Pith Number

pith:FCAG2NVQ

pith:2026:FCAG2NVQI62RQVXBHKZG2XS7PL

not attested not anchored not stored refs resolved

Model of Simplicial Complexes with dimension-wise preferential attachment

Diego Febbe, Duccio Fanelli, Timoteo Carletti

A simplicial complex grows when new vertices attach to existing simplexes through independent preferential attachment rules at each dimension.

arxiv:2605.17004 v1 · 2026-05-16 · cond-mat.stat-mech

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FCAG2NVQI62RQVXBHKZG2XS7PL}

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.

Claims

C1strongest claim

The model returns a power law distribution for the generalized degree of simplexes of different dimension.

C2weakest assumption

The preferential attachment mechanism can be applied independently and dimension-wise without additional coupling terms between dimensions.

C3one line summary

A dimension-wise preferential attachment model for simplicial complexes yields power-law generalized degree distributions for simplices of varying dimension.

References

55 extracted · 55 resolved · 0 Pith anchors

[1] Emergence of scaling in random networks.science, 286(5439):509–512, 1999 1999

[2] Exploring complex networks.nature, 410(6825):268–276, 2001 2001

[3] Statistical mechanics of complex networks.Reviews of modern physics, 74(1):47, 2002 2002

[4] Oxford university press, 2010 2010

[5] Albert-L´ aszl´ o Barabasi and Zoltan N. Oltvai. Network biology: understanding the cell’s functional organization.Nature Reviews Genetics, 5(2):101–113, 2004 2004

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:35.548310Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

28806d36b047b51856e13ab26d5e5f7ac3be3a94a0de5f42b9a2f85b14c8883e

Aliases

arxiv: 2605.17004 · arxiv_version: 2605.17004v1 · doi: 10.48550/arxiv.2605.17004 · pith_short_12: FCAG2NVQI62R · pith_short_16: FCAG2NVQI62RQVXB · pith_short_8: FCAG2NVQ

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/FCAG2NVQI62RQVXBHKZG2XS7PL \
  | 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: 28806d36b047b51856e13ab26d5e5f7ac3be3a94a0de5f42b9a2f85b14c8883e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6168e5f9c03ddc7a8e6d21e5a5ce5988c676a8819f37cca8a2310d9847901e73",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2026-05-16T14:03:27Z",
    "title_canon_sha256": "55df97c248f077a1b468a23f61299442061c4e260842c6ed0fa508191fd3cc0a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17004",
    "kind": "arxiv",
    "version": 1
  }
}