Pith Number

pith:EWJ55ZRK

pith:2011:EWJ55ZRKQJ5XZOGHER2VPXYOAW

not attested not anchored not stored refs pending

On the spectral theory of operators on trees

Matthias Keller

arxiv:1101.2975 v1 · 2011-01-15 · math.SP · math-ph · math.FA · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{EWJ55ZRKQJ5XZOGHER2VPXYOAW}

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	2026-05-18T02:22:57.197220Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2593dee62a827b7cb8c7247557df0e05956ffd8acd21c8051d5d14f10f55bbbd

Aliases

arxiv: 1101.2975 · arxiv_version: 1101.2975v1 · doi: 10.48550/arxiv.1101.2975 · pith_short_12: EWJ55ZRKQJ5X · pith_short_16: EWJ55ZRKQJ5XZOGH · pith_short_8: EWJ55ZRK

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/EWJ55ZRKQJ5XZOGHER2VPXYOAW \
  | 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: 2593dee62a827b7cb8c7247557df0e05956ffd8acd21c8051d5d14f10f55bbbd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f3b6b7338a1a36578df4bb8ec493d3e395d213b45a1b5b35a663a85c7d7f5bf2",
    "cross_cats_sorted": [
      "math-ph",
      "math.FA",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2011-01-15T11:34:25Z",
    "title_canon_sha256": "387b8acb5045b7532b7f151b56b6d95dc99b9439043df00a49b7285163482e8b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.2975",
    "kind": "arxiv",
    "version": 1
  }
}