Pith Number

pith:T7ZMLRPT

pith:2021:T7ZMLRPTSIOGIUJ4HVZD2VC2S4

not attested not anchored not stored refs pending

Phase transitions in growing groups: How cohesion can persist

Enrico Maria Fenoaltea, Fanyuan Meng, Matus Medo, Run-Ran Liu

arxiv:2107.07324 v4 · 2021-07-15 · 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{T7ZMLRPTSIOGIUJ4HVZD2VC2S4}

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	2026-07-05T05:29:24.501452Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9ff2c5c5f3921c64513c3d723d545a97163b725b79804923336684210a27e1ef

Aliases

arxiv: 2107.07324 · arxiv_version: 2107.07324v4 · doi: 10.48550/arxiv.2107.07324 · pith_short_12: T7ZMLRPTSIOG · pith_short_16: T7ZMLRPTSIOGIUJ4 · pith_short_8: T7ZMLRPT

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/T7ZMLRPTSIOGIUJ4HVZD2VC2S4 \
  | 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: 9ff2c5c5f3921c64513c3d723d545a97163b725b79804923336684210a27e1ef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "685f50e0b447e9101306f4813655a6b112fd9116c951ec6a4e59620a5aa21a87",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.soc-ph",
    "submitted_at": "2021-07-15T13:48:58Z",
    "title_canon_sha256": "527a40c71179ad57ee4b6815fcef24b74011935ce213a32e196f7c714707d369"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2107.07324",
    "kind": "arxiv",
    "version": 4
  }
}