Pith Number

pith:AT4VAZAM

pith:2012:AT4VAZAMXE3H4GPIBGLPO5VNJZ

not attested not anchored not stored refs pending

The Frobenius functor and injective modules

Thomas Marley

arxiv:1201.1263 v2 · 2012-01-05 · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AT4VAZAMXE3H4GPIBGLPO5VNJZ}

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	2026-05-18T04:01:12.869306Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

04f950640cb9367e19e80996f776ad4e438cdd6ec6bafd317c192d2b90a3b69a

Aliases

arxiv: 1201.1263 · arxiv_version: 1201.1263v2 · doi: 10.48550/arxiv.1201.1263 · pith_short_12: AT4VAZAMXE3H · pith_short_16: AT4VAZAMXE3H4GPI · pith_short_8: AT4VAZAM

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/AT4VAZAMXE3H4GPIBGLPO5VNJZ \
  | 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: 04f950640cb9367e19e80996f776ad4e438cdd6ec6bafd317c192d2b90a3b69a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "64716413d4956aa286b147b20849110f8c8d58b63430893c094af4aa272fafd1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2012-01-05T19:02:48Z",
    "title_canon_sha256": "72111c96b8faa3a99f5673176cafcecb6b96dd9ff13dc315a8c05ab4ca8de0bf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.1263",
    "kind": "arxiv",
    "version": 2
  }
}