Pith Number

pith:EHPKVMDD

pith:2014:EHPKVMDDR6OLQEW4R2SFQ27SPE

not attested not anchored not stored refs pending

Li-Yau inequality on finite graphs via non-linear curvature dimension conditions

Florentin M\"unch

arxiv:1412.3340 v1 · 2014-12-10 · 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{EHPKVMDDR6OLQEW4R2SFQ27SPE}

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	2026-05-18T02:31:36.918386Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

21deaab0638f9cb812dc8ea4586bf27908e33b2887b72baf1cddce03d334169d

Aliases

arxiv: 1412.3340 · arxiv_version: 1412.3340v1 · doi: 10.48550/arxiv.1412.3340 · pith_short_12: EHPKVMDDR6OL · pith_short_16: EHPKVMDDR6OLQEW4 · pith_short_8: EHPKVMDD

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/EHPKVMDDR6OLQEW4R2SFQ27SPE \
  | 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: 21deaab0638f9cb812dc8ea4586bf27908e33b2887b72baf1cddce03d334169d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "979b3ee3b4cb50a48cf51ee686eefe89ca8c39ce0e45fd1164311f3ecc23ee74",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2014-12-10T15:33:34Z",
    "title_canon_sha256": "e548ab523f3226ab3171615f8c444ade9786dbb9e9b977c7b971133e398ad120"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.3340",
    "kind": "arxiv",
    "version": 1
  }
}