Pith Number

pith:QWRJPQR6

pith:2007:QWRJPQR6T2JAF2LYCZL5FLZWRG

not attested not anchored not stored refs pending

Cotorsion pairs generated by modules of bounded projective dimension

Dolors Herbera, Silvana Bazzoni

arxiv:0707.2026 v2 · 2007-07-13 · math.RA · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QWRJPQR6T2JAF2LYCZL5FLZWRG}

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	2026-05-18T04:09:15.593599Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

85a297c23e9e9202e9781657d2af368990016f113a2f7254f6aaaf1663b302c9

Aliases

arxiv: 0707.2026 · arxiv_version: 0707.2026v2 · doi: 10.48550/arxiv.0707.2026 · pith_short_12: QWRJPQR6T2JA · pith_short_16: QWRJPQR6T2JAF2LY · pith_short_8: QWRJPQR6

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/QWRJPQR6T2JAF2LYCZL5FLZWRG \
  | 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: 85a297c23e9e9202e9781657d2af368990016f113a2f7254f6aaaf1663b302c9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "570480bf9360d91ab202126e741c7aa9113b31a499db140bedc045e29123840f",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "",
    "primary_cat": "math.RA",
    "submitted_at": "2007-07-13T15:00:46Z",
    "title_canon_sha256": "9f5bf594a2d033ad5091afb0ccd85f430874ff54c9053a0f380c202a221c2d67"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0707.2026",
    "kind": "arxiv",
    "version": 2
  }
}