Pith Number

pith:XNQQHHAG

pith:2025:XNQQHHAG5MVNMKGVILQTYJ647O

not attested not anchored not stored refs pending

Infinite graphs satisfying the Bakry-Emery curvature condition CD(0, n): The modified heat equation and applications to geometric analysis

Emmanuel Russ (I2M), Herv\'e Pajot (IF)

arxiv:2507.19235 v1 · 2025-07-25 · 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{XNQQHHAG5MVNMKGVILQTYJ647O}

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	2026-07-05T11:43:21.982739Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bb61039c06eb2ad628d542e13c27dcfba85cdff92e03a29076b50c4300689e50

Aliases

arxiv: 2507.19235 · arxiv_version: 2507.19235v1 · doi: 10.48550/arxiv.2507.19235 · pith_short_12: XNQQHHAG5MVN · pith_short_16: XNQQHHAG5MVNMKGV · pith_short_8: XNQQHHAG

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/XNQQHHAG5MVNMKGVILQTYJ647O \
  | 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: bb61039c06eb2ad628d542e13c27dcfba85cdff92e03a29076b50c4300689e50

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "71e047968b4e2d510f03e11dca2e575e28e8546e623cf5397ad727435c5ecb25",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2025-07-25T12:58:56Z",
    "title_canon_sha256": "9f049f871afc438445cd2ce63cafef524cc6a06023294cd500f87680d673dd2e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.19235",
    "kind": "arxiv",
    "version": 1
  }
}