Pith Number

pith:5ZKYXERU

pith:2013:5ZKYXERULLUD2UA5WSDJWQ2TYC

not attested not anchored not stored refs pending

Initial forms of stable invariants for additive group actions

Shigeru Kuroda

arxiv:1304.0313 v2 · 2013-04-01 · math.AC · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5ZKYXERULLUD2UA5WSDJWQ2TYC}

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	2026-05-18T03:26:42.419750Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee558b92345ae83d501db4869b4353c0b1066a59f54ace99d80bcd73c0556a88

Aliases

arxiv: 1304.0313 · arxiv_version: 1304.0313v2 · doi: 10.48550/arxiv.1304.0313 · pith_short_12: 5ZKYXERULLUD · pith_short_16: 5ZKYXERULLUD2UA5 · pith_short_8: 5ZKYXERU

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/5ZKYXERULLUD2UA5WSDJWQ2TYC \
  | 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: ee558b92345ae83d501db4869b4353c0b1066a59f54ace99d80bcd73c0556a88

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d2ef04654b11e5dc73d0a46601f44d4a697ae514b31c2a48b77582e190055181",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2013-04-01T08:37:55Z",
    "title_canon_sha256": "e16972a90b025dd6b31d6a201dfbfb18bc6ecf8de0fc02dc59199054796d65fe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.0313",
    "kind": "arxiv",
    "version": 2
  }
}