Pith Number

pith:AHY4SCVV

pith:2016:AHY4SCVVD2YVTSFS7BT6DGN3G5

not attested not anchored not stored refs pending

Sharp Davies-Gaffney-Grigor'yan Lemma on Graphs

Bobo Hua, Frank Bauer, Shing-Tung Yau

arxiv:1604.01911 v1 · 2016-04-07 · math.DG · math.MG · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AHY4SCVVD2YVTSFS7BT6DGN3G5}

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	2026-05-18T01:17:31.739348Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

01f1c90ab51eb159c8b2f867e199bb3768742daeba3315165ce4e210b12631ae

Aliases

arxiv: 1604.01911 · arxiv_version: 1604.01911v1 · doi: 10.48550/arxiv.1604.01911 · pith_short_12: AHY4SCVVD2YV · pith_short_16: AHY4SCVVD2YVTSFS · pith_short_8: AHY4SCVV

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/AHY4SCVVD2YVTSFS7BT6DGN3G5 \
  | 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: 01f1c90ab51eb159c8b2f867e199bb3768742daeba3315165ce4e210b12631ae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "acf0b3ab1dd22cc06912895eb3a1ae6a8b2ce086d93a57a4d7e6bc594f453788",
    "cross_cats_sorted": [
      "math.MG",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2016-04-07T08:10:29Z",
    "title_canon_sha256": "c6b84170b47abc78496bb12737f7b38163c85bbf7a7e67855cc1429ee0c792dc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.01911",
    "kind": "arxiv",
    "version": 1
  }
}