Pith Number

pith:ZZBBSD6F

pith:2026:ZZBBSD6FCCECX76KGJQ7DXYLTP

not attested not anchored not stored refs pending

Optimal Sparsifiers for Abelian Cayley Graphs

Arpon Basu, Pravesh K. Kothari, Raghu Meka, Stefan Tudose

arxiv:2607.08261 v1 · 2026-07-09 · cs.DS · 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{ZZBBSD6FCCECX76KGJQ7DXYLTP}

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	2026-07-10T01:19:31.175044Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ce42190fc510882bffca3261f1df0b9bcf05ce55d0ff6f9e628cc4d902c5a89b

Aliases

arxiv: 2607.08261 · arxiv_version: 2607.08261v1 · doi: 10.48550/arxiv.2607.08261 · pith_short_12: ZZBBSD6FCCEC · pith_short_16: ZZBBSD6FCCECX76K · pith_short_8: ZZBBSD6F

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/ZZBBSD6FCCECX76KGJQ7DXYLTP \
  | 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: ce42190fc510882bffca3261f1df0b9bcf05ce55d0ff6f9e628cc4d902c5a89b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fa570d5647bd3da4b3793a7fb602ca4be18674aeaa8d031cf69361f5b06f7a1a",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2026-07-09T09:05:00Z",
    "title_canon_sha256": "10eeedae30ae2daf32f3a47c85a904952c1e3fa31bdc0b629ba1853c75db2e1a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.08261",
    "kind": "arxiv",
    "version": 1
  }
}