Pith Number

pith:SKBDODPI

pith:2026:SKBDODPIX47JSIWSAUC37SO6XB

not attested not anchored not stored refs pending

The role of expanders in the spectral geometry of metric graphs

Delio Mugnolo

arxiv:2607.14312 v1 · 2026-07-15 · math.SP · math.CO · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SKBDODPIX47JSIWSAUC37SO6XB}

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	2026-07-17T00:21:04.767787Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9282370de8bf3e9922d20505bfc9deb876a0114b7ac2012f4f925837b116360a

Aliases

arxiv: 2607.14312 · arxiv_version: 2607.14312v1 · doi: 10.48550/arxiv.2607.14312 · pith_short_12: SKBDODPIX47J · pith_short_16: SKBDODPIX47JSIWS · pith_short_8: SKBDODPI

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/SKBDODPIX47JSIWSAUC37SO6XB \
  | 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: 9282370de8bf3e9922d20505bfc9deb876a0114b7ac2012f4f925837b116360a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a434f7ba5a3e23bd02883191463983f40be9ac912290b7fc749b4c979eb3e42a",
    "cross_cats_sorted": [
      "math.CO",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2026-07-15T19:19:39Z",
    "title_canon_sha256": "4121396fc7457680539894e8fea1910051788af0cd353e584970f10c1144a376"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.14312",
    "kind": "arxiv",
    "version": 1
  }
}