pith_short_16: SDLF42CQLAZJG57Y · pith_short_8: SDLF42CQ

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/SDLF42CQLAZJG57YO4IZVMGNVY \
  | 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: 90d65e685058329377f877119ab0cdae1113cb5dfa54f880126d8d6ce6014752

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "39984c6308e0e6eea23bf77e2fe7c4342b5be20fb0ef7fb6c2772a48706c208f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-11-30T14:56:01Z",
    "title_canon_sha256": "68c90fc781134eb779a0f42de4a9c2cbd7fe5d74824567469b96e4ed8d45b878"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.09338",
    "kind": "arxiv",
    "version": 1
  }
}