Pith Number

pith:DWLCGUBP

pith:2026:DWLCGUBPTMGVH7VZYAHKZJBOGS

not attested not anchored not stored refs pending

Eigenvalue growth of the discrete Hodge Laplacian across dimensions

Matthias Keller, Philipp Bartmann

arxiv:2608.11170 v1 · 2026-08-11 · math.CO · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DWLCGUBPTMGVH7VZYAHKZJBOGS}

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	2026-08-12T01:24:44.754200Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1d9623502f9b0d53feb9c00eaca42e34bc8834dfd9ed55e9d48cf5eb7bcd7e78

Aliases

arxiv: 2608.11170 · arxiv_version: 2608.11170v1 · doi: 10.48550/arxiv.2608.11170 · pith_short_12: DWLCGUBPTMGV · pith_short_16: DWLCGUBPTMGVH7VZ · pith_short_8: DWLCGUBP

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/DWLCGUBPTMGVH7VZYAHKZJBOGS \
  | 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: 1d9623502f9b0d53feb9c00eaca42e34bc8834dfd9ed55e9d48cf5eb7bcd7e78

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ea13350de8e6f30b7d5b4f9830a5e49c38ac808d19171b43f58390cab94f19a7",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-08-11T17:29:57Z",
    "title_canon_sha256": "1664d37b64e03fa1d71528bf5eed7bf6547ebec25eb4596c6da9e09750fdbb7f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.11170",
    "kind": "arxiv",
    "version": 1
  }
}