Pith Number

pith:4FD2JBCH

pith:2007:4FD2JBCH7SMFTOOPRZBTIRZHAN

not attested not anchored not stored refs pending

Formally smooth bimodules

A. Ardizzoni, C. Menini, Tomasz Brzezinski

arxiv:math/0701473 v1 · 2007-01-17 · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4FD2JBCH7SMFTOOPRZBTIRZHAN}

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	2026-05-18T04:41:45.014822Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e147a48447fc9859b9cf8e43344727037123ad07260c8ee6b24a02e808545d86

Aliases

arxiv: math/0701473 · arxiv_version: math/0701473v1 · doi: 10.48550/arxiv.math/0701473 · pith_short_12: 4FD2JBCH7SMF · pith_short_16: 4FD2JBCH7SMFTOOP · pith_short_8: 4FD2JBCH

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/4FD2JBCH7SMFTOOPRZBTIRZHAN \
  | 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: e147a48447fc9859b9cf8e43344727037123ad07260c8ee6b24a02e808545d86

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f639831197c3cc8d7b80b6d34c9f707c7b061b160ddceee53a45a25ba692f8e1",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.RA",
    "submitted_at": "2007-01-17T10:05:33Z",
    "title_canon_sha256": "e8fac24bf6780c2a1e6e57d615608aaf63b7825d4d77c4859f349b7d633b86b2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0701473",
    "kind": "arxiv",
    "version": 1
  }
}