Pith Number

pith:ZSRJCI3T

pith:2026:ZSRJCI3TDQZNHCNGOB77NDTCCZ

not attested not anchored not stored refs pending

Betti numbers of split graphs

Ralf Fr\"oberg

arxiv:2606.03101 v1 · 2026-06-02 · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZSRJCI3TDQZNHCNGOB77NDTCCZ}

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	2026-06-03T01:05:31.702700Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cca29123731c32d389a6707ff68e62167b3b73d2b9892d4954106699adb1f89f

Aliases

arxiv: 2606.03101 · arxiv_version: 2606.03101v1 · doi: 10.48550/arxiv.2606.03101 · pith_short_12: ZSRJCI3TDQZN · pith_short_16: ZSRJCI3TDQZNHCNG · pith_short_8: ZSRJCI3T

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/ZSRJCI3TDQZNHCNGOB77NDTCCZ \
  | 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: cca29123731c32d389a6707ff68e62167b3b73d2b9892d4954106699adb1f89f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ebe90bf0a9b40c1dce198bd6c5dc31e56374ffc48b5bb7ef6ac410d02e3ba290",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2026-06-02T03:39:24Z",
    "title_canon_sha256": "94ee575718857cf79832353c837c71e9f471323da9d0b16b95656b10986a2938"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.03101",
    "kind": "arxiv",
    "version": 1
  }
}