Pith Number

pith:DJ3FNW4I

pith:2026:DJ3FNW4I6VIWTHXZH44CZS7467

not attested not anchored not stored refs pending

The Multiset Dimension of Graphs: Extremal Values and King Grids

Jaan Allikvere

arxiv:2607.28813 v1 · 2026-07-30 · 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{DJ3FNW4I6VIWTHXZH44CZS7467}

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	2026-08-03T00:13:06.024362Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1a7656db88f551699ef93f382ccbfcf7c3ea808f5283eb1fa9fba5be05578ef2

Aliases

arxiv: 2607.28813 · arxiv_version: 2607.28813v1 · doi: 10.48550/arxiv.2607.28813 · pith_short_12: DJ3FNW4I6VIW · pith_short_16: DJ3FNW4I6VIWTHXZ · pith_short_8: DJ3FNW4I

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/DJ3FNW4I6VIWTHXZH44CZS7467 \
  | 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: 1a7656db88f551699ef93f382ccbfcf7c3ea808f5283eb1fa9fba5be05578ef2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fd6f40f838cb33a4307c8d3b863ad2b3a2b68d5d3bcd22f44de5c13a25d5727f",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-30T20:15:44Z",
    "title_canon_sha256": "e91a2fbbcb4d3ad1108ac43236f9cdbe69314782519d413cda286146f13b01f6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.28813",
    "kind": "arxiv",
    "version": 1
  }
}