Pith Number

pith:4Y3ST7PU

pith:2012:4Y3ST7PUIYD3EMYYYZEIPOWZXO

not attested not anchored not stored refs pending

NAK for Ext and Ascent of module structures

Benjamin J. Anderson, Sean Sather-Wagstaff

arxiv:1201.3039 v2 · 2012-01-14 · 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{4Y3ST7PUIYD3EMYYYZEIPOWZXO}

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	2026-05-18T03:55:46.604852Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e63729fdf44607b23318c64887bad9bbb090b50a43c631082cc03ac5523e166d

Aliases

arxiv: 1201.3039 · arxiv_version: 1201.3039v2 · doi: 10.48550/arxiv.1201.3039 · pith_short_12: 4Y3ST7PUIYD3 · pith_short_16: 4Y3ST7PUIYD3EMYY · pith_short_8: 4Y3ST7PU

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/4Y3ST7PUIYD3EMYYYZEIPOWZXO \
  | 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: e63729fdf44607b23318c64887bad9bbb090b50a43c631082cc03ac5523e166d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e46eb21bd09ec57f4bb73d32d5d391eeafc4852443c0a3d09d85ac630c3d2d7d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2012-01-14T19:36:15Z",
    "title_canon_sha256": "1e030292c3ecf639d60685c0ac1517c15bfa996853131a7a358ee45e3d304be6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.3039",
    "kind": "arxiv",
    "version": 2
  }
}