Pith Number

pith:B7TRPTXY

pith:2010:B7TRPTXYPPTI7WKIYDFYXNYUEU

not attested not anchored not stored refs pending

Isoparametric functions and exotic spheres

Jianquan Ge, Zizhou Tang

arxiv:1003.0355 v2 · 2010-03-01 · math.DG · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{B7TRPTXYPPTI7WKIYDFYXNYUEU}

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	2026-05-18T04:04:43.835384Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0fe717cef87be68fd948c0cb8bb7142503c7695badf4b29943b81d3be4d609f2

Aliases

arxiv: 1003.0355 · arxiv_version: 1003.0355v2 · doi: 10.48550/arxiv.1003.0355 · pith_short_12: B7TRPTXYPPTI · pith_short_16: B7TRPTXYPPTI7WKI · pith_short_8: B7TRPTXY

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/B7TRPTXYPPTI7WKIYDFYXNYUEU \
  | 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: 0fe717cef87be68fd948c0cb8bb7142503c7695badf4b29943b81d3be4d609f2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "10e5ca673f3b370e931d37eb18743461519eb87563016d889ba94bac29cba3d5",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2010-03-01T14:19:18Z",
    "title_canon_sha256": "25c091bd0dd6f7d0182e5a3e6e8d5270c7bfce395d4365fb670e5a639851befd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1003.0355",
    "kind": "arxiv",
    "version": 2
  }
}