Pith Number

pith:5RZXYZWQ

pith:2011:5RZXYZWQSO75KBOACT47YIBL5Y

not attested not anchored not stored refs pending

On the {\L}ojasiewicz exponent, special direction and maximal polar quotient

Andrzej Lenarcik

arxiv:1112.5578 v1 · 2011-12-23 · 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{5RZXYZWQSO75KBOACT47YIBL5Y}

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	2026-05-18T04:05:46.491527Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ec737c66d093bfd505c014f9fc202bee17db1f4b13d5d0ba0eafd296744c7a4e

Aliases

arxiv: 1112.5578 · arxiv_version: 1112.5578v1 · doi: 10.48550/arxiv.1112.5578 · pith_short_12: 5RZXYZWQSO75 · pith_short_16: 5RZXYZWQSO75KBOA · pith_short_8: 5RZXYZWQ

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/5RZXYZWQSO75KBOACT47YIBL5Y \
  | 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: ec737c66d093bfd505c014f9fc202bee17db1f4b13d5d0ba0eafd296744c7a4e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "93c2ecc21a76afd1d742491259be1ec9471fcdd540f907903c9f7c21b5124547",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2011-12-23T12:55:35Z",
    "title_canon_sha256": "08146a0b50a74cdba59d986b84b77f42701b3fe6916ce0b210dccccb2ffbf987"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.5578",
    "kind": "arxiv",
    "version": 1
  }
}