Pith Number

pith:GRAKVKMN

pith:2026:GRAKVKMNMHZCNFHPIXOAYGMVM3

not attested not anchored not stored refs pending

Topological measures in weighted hypergraphs

Andrei M. Raigorodskii, Charo. I. del Genio, Daniil Musatov, Ekaterina Vasilyeva, Liubov Tupikina, Stefano Boccaletti

arxiv:2607.20962 v1 · 2026-07-23 · physics.soc-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GRAKVKMNMHZCNFHPIXOAYGMVM3}

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	2026-07-24T01:23:44.385750Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3440aaa98d61f22694ef45dc0c199566f771e4575925edada870ca7a24d3d643

Aliases

arxiv: 2607.20962 · arxiv_version: 2607.20962v1 · doi: 10.48550/arxiv.2607.20962 · pith_short_12: GRAKVKMNMHZC · pith_short_16: GRAKVKMNMHZCNFHP · pith_short_8: GRAKVKMN

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/GRAKVKMNMHZCNFHPIXOAYGMVM3 \
  | 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: 3440aaa98d61f22694ef45dc0c199566f771e4575925edada870ca7a24d3d643

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2e2f9425fb5e540067382e7e7ca70852a5727f9b702885ab6ddff3f77b99d049",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "physics.soc-ph",
    "submitted_at": "2026-07-23T06:41:12Z",
    "title_canon_sha256": "8922831b20b7c1a026890786f8de74b29998d427f9f01899c7d7b106ebb0bf59"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.20962",
    "kind": "arxiv",
    "version": 1
  }
}