Pith Number

pith:27CJI4QX

pith:2016:27CJI4QXOUCNV6TYCUKLG6FBKL

not attested not anchored not stored refs pending

Differential forms on Dirichlet spaces and Bakry-\'Emery estimates on metric graphs

Daniel J. Kelleher, Fabrice Baudoin

arxiv:1604.02520 v4 · 2016-04-09 · math.PR · math.DG · 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{27CJI4QXOUCNV6TYCUKLG6FBKL}

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	2026-05-18T00:40:51.768468Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d7c49472177504dafa781514b378a152d8d6301e753c006a2bd3357725de6d6c

Aliases

arxiv: 1604.02520 · arxiv_version: 1604.02520v4 · doi: 10.48550/arxiv.1604.02520 · pith_short_12: 27CJI4QXOUCN · pith_short_16: 27CJI4QXOUCNV6TY · pith_short_8: 27CJI4QX

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/27CJI4QXOUCNV6TYCUKLG6FBKL \
  | 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: d7c49472177504dafa781514b378a152d8d6301e753c006a2bd3357725de6d6c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e66c4b078977439dbab1dca15165d190793ca7c8c2616d37f94b3176dc8c9a17",
    "cross_cats_sorted": [
      "math.DG",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-04-09T04:15:37Z",
    "title_canon_sha256": "e6d931ac2d2b4405874eb15047fb41c45386ebd943c8e31003bfaf48e26f2ee7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.02520",
    "kind": "arxiv",
    "version": 4
  }
}