Pith Number

pith:PGGR3ADJ

pith:2026:PGGR3ADJOWOMOYZPRNDMXPX3HO

not attested not anchored not stored refs pending

On $\varepsilon$-Matrix Product Factorization of graphs

Bobby Miraftab, Farzad Maghsoudi, Sho Suda

arxiv:2607.27407 v1 · 2026-07-29 · math.CO · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PGGR3ADJOWOMOYZPRNDMXPX3HO}

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	2026-07-31T00:11:43.810202Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

798d1d8069759cc7632f8b46cbbefb3b8ec810077bc5186c128f569f5ba597de

Aliases

arxiv: 2607.27407 · arxiv_version: 2607.27407v1 · doi: 10.48550/arxiv.2607.27407 · pith_short_12: PGGR3ADJOWOM · pith_short_16: PGGR3ADJOWOMOYZP · pith_short_8: PGGR3ADJ

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/PGGR3ADJOWOMOYZPRNDMXPX3HO \
  | 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: 798d1d8069759cc7632f8b46cbbefb3b8ec810077bc5186c128f569f5ba597de

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "96f1d942a2ef859a791c3792323aad406f421ea1e8833befe2c3120aff5e7abf",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-29T19:25:10Z",
    "title_canon_sha256": "3cb9cce3bace3351f6670b2098945da01925fb26f03fbd755d118e4e6178767b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.27407",
    "kind": "arxiv",
    "version": 1
  }
}