Pith Number

pith:42T35L4P

pith:2011:42T35L4PAYO6FPX6V4IA64N7UQ

not attested not anchored not stored refs pending

The structure of crossed products by endomorphisms

Eduard Ortega, Enrique Pardo

arxiv:1109.4073 v1 · 2011-09-19 · 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{42T35L4PAYO6FPX6V4IA64N7UQ}

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	2026-05-18T03:35:41.329433Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e6a7beaf8f061de2befeaf100f71bfa401d05186307bada254d01900ca45a160

Aliases

arxiv: 1109.4073 · arxiv_version: 1109.4073v1 · doi: 10.48550/arxiv.1109.4073 · pith_short_12: 42T35L4PAYO6 · pith_short_16: 42T35L4PAYO6FPX6 · pith_short_8: 42T35L4P

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/42T35L4PAYO6FPX6V4IA64N7UQ \
  | 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: e6a7beaf8f061de2befeaf100f71bfa401d05186307bada254d01900ca45a160

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4cbb7c6fe28c01b9890ac7442a5762050fbb1f3488fd441eb30da15ba7d930fc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2011-09-19T16:06:26Z",
    "title_canon_sha256": "b4f90b2696c46fb401d3357d8b17559128fe8f6633478870dc74af3b8ff0332a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.4073",
    "kind": "arxiv",
    "version": 1
  }
}