Pith Number

pith:U26JOPWF

pith:2026:U26JOPWFSA7C7DTSMSV4XEC752

not attested not anchored not stored refs pending

Spectral Theory for Borel PMP Graphs

Alexander Tenenbaum, Cecelia Higgins, Pieter Spaas

arxiv:2602.05185 v2 · 2026-02-05 · math.LO · math.CO · math.OA · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{U26JOPWFSA7C7DTSMSV4XEC752}

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	2026-06-11T00:08:12.222962Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a6bc973ec5903e2f8e7264abcb905fee85687582c22fa3b621621bc8ef14d5d7

Aliases

arxiv: 2602.05185 · arxiv_version: 2602.05185v2 · doi: 10.48550/arxiv.2602.05185 · pith_short_12: U26JOPWFSA7C · pith_short_16: U26JOPWFSA7C7DTS · pith_short_8: U26JOPWF

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/U26JOPWFSA7C7DTSMSV4XEC752 \
  | 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: a6bc973ec5903e2f8e7264abcb905fee85687582c22fa3b621621bc8ef14d5d7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9653afd28afee7588f13873545d5940d989500752017462c23d5293ca9c2369d",
    "cross_cats_sorted": [
      "math.CO",
      "math.OA",
      "math.SP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2026-02-05T01:26:32Z",
    "title_canon_sha256": "7e56e49d60566c1976ac023ee669ece880faa776391a8e02e26476af7800888b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.05185",
    "kind": "arxiv",
    "version": 2
  }
}