Pith Number

pith:G32CHCYG

pith:2024:G32CHCYGXDIEKITNXARL7MQKPA

not attested not anchored not stored refs pending

On gradient estimates of the heat semigroups on step-two Carnot groups

Sheng-Chen Mao, Ye Zhang

arxiv:2405.08605 v2 · 2024-05-14 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{G32CHCYGXDIEKITNXARL7MQKPA}

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	2026-05-17T23:39:18.430761Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

36f4238b06b8d045226db822bfb20a783f9157f34a3c226595957f696e122bfb

Aliases

arxiv: 2405.08605 · arxiv_version: 2405.08605v2 · doi: 10.48550/arxiv.2405.08605 · pith_short_12: G32CHCYGXDIE · pith_short_16: G32CHCYGXDIEKITN · pith_short_8: G32CHCYG

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/G32CHCYGXDIEKITNXARL7MQKPA \
  | 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: 36f4238b06b8d045226db822bfb20a783f9157f34a3c226595957f696e122bfb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aa4728d81fec9ad43c8199cf2158ead7904ba0ed852b2f736d8379acf90b366c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2024-05-14T13:42:47Z",
    "title_canon_sha256": "dd451c875d5be67094fa29cf7ac504178a21923968443263f7c4eec76b48ee05"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2405.08605",
    "kind": "arxiv",
    "version": 2
  }
}