Pith Number

pith:IUX7QQWU

pith:2005:IUX7QQWUVD2RS2TA3FEUPNO5PO

not attested not anchored not stored refs pending

The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems

H\'ector Giacomini, Jaume Gin\'e, Jaume Llibre

arxiv:math/0506116 v2 · 2005-06-07 · math.DS · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IUX7QQWUVD2RS2TA3FEUPNO5PO}

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	2026-05-18T00:44:18.913344Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

452ff842d4a8f5196a60d94947b5dd7b8296cff6141b32b2773b35b196aa1ca5

Aliases

arxiv: math/0506116 · arxiv_version: math/0506116v2 · doi: 10.48550/arxiv.math/0506116 · pith_short_12: IUX7QQWUVD2R · pith_short_16: IUX7QQWUVD2RS2TA · pith_short_8: IUX7QQWU

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/IUX7QQWUVD2RS2TA3FEUPNO5PO \
  | 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: 452ff842d4a8f5196a60d94947b5dd7b8296cff6141b32b2773b35b196aa1ca5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6c5f70db6dda116fc648fa68650f9b8ae973ce41e61654e05b25cd52ea75e8fb",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "",
    "primary_cat": "math.DS",
    "submitted_at": "2005-06-07T14:26:28Z",
    "title_canon_sha256": "a523d6310c12c204e9ef5249bca1fc7f4ddf3ab62c1c40eeb5bef28793375c54"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0506116",
    "kind": "arxiv",
    "version": 2
  }
}