Pith Number

pith:AVTLAEN7

pith:2014:AVTLAEN7YTJYN6H2XYODHNDZKZ

not attested not anchored not stored refs pending

Volume doubling, Poincar\'e inequality and Guassian heat kernel estimate for nonnegative curvature graphs

Paul Horn, Shing-Tung Yau, Shuang Liu, Yong Lin

arxiv:1411.5087 v4 · 2014-11-19 · math.DG · math.CO · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AVTLAEN7YTJYN6H2XYODHNDZKZ}

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	2026-05-18T01:25:16.064548Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0566b011bfc4d386f8fabe1c33b479565f3a1d854c7e0137dc870dea1f4c3234

Aliases

arxiv: 1411.5087 · arxiv_version: 1411.5087v4 · doi: 10.48550/arxiv.1411.5087 · pith_short_12: AVTLAEN7YTJY · pith_short_16: AVTLAEN7YTJYN6H2 · pith_short_8: AVTLAEN7

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/AVTLAEN7YTJYN6H2XYODHNDZKZ \
  | 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: 0566b011bfc4d386f8fabe1c33b479565f3a1d854c7e0137dc870dea1f4c3234

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aaeaa78ca950b4a7b833adf5632b5c2fb1aac9dadac4526f93374001a37a7a8e",
    "cross_cats_sorted": [
      "math.CO",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2014-11-19T01:26:59Z",
    "title_canon_sha256": "1b00552931bea208c08feae3e83d302bb8ea5b777a587817d0154de8a7adbb6c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1411.5087",
    "kind": "arxiv",
    "version": 4
  }
}