Pith Number

pith:4IC6PV3M

pith:2010:4IC6PV3MQYCVNVEKUUAEP5JX2M

not attested not anchored not stored refs pending

When an abelian category with a tilting object is equivalent to a module category

Alberto Tonolo, Francesca Mantese, Riccardo Colpi

arxiv:1011.5345 v1 · 2010-11-24 · math.CT · 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{4IC6PV3MQYCVNVEKUUAEP5JX2M}

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	2026-05-18T04:34:47.500294Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e205e7d76c860556d48aa50047f537d30d5dfa999370e08d2929c281c5712315

Aliases

arxiv: 1011.5345 · arxiv_version: 1011.5345v1 · doi: 10.48550/arxiv.1011.5345 · pith_short_12: 4IC6PV3MQYCV · pith_short_16: 4IC6PV3MQYCVNVEK · pith_short_8: 4IC6PV3M

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/4IC6PV3MQYCVNVEKUUAEP5JX2M \
  | 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: e205e7d76c860556d48aa50047f537d30d5dfa999370e08d2929c281c5712315

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f022e565bc89e0bacbf7516be680a47678e008d1cc4f700d0be670e9ce1a71e6",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2010-11-24T11:40:23Z",
    "title_canon_sha256": "75bf2731c36dc56ff6015af11429286559e6945553a8cb11ff1c114600f84549"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.5345",
    "kind": "arxiv",
    "version": 1
  }
}