Pith Number

pith:XYL75LCZ

pith:2006:XYL75LCZHFBXFABF5H7XQ4JVV6

not attested not anchored not stored refs pending

A New Route to the Interpretation of Hopf Invariant

Ji-rong Ren, Ran Li, Yi-Shi Duan

arxiv:math-ph/0607001 v3 · 2006-07-01 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XYL75LCZHFBXFABF5H7XQ4JVV6}

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	2026-07-04T15:33:43.462018Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be17feac593943728025e9ff787135afa735a41e512ccb051d9c4dfc9e634fd9

Aliases

arxiv: math-ph/0607001 · arxiv_version: math-ph/0607001v3 · doi: 10.48550/arxiv.math-ph/0607001 · pith_short_12: XYL75LCZHFBX · pith_short_16: XYL75LCZHFBXFABF · pith_short_8: XYL75LCZ

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/XYL75LCZHFBXFABF5H7XQ4JVV6 \
  | 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: be17feac593943728025e9ff787135afa735a41e512ccb051d9c4dfc9e634fd9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6619b295bf27aa00ca8495fd37994774361242c4ec2bf4c219cb4706901e45a6",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2006-07-01T07:49:11Z",
    "title_canon_sha256": "e97699c17ba30080cfa988f089eaab6622d92bbd08997c94259e7fc650ec1e09"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0607001",
    "kind": "arxiv",
    "version": 3
  }
}