Pith Number

pith:KYKZROHL

pith:2009:KYKZROHLOIBQ7P7E6MAQAX6KB7

not attested not anchored not stored refs pending

Modular Theory by example

Fernando Lled\'o

arxiv:0901.1004 v1 · 2009-01-08 · math.OA · 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{KYKZROHLOIBQ7P7E6MAQAX6KB7}

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	2026-05-18T03:28:19.966192Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

561598b8eb72030fbfe4f301005fca0fd80236757384602d7b180c3211d29aa2

Aliases

arxiv: 0901.1004 · arxiv_version: 0901.1004v1 · doi: 10.48550/arxiv.0901.1004 · pith_short_12: KYKZROHLOIBQ · pith_short_16: KYKZROHLOIBQ7P7E · pith_short_8: KYKZROHL

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/KYKZROHLOIBQ7P7E6MAQAX6KB7 \
  | 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: 561598b8eb72030fbfe4f301005fca0fd80236757384602d7b180c3211d29aa2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c0eff8d3ee6a3b749cbe832e111d51b9348ef62d9a9324965a3a6403d2890c23",
    "cross_cats_sorted": [
      "math-ph",
      "math.FA",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2009-01-08T10:10:53Z",
    "title_canon_sha256": "70feda4809bb599cf77e02ce7e6ee5a582de59ad98b156011408ea853c4744af"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0901.1004",
    "kind": "arxiv",
    "version": 1
  }
}