Pith Number

pith:5BP7OZA4

pith:2010:5BP7OZA4EJQAZ4F6ECVTORHSNP

not attested not anchored not stored refs pending

Composition Operators and Endomorphisms

Dennis Courtney, Paul S. Muhly, Samuel W. Schmidt

arxiv:1003.2806 v1 · 2010-03-14 · math.FA · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5BP7OZA4EJQAZ4F6ECVTORHSNP}

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	2026-05-18T03:56:10.867298Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e85ff7641c22600cf0be20ab3744f26bd3bab40826f04f56628b1afb9f65b952

Aliases

arxiv: 1003.2806 · arxiv_version: 1003.2806v1 · doi: 10.48550/arxiv.1003.2806 · pith_short_12: 5BP7OZA4EJQA · pith_short_16: 5BP7OZA4EJQAZ4F6 · pith_short_8: 5BP7OZA4

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/5BP7OZA4EJQAZ4F6ECVTORHSNP \
  | 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: e85ff7641c22600cf0be20ab3744f26bd3bab40826f04f56628b1afb9f65b952

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d6d0120bd1847f4c62474cdd5f3e61e08f981b4042f9a562b84e337a96bcac74",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2010-03-14T19:30:51Z",
    "title_canon_sha256": "3d51305057e2cf8e04a629f5ff8badba5234084ca80ab6649cbff1deb883eae2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1003.2806",
    "kind": "arxiv",
    "version": 1
  }
}