Pith Number

pith:O7TXYJC4

pith:2011:O7TXYJC4U4XZJSUNXSBPULZJWJ

not attested not anchored not stored refs pending

Positive curvature property for sub-Laplace on nilpotent Lie group of rank two

Bin Qian

arxiv:1112.3402 v1 · 2011-12-15 · math.PR · math.AP · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{O7TXYJC4U4XZJSUNXSBPULZJWJ}

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	2026-05-18T04:06:09.210534Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

77e77c245ca72f94ca8dbc82fa2f29b26d4d955ee8530c2ce8024258cf810a83

Aliases

arxiv: 1112.3402 · arxiv_version: 1112.3402v1 · doi: 10.48550/arxiv.1112.3402 · pith_short_12: O7TXYJC4U4XZ · pith_short_16: O7TXYJC4U4XZJSUN · pith_short_8: O7TXYJC4

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/O7TXYJC4U4XZJSUNXSBPULZJWJ \
  | 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: 77e77c245ca72f94ca8dbc82fa2f29b26d4d955ee8530c2ce8024258cf810a83

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "994faff09d22fb3827606a7518c9609b44827ad3726f3e02c79504fe992d533f",
    "cross_cats_sorted": [
      "math.AP",
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-12-15T01:02:33Z",
    "title_canon_sha256": "cfefd76cda9ed107293be1f0f9fcfa71d116328c11a64b67c1caac51da58cacc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.3402",
    "kind": "arxiv",
    "version": 1
  }
}