Pith Number

pith:ZGUAXLOH

pith:2005:ZGUAXLOHAF5H6R76FBVXHAY43P

not attested not anchored not stored refs pending

Lyapunov exponents and bifurcation current for polynomial-like maps

Ngoc-mai Pham

arxiv:math/0512557 v1 · 2005-12-24 · math.DS · 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{ZGUAXLOHAF5H6R76FBVXHAY43P}

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	2026-07-04T14:52:17.535182Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c9a80badc7017a7f47fe286b73831cdbef5371026785dd226265fe6a1e068e66

Aliases

arxiv: math/0512557 · arxiv_version: math/0512557v1 · doi: 10.48550/arxiv.math/0512557 · pith_short_12: ZGUAXLOHAF5H · pith_short_16: ZGUAXLOHAF5H6R76 · pith_short_8: ZGUAXLOH

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/ZGUAXLOHAF5H6R76FBVXHAY43P \
  | 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: c9a80badc7017a7f47fe286b73831cdbef5371026785dd226265fe6a1e068e66

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1fd5622a769e34aaceb39b49421b0d8563530c58aa22ff0a77d6614efa8368d7",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "",
    "primary_cat": "math.DS",
    "submitted_at": "2005-12-24T02:13:57Z",
    "title_canon_sha256": "32d95f5c8e307c29c2ec205899f314a6397d68952f89cdf4ba51f799875fdf33"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0512557",
    "kind": "arxiv",
    "version": 1
  }
}