Pith Number

pith:FCQBPAXN

pith:2019:FCQBPAXNF3YXQQV77MHMBJ2NML

not attested not anchored not stored refs pending

The sequence of mixed \L ojasiewicz exponents associated to pairs of ideals

Carles Bivi\`a-Ausina

arxiv:1904.05292 v1 · 2019-04-10 · math.AC · math.AG · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FCQBPAXNF3YXQQV77MHMBJ2NML}

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	2026-05-17T23:48:53.596724Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

28a01782ed2ef17842bffb0ec0a74d62c0818772727a5f671ea357f8dfd12dcc

Aliases

arxiv: 1904.05292 · arxiv_version: 1904.05292v1 · doi: 10.48550/arxiv.1904.05292 · pith_short_12: FCQBPAXNF3YX · pith_short_16: FCQBPAXNF3YXQQV7 · pith_short_8: FCQBPAXN

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/FCQBPAXNF3YXQQV77MHMBJ2NML \
  | 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: 28a01782ed2ef17842bffb0ec0a74d62c0818772727a5f671ea357f8dfd12dcc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "848e2f0e7dc9cc57808ca35b2122b91e8cae90951c88c35781f6c93193211645",
    "cross_cats_sorted": [
      "math.AG",
      "math.CV"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2019-04-10T16:54:12Z",
    "title_canon_sha256": "7b8edc4ac70daa3f4f707f622e48e1e0fbb05a159f540c007c05785c377d1d06"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1904.05292",
    "kind": "arxiv",
    "version": 1
  }
}