Pith Number

pith:QM55NYH3

pith:2012:QM55NYH3XCDOCZPDWPD45OT7DV

not attested not anchored not stored refs pending

Small time asymptotics for an example of strictly hypoelliptic heat kernel

Jacques Franchi

arxiv:1209.1946 v1 · 2012-09-10 · 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{QM55NYH3XCDOCZPDWPD45OT7DV}

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	2026-05-18T03:45:54.026029Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

833bd6e0fbb886e165e3b3c7ceba7f1d4b1884e835d820b0ffa49118feb7c9e2

Aliases

arxiv: 1209.1946 · arxiv_version: 1209.1946v1 · doi: 10.48550/arxiv.1209.1946 · pith_short_12: QM55NYH3XCDO · pith_short_16: QM55NYH3XCDOCZPD · pith_short_8: QM55NYH3

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/QM55NYH3XCDOCZPDWPD45OT7DV \
  | 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: 833bd6e0fbb886e165e3b3c7ceba7f1d4b1884e835d820b0ffa49118feb7c9e2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6b0c33eecfa3b5d9c6ce8aa1a883e285f777c4ed5507120e91bed74c265f13b8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-09-10T11:15:51Z",
    "title_canon_sha256": "7373da40ae5e6a7a9949e45b232b077858912b1927bacd117b105be3ae023807"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.1946",
    "kind": "arxiv",
    "version": 1
  }
}