Pith Number

pith:K5M3PDGB

pith:2026:K5M3PDGBJ37DSGXBC6WWMNTNA5

not attested not anchored not stored refs pending

Preferential Attachment as a Simpliciality-Enforcing Mechanism in Hypergraphs

Brendan Rooney, Jason LaRuez

arxiv:2608.09788 v1 · 2026-08-10 · math.AT · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{K5M3PDGBJ37DSGXBC6WWMNTNA5}

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	2026-08-11T02:25:06.095176Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5759b78cc14efe391ae117ad66366d07679855073958f6e2a485d7927b27c3d8

Aliases

arxiv: 2608.09788 · arxiv_version: 2608.09788v1 · doi: 10.48550/arxiv.2608.09788 · pith_short_12: K5M3PDGBJ37D · pith_short_16: K5M3PDGBJ37DSGXB · pith_short_8: K5M3PDGB

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/K5M3PDGBJ37DSGXBC6WWMNTNA5 \
  | 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: 5759b78cc14efe391ae117ad66366d07679855073958f6e2a485d7927b27c3d8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3c9b2a589f4c2dcff650901544a5eac4bbb8b7dfd678128eaf9175eda1ad8567",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2026-08-10T16:11:52Z",
    "title_canon_sha256": "c7f33e9a0150946a1af5433260e450573b38bbaa79ff1bb87c4d8084e9e773ee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.09788",
    "kind": "arxiv",
    "version": 1
  }
}