Pith Number

pith:C2IZDSLS

pith:2023:C2IZDSLS7T3JPO4U3LFEEM3D2K

not attested not anchored not stored refs pending

Weak saturation numbers in random graphs

Ali Mohammadian, Behruz Tayfeh-Rezaie, Meysam Miralaei, Olga Kalinichenko

arxiv:2306.10375 v3 · 2023-06-17 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{C2IZDSLS7T3JPO4U3LFEEM3D2K}

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.

Cited by

1 paper in Pith

When does a tree activate the random graph?

Receipt and verification

First computed	2026-07-05T07:54:01.716648Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

169191c972fcf697bb94daca423363d28d66821e8d47394f3f4d8f8ebf7608b5

Aliases

arxiv: 2306.10375 · arxiv_version: 2306.10375v3 · doi: 10.48550/arxiv.2306.10375 · pith_short_12: C2IZDSLS7T3J · pith_short_16: C2IZDSLS7T3JPO4U · pith_short_8: C2IZDSLS

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/C2IZDSLS7T3JPO4U3LFEEM3D2K \
  | 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: 169191c972fcf697bb94daca423363d28d66821e8d47394f3f4d8f8ebf7608b5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "280bc9ee52a78b9ab8f61b2cd0777c62aab34926077005ce3ba442a403f2ddde",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2023-06-17T15:23:13Z",
    "title_canon_sha256": "f938ad616a718b3d3ac650437f2eb736cb6de2e1407ccd47a684e3d1f44a6499"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2306.10375",
    "kind": "arxiv",
    "version": 3
  }
}