Pith Number

pith:P7VWJ4AO

pith:2016:P7VWJ4AOGSUKLTICH3E7KBYDBY

not attested not anchored not stored refs pending

Characterizations of the upper bound of Bakry-Emery curvature

Bo Wu

arxiv:1612.03714 v2 · 2016-12-12 · math.PR · 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{P7VWJ4AOGSUKLTICH3E7KBYDBY}

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	2026-05-17T23:59:03.858797Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7feb64f00e34a8a5cd023ec9f507030e2d843bcc11848f40220af423d5a2b83e

Aliases

arxiv: 1612.03714 · arxiv_version: 1612.03714v2 · doi: 10.48550/arxiv.1612.03714 · pith_short_12: P7VWJ4AOGSUK · pith_short_16: P7VWJ4AOGSUKLTIC · pith_short_8: P7VWJ4AO

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/P7VWJ4AOGSUKLTICH3E7KBYDBY \
  | 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: 7feb64f00e34a8a5cd023ec9f507030e2d843bcc11848f40220af423d5a2b83e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c1587d7de92b3e5e35c812db944f92337a7eebe2382204f7bf117aecc708925b",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-12-12T14:40:17Z",
    "title_canon_sha256": "116f7284b4363a01db489e471b4da076dcbd5bd26fb7307cb8364bdf6d50b400"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.03714",
    "kind": "arxiv",
    "version": 2
  }
}