Pith Number

pith:TWDWKUMO

pith:2026:TWDWKUMONCXE5ZZOJDKL7FBYHR

not attested not anchored not stored refs pending

Sharp Asymptotics for the Largest Component in the Subcritical Regime of Preferential Attachment Without Vertex Growth

Yiming Chen

arxiv:2607.00731 v1 · 2026-07-01 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TWDWKUMONCXE5ZZOJDKL7FBYHR}

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	2026-07-02T01:17:52.853433Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9d8765518e68ae4ee72e48d4bf94383c452c65bb482063f1ce1c4ebf0abd07c5

Aliases

arxiv: 2607.00731 · arxiv_version: 2607.00731v1 · doi: 10.48550/arxiv.2607.00731 · pith_short_12: TWDWKUMONCXE · pith_short_16: TWDWKUMONCXE5ZZO · pith_short_8: TWDWKUMO

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/TWDWKUMONCXE5ZZOJDKL7FBYHR \
  | 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: 9d8765518e68ae4ee72e48d4bf94383c452c65bb482063f1ce1c4ebf0abd07c5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f71b4e9d2063675628617f64cfd2c815077b55ce2eb297139f46d97828010b7a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-07-01T10:17:10Z",
    "title_canon_sha256": "d90539d126d8c600c260341ce4c0ff85543a1fcbdf3bb887b2bf9296b53d53ae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.00731",
    "kind": "arxiv",
    "version": 1
  }
}