Pith Number

pith:4MZ45EQD

pith:2021:4MZ45EQDCZFCL2WF4MJYGCMZXV

not attested not anchored not stored refs pending

Bifurcations for Hamiltonian systems

Guangcun Lu

arxiv:2112.10726 v6 · 2021-12-20 · math.DS · math.CA · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4MZ45EQDCZFCL2WF4MJYGCMZXV}

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	2026-05-22T02:04:34.649896Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e333ce9203164a25eac5e313830999bd44780828f0fe95513dd99bd11a539e44

Aliases

arxiv: 2112.10726 · arxiv_version: 2112.10726v6 · doi: 10.48550/arxiv.2112.10726 · pith_short_12: 4MZ45EQDCZFC · pith_short_16: 4MZ45EQDCZFCL2WF · pith_short_8: 4MZ45EQD

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/4MZ45EQDCZFCL2WF4MJYGCMZXV \
  | 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: e333ce9203164a25eac5e313830999bd44780828f0fe95513dd99bd11a539e44

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "22808d4b384709b3ebd3272917e002b7d1ef123925ed83f6b14cad2b9e637ef0",
    "cross_cats_sorted": [
      "math.CA",
      "math.FA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2021-12-20T18:18:35Z",
    "title_canon_sha256": "d7da5c7cea01ff828ebe36e3e8196c3613581e29db7e56bc7aa89c2a557341a7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2112.10726",
    "kind": "arxiv",
    "version": 6
  }
}