Pith Number

pith:O5W3OJKG

pith:2015:O5W3OJKGEJYOYE2HWY6MUIAVQ5

not attested not anchored not stored refs pending

Higher Weak Derivatives and Reflexive Algebras of Operators

Erik Christensen

arxiv:1504.03521 v2 · 2015-04-14 · 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{O5W3OJKGEJYOYE2HWY6MUIAVQ5}

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	2026-05-18T01:37:07.388515Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

776db725462270ec1347b63cca2015877332de30a405b51c9e1e8639ad9c791c

Aliases

arxiv: 1504.03521 · arxiv_version: 1504.03521v2 · doi: 10.48550/arxiv.1504.03521 · pith_short_12: O5W3OJKGEJYO · pith_short_16: O5W3OJKGEJYOYE2H · pith_short_8: O5W3OJKG

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/O5W3OJKGEJYOYE2HWY6MUIAVQ5 \
  | 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: 776db725462270ec1347b63cca2015877332de30a405b51c9e1e8639ad9c791c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "db06b50bbddd99365dc00910136cdd6d52015dc32bf6c570e02b4afc2e37c22b",
    "cross_cats_sorted": [
      "math-ph",
      "math.FA",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2015-04-14T12:41:25Z",
    "title_canon_sha256": "1acdde0f6fe0fd5dc08749e4876350904b44b073f7ee1459b185bb8cdeb1a712"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.03521",
    "kind": "arxiv",
    "version": 2
  }
}