Pith Number

pith:BX7OJZG5

pith:2026:BX7OJZG5OP5YWW353YQQ2K22GS

not attested not anchored not stored refs pending

Nonnegative Bakry--\'Emery Curvature on Bounded-Degree Graphs Implies Volume Doubling and Poincar\'e Inequalities

Qi Guo, Xueping Huang, Yi C. Huang

arxiv:2607.15522 v1 · 2026-07-17 · math.DG · math.CO · 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{BX7OJZG5OP5YWW353YQQ2K22GS}

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	2026-07-20T00:18:38.130603Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0dfee4e4dd73fb8b5b7dde210d2b5a34b3535307bc360b0777195b1dd4d7d4fa

Aliases

arxiv: 2607.15522 · arxiv_version: 2607.15522v1 · doi: 10.48550/arxiv.2607.15522 · pith_short_12: BX7OJZG5OP5Y · pith_short_16: BX7OJZG5OP5YWW35 · pith_short_8: BX7OJZG5

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/BX7OJZG5OP5YWW353YQQ2K22GS \
  | 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: 0dfee4e4dd73fb8b5b7dde210d2b5a34b3535307bc360b0777195b1dd4d7d4fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "514c5f00378e2e6d89a7cbfe62fa11b08afbe8eb5bd3852522efe5a851593110",
    "cross_cats_sorted": [
      "math.CO",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-07-17T00:13:49Z",
    "title_canon_sha256": "338eb3ef18ab148f6396aa59c2a7fcd76231d898fc7ba716d4acc25fb5a653cf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.15522",
    "kind": "arxiv",
    "version": 1
  }
}