Pith Number

pith:AHEMVFXK

pith:2026:AHEMVFXKMG2VW3BASIR4JKY47X

not attested not anchored not stored refs pending

Multi-Granularity Position Embedding of Graphs via Granular-Ball for Link Prediction

Cheng Liu, Sen Zhao, Shuyin Xia, Wei Wang, Yi Liu, Yi Wang, Zhiyuan Liu

arxiv:2607.29115 v1 · 2026-07-31 · cs.SI · cs.AI

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AHEMVFXKMG2VW3BASIR4JKY47X}

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	2026-08-03T01:19:09.142509Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

01c8ca96ea61b55b6c209223c4ab1cfdd134c0e96814654e4652ab5a58164c20

Aliases

arxiv: 2607.29115 · arxiv_version: 2607.29115v1 · doi: 10.48550/arxiv.2607.29115 · pith_short_12: AHEMVFXKMG2V · pith_short_16: AHEMVFXKMG2VW3BA · pith_short_8: AHEMVFXK

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/AHEMVFXKMG2VW3BASIR4JKY47X \
  | 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: 01c8ca96ea61b55b6c209223c4ab1cfdd134c0e96814654e4652ab5a58164c20

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4b9c6fb216bfc07add6accf0170bbbcdecaec0e02603f7c56f9bc855f62f18db",
    "cross_cats_sorted": [
      "cs.AI"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.SI",
    "submitted_at": "2026-07-31T07:44:11Z",
    "title_canon_sha256": "4297dab50dca6d192f1b2e9cf2110c0e4a4cb436b940dc751766ddf84083b010"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.29115",
    "kind": "arxiv",
    "version": 1
  }
}