Pith Number

pith:F3U4AKGF

pith:2012:F3U4AKGF5T6F5UDFV2GDUTFBOB

not attested not anchored not stored refs pending

Stratifications of finite directed categories and generalized APR tilting modules

Liping Li

arxiv:1212.0896 v2 · 2012-12-04 · math.RT · 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{F3U4AKGF5T6F5UDFV2GDUTFBOB}

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	2026-05-18T03:07:54.876642Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2ee9c028c5ecfc5ed065ae8c3a4ca1706730d5a0d8ca91ee9d6a6092293d56f8

Aliases

arxiv: 1212.0896 · arxiv_version: 1212.0896v2 · doi: 10.48550/arxiv.1212.0896 · pith_short_12: F3U4AKGF5T6F · pith_short_16: F3U4AKGF5T6F5UDF · pith_short_8: F3U4AKGF

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/F3U4AKGF5T6F5UDFV2GDUTFBOB \
  | 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: 2ee9c028c5ecfc5ed065ae8c3a4ca1706730d5a0d8ca91ee9d6a6092293d56f8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f4a60eac988e04793b98fa1ac2cefd06b67591b2d2ae5dd235b16b63159ce9d6",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2012-12-04T22:31:10Z",
    "title_canon_sha256": "ecdc7d882bc6a76175fd0a0c905ebe9b464dfa2dcf9dfa686d936bc1d6f6e10e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.0896",
    "kind": "arxiv",
    "version": 2
  }
}